Minimal-control-energy strategies are substantiated and illustrated for linear-quadratic problems with penalized endpoints and no state-trajectory cost, when bounds in control values are imposed. The optimal solution for a given process with restricted controls, starting at a known initial state, is shown to coincide with the saturated solution to the unrestricted problem that has the same coefficients but starts at a generally different initial state. This result reduces the searching span for the solution: from the infinite-dimensional set of admissible control trajectories to the finite-dimensional Euclidean space of initial conditions. An efficient real-time scheme is proposed here to approximate (eventually to find) the optimal control strategy, based on the detection of the appropriate initial state while avoiding as much as possible the generation and evaluation of state and control trajectories. Numerical (including model predictive control) simulations are provided, compared, and checked against the analytical solution to ‘the cheapest stop of a train’ problem in its pure-upper-bounded brake, flexible-endpoint setting.Copyright © 2013 John Wiley & Sons, Ltd.

We propose a linearized formulation for min–max control problems with separated dynamics. First, we investigate the existence of the value function and saddle points for semicontinuous costs. Second, we obtain dual formulations and dynamic programming principles.Copyright © 2013 John Wiley & Sons, Ltd.

In this paper, an algebraic rule for tuning the integer realizations of fractional-order PI controllers is developed, with an integral square error performance index, which outperforms that of an optimal ordinary PI controller. To this end, the PI^λ control structure is used in conjunction with a third-order integer approximating filter to provide a three parameter fixed-structure extension of the ordinary PI controller. Next, the extra degree of freedom in setting the order of integration λ is leveraged to introduce a steepest descent direction in the extended controller parameter space. It is then stated that shifting the parameters of an ordinary PI controller along the proposed descent direction will result in a fractional-based three parameter controller with a performance index, which is superior to that of the original PI controller. The stability of the controller parameters derived in this manner is then analyzed, and examples and simulation results are offered to verify the theoretical expectations and analyses.Copyright © 2013 John Wiley & Sons, Ltd.

This paper presents a feedback controller designing approach for a large class of finite-time optimal control problems. This approach involves a piecewise truncated variational iteration method (PTVIM) for solving the nonlinear Hamilton–Jacobi–Bellman equation. By using the finite iterations of PTVIM, an analytic approximate solution for value function and suboptimal feedback control law is obtained. Some illustrative examples are employed to demonstrate the accuracy and efficiency of the proposed approach. Copyright © 2013 John Wiley & Sons, Ltd.

A key factor to success in implementations of real time optimal control, such as receding horizon control (RHC), is making efficient use of computational resources. The main trade-off is then between efficiency and accuracy of each RHC iteration, and the resulting overall optimality properties of the concatenated iterations, that is, how closely this represents a solution to the underlying infinite time optimal control problem (OCP). Both these issues can be addressed by adapting the RHC solution strategy to the expected form of the solution. Using gradual dense–sparse (GDS) node distributions in direct transcription formulations of the finite time OCP solved in each RHC iteration is a way of adapting the node distribution of this OCP to the fact that it is actually part of an RHC scheme. We have previously argued that this is reasonable, because the near future plan must be implemented now, but the far future plan can and will be revised later. In this paper, we investigate RHC applications where the asymptotic qualitative behavior of the OCP solution can be analyzed in advance. For some classes of systems, explicit exponential convergence rates of the solutions can be computed. We establish such convergence rates for a class of control affine nonlinear systems with a locally quadratic cost and propose to use versions of GDS node distributions for such systems because they will (eventually) be better adapted to the form of the solution. The advantages of the GDS approach in such settings is illustrated with simulations. Copyright © 2013 John Wiley & Sons, Ltd.

In this paper, the optimal control problem with a quadratic functional for Helmholtz equation with non-local boundary conditions is considered. Necessary and sufficient conditions of optimality are obtained on the basis of which the existence and uniqueness of a solution to the optimal problem are proved. Copyright © 2013 John Wiley & Sons, Ltd.

In this paper, we introduce a new analytic technique for a class of nonlinear optimal control problems and present a theorem of convergence of the method. In this scheme, first, the original optimal control problem is transformed into a nonlinear two-point boundary value problem via the Pontryagin's maximum principle, and then, we apply a new method for solving two-point boundary value problem. The proposed modification is made by introducing He's polynomials in the correction functional. The suggested algorithm is quite efficient and is practically well suited for using in these problems. The proposed iterative scheme finds the solution without any discretization, linearization, or restrictive assumptions.Copyright © 2013 John Wiley & Sons, Ltd.

Patients with type 1 diabetes mellitus require exogenous insulin infusion to avoid chronic complications related to elevated glucose levels. With diabetes reaching epidemic proportions, recent times have witnessed an increased attention in the field of optimal glucose management by closed-loop insulin delivery system. A proper glucose management scheme, in addition of maintaining the glucose level within the normal range of 80–120 mg/dL, should avoid excessive insulin delivery leading to hypoglycemia. By considering the glucose regulation as a linear quadratic problem, a constrained novel sub-optimal controller is proposed in the present work, for the maintenance of normal glucose level in type 1 diabetic subjects. The observer free state feedback controller is based on the feedback of only physiological variables (plasma glucose and plasma insulin). Constraining the feedback elements corresponding to the non-physiological variables avoids the use of an observer while maintaining the advantages of state feedback control. The implementation of the proposed scheme requires simple measurement protocol with no online computation. The closed-loop performance of the controller is evaluated on a physiologically relevant model for a meal disturbance and continuous glucose infusion.Copyright © 2013 John Wiley & Sons, Ltd.

This paper presents an algorithm for the indirect solution of optimal control problems that contain mixed state and control variable inequality constraints. The necessary conditions for optimality lead to an inequality constrained two-point BVP with index-1 differential-algebraic equations (BVP-DAEs). These BVP-DAEs are solved using a multiple shooting method where the DAEs are approximated using a single-step linearly implicit Runge–Kutta (Rosenbrock–Wanner) method. An interior-point Newton method is used to solve the residual equations associated with the multiple shooting discretization. The elements of the residual equations, and the Jacobian of the residual equations, are constructed in parallel. The search direction for the interior-point method is computed by solving a sparse bordered almost block diagonal (BABD) linear system. Here, a parallel-structured orthogonal factorization algorithm is used to solve the BABD system. Examples are presented to illustrate the efficiency of the parallel algorithm. It is shown that an American National Standards Institute C implementation of the parallel algorithm achieves significant speedup with the increase in the number of processors used.Copyright © 2013 John Wiley & Sons, Ltd.

This paper presents an inverse optimal control approach for stabilization and trajectory tracking of discrete-time nonlinear systems, avoiding to solve the associated Hamilton–Jacobi–Bellman equation, and minimizing a meaningful cost functional. The proposed controller is based on a discrete-time control Lyapunov function and passivity theory; its applicability is illustrated via simulations for an unstable nonlinear system and a planar robot. Copyright © 2013 John Wiley & Sons, Ltd.

We show how to introduce the Value at Risk (VaR) concept in optimization algorithms with emphasis in calculation complexity issues. To do so, we assume known the PDF of the uncertainties. Our aim is to quantify our confidence on the optimal solution at low complexity without sampling of the control space. The notion of over-solving appears naturally where it becomes useless to solve accurately near an optimum when the variations in control parameters fall below the uncertainties. Examples show the behavior of this VaR-based correction and link the approach to momentum-based optimization where the mean and variance of a functional are considered. The approach is then applied to an inverse problem with fluids with uncertainties in the definition of the injection devices. It is shown that an optimization problem with an admissible solution in the control space in the deterministic case can lose its solution in the presence of uncertainties on the control parameters, which suggests that the control space itself should be redefined in such a situation to recover an admissible problem. This permits to evaluate the cost of making reliable a system that has been deterministically designed but has uncertain parameters. A shape optimization problem closes the paper showing the importance of including VaR information during the design iterations and not only at the end of the procedure.Copyright © 2013 John Wiley & Sons, Ltd.

This paper studies the problem of stability analysis for continuous-time systems with two additive time-varying delay components. By taking the independence and the variation of the additive delay components into consideration, more general type of Lyapunov functionals are defined. Together with a tighter estimation of the upper bound of the cross-product terms derived from the derivatives of the Lyapunov functionals, less conservative delay-dependent stability criteria are established in terms of LMIs. Combining with a reciprocally convex combination technique, the newly obtained stability conditions are also less complex. Two numerical examples are given to illustrate the effectiveness and the significant improvement of the proposed method. Copyright © 2013 John Wiley & Sons, Ltd.

In this paper, the finite volume element method (FVEM) is applied to solve the distributed optimal control problems governed by parabolic equation. We use the method of variational discretization concept to approximate the problems. We consider a semi-discrete and a fully discrete piecewise linear FVEMs. For the semi-discrete method, the optimal order error estimates in continuous L^∞(J; L²) and L^∞(J; H¹)-norm are obtained; the suboptimal error estimates in continuous L^∞(J; L^∞)-norm are also obtained. For the fully discrete method, the optimal order error estimates in discrete L²(J; L²) and L^∞(J; L²)-norm are derived. Numerical experiments are presented to test these theoretical results.Copyright © 2012 John Wiley & Sons, Ltd.

This paper is concerned with the problem of robust stability of Markovian jump singularly perturbed descriptor systems with uncertain switchings and nonlinear perturbations for any , where is a pre-defined positive scalar. A linear matrix inequality (LMI) condition is firstly established to guarantee the existence and uniqueness of a solution. Then, an ε-independent condition in terms of LMI related to is derived via using an ε-dependent Lyapunov function, where the solution exists uniquely and is globally exponentially mean-square stable simultaneously. Finally, numerical examples are used to show the feasibility and effectiveness of the given theoretical results.Copyright © 2012 John Wiley & Sons, Ltd.

This paper proposes a new approach for estimating the robust domain of attraction (RDA) and directional enlargement of the DA for dynamical systems. The proposed method analyzes stability of dynamical systems by Markov modeling and employs invariant measure as the stability indicator. Markov chains analysis focuses on asymptotic behaviors of systems and ignores the transient ones. The proposed method expresses the problem of estimating RDA and directional enlargement of DA as an infinite dimensional linear problem. The resulting linear problem is converted to a finite dimensional optimization problem using approximated Markov transition function. As a novel application, the directional enlargement of DA is used in order to increase the critical clearing time of power systems. The efficiency of proposed methods is shown via simulations. Copyright © 2012 John Wiley & Sons, Ltd.

In this paper, a mathematical model for the scheduling of angiogenic inhibitors with a killing agent is used to derive a robust state feedback control for the combined therapy of cancer. Robustness is considered against parameter uncertainties through the solution of the associated Hamilton–Jacobi–Isaacs (HJI) partial differential equation. Unlike open-loop optimal control paradigm, solving the HJI equation provides a guaranteed-cost feedback control and a whole visibility of the achievable performance for any possible initial state within the region of interest and for any predefined level of parameter uncertainties. Numerical investigation is proposed using an existing model that has been partially validated using human data. Copyright © 2012 John Wiley & Sons, Ltd.

This paper is concerned with the relationship between maximum principle and dynamic programming principle for stochastic recursive optimal control problems of jump diffusions. Under the assumption that the value function is smooth, relations among the adjoint processes, the generalized Hamiltonian function, and the value function are given. A linear quadratic recursive utility portfolio optimization problem in the financial market is discussed to show the applications of the main result. Copyright © 2012 John Wiley & Sons, Ltd.

This paper is concerned with the design of networked control systems with random network data dropout. It presents a new control scheme, which is termed networked predictive control. This scheme mainly consists of the control prediction generator and network data dropout compensator. Besides, the control prediction generator provides a set of future control predictions to make the closed-loop system achieve the desired control performance, and the network data dropout compensator removes the effects of the network transmission data dropout. Simulation results are presented to illustrate the effectiveness of the control strategy via comparing with other three existing control schemes. Copyright © 2012 John Wiley & Sons, Ltd.

This paper investigates the observer-based H_∞ control problem for a class of mixed-delay Markovian jump systems with random communication packet losses and multiplicative noises. The mixed delays comprise both discrete time-varying delays and distributed delays, the random packet losses are described by a Bernoulli distributed white sequence that obeys a conditional probability distribution, and the multiplicative disturbances are in the form of a scalar Gaussian white noise with unit variance. In the presence of mixed delays, random packet losses and multiplicative noises, sufficient conditions for the existence of an observer-based feedback controller are derived such that the closed-loop control system is asymptotically mean-square stable and preserves a guaranteed H_∞ performance. Then, a linear matrix inequality approach for designing such an observer-based H_∞ controller is presented. Finally, a numerical example is provided to illustrate the effectiveness of the developed theoretical results. Copyright © 2012 John Wiley & Sons, Ltd.

This paper studies the design problem of a robust delay-dependent H_∞ feedforward controller design for a class of linear uncertain time-delay system having state and control delays when the system is subject to -type disturbances. The proposed controller scheme involves two main controllers, which are static state-feedback and dynamic feedforward controllers. The state-feedback controller is used for stabilizing the delay and uncertainty-free system, whereas the feedforward controller performs disturbance attenuation. Dynamic type integral quadratic constraints (IQCs), which consist of frequency-dependent multipliers, have been introduced to represent the delays and parametric uncertainties in the system where the degree of the multiplier used in IQC representation is in an adjustable nature. This scheme allows the designer to obtain less conservative controllers with increasing precision. Sufficient delay-dependent criteria in terms of linear matrix inequalities are obtained such that the uncertain linear time-delay system is guaranteed to be globally, uniformly, asymptotically stable with a minimum disturbance attenuation level. Several numerical examples together with the simulation studies provided at the end illustrate the usefulness of the proposed design. Copyright © 2012 John Wiley & Sons, Ltd.

A generalized approach to the problem of quantized filtering is investigated by designing a set of decentralized filters for a class of linear interconnected continuous-time systems with unknown-but-bounded couplings and interval delays and where the quantizer has arbitrary form. An LMI-based method using a decentralized quantized filter is designed at the subsystem level to render the global filtered system delay-dependent asymptotically stable with guaranteed γ − level. It is established that this setting encompasses several special cases of interest including interconnected delay-free systems, single time-delay systems and single systems. We illustrate the theoretical developments by numerical simulations.Copyright © 2012 John Wiley & Sons, Ltd.

This paper considers the problem of sliding mode control for uncertain stochastic systems with possible occurrence of actuator faults. There exist parameter uncertainties and state-dependent noise. Moreover, the faults may happen in any of the actuators. The reliable designing on both passive and adaptive sliding mode controllers is investigated, respectively. Both the reachability of the specified sliding surface and the stochastic stability of the sliding motion are analyzed using the stochastic Lyapunov theory. Finally, numerical simulation results are given.Copyright © 2012 John Wiley & Sons, Ltd.

In this paper, two nonlinear model predictive control (MPC) strategies are applied to solve a low thrust interplanetary rendezvous problem. Each employs a unique, nonclassical parameterization of the control to adapt the nonlinear MPC approach to interplanetary orbital dynamics with low control authority. The approach is demonstrated numerically for a minimum-fuel Earth-to-Mars rendezvous maneuver, cast as a simplified coplanar circular orbit heliocentric transfer problem. The interplanetary transfer is accomplished by repeated solution of an optimal control problem over (i) a receding horizon with fixed number of control subintervals and (ii) a receding horizon with shrinking number of control subintervals, with a doubling strategy to maintain controllability. In both cases, the end time is left unconstrained. The performances of the nonlinear MPC strategies in terms of computation time, fuel consumption, and transfer time are compared for a constant thrust nuclear-electric propulsion system. For this example, the ability to withstand unmodeled effects and control allocation errors is verified. The second strategy, with shrinking number of control subintervals, is also shown to easily handle the more complicated bounded thrust nuclear-electric case, as well as a state-control-constrained solar-electric case. Copyright © 2012 John Wiley & Sons, Ltd.

In this contribution, a suboptimal robust control law for a specific class of underactuated delayed system is synthesized. The control strategy based on very well-known results for delay-dependent stability considers the time delay involved in the dynamical system, which affects to control signal. This contribution illustrates how the theoretical results can be used to improve the real-time performance of the closed-loop system considered. The delay is introduced into the control system by the vision module, due to the time required to perform the image treatment. In order to show the good performance of the control law proposed, real-time experiments are developed by applying a visual servoing technique on the cart-inverted pendulum system. Obtained results also illustrate how the conservativeness of theoretical results affects the performance of the closed-loop system and the negative effects of delays in the control loop. Furthermore, a robust stability analysis is done to establish the robustness of control law with respect to the amount of delay presented in the system.Copyright © 2012 John Wiley & Sons, Ltd.

A control problem motivated by tissue engineering is formulated and solved, in which control of the uptake of growth factors (signaling molecules) is necessary to spatially and temporally regulate cellular processes for the desired growth or regeneration of a tissue. Four approaches are compared for determining one-dimensional optimal boundary control trajectories for a distributed parameter model with reaction, diffusion, and convection: (i) basis function expansion, (ii) method of moments, (iii) internal model control, and (iv) model predictive control (MPC). The proposed method of moments approach is computationally efficient while enforcing a nonnegativity constraint on the control input. Although more computationally expensive than methods (i)–(iii), the MPC formulation significantly reduced the computational cost compared with simultaneous optimization of the entire control trajectory. A comparison of the pros and cons of each of the four approaches suggests that an algorithm that combines multiple approaches is most promising for solving the optimal control problem for multiple spatial dimensions. Copyright © 2012 John Wiley & Sons, Ltd.

An efficient robust LMI-based scheme is developed for decentralized state-estimation of linear interconnected systems with static nonlinear interconnections and subjected to sensor nonlinearities. The interconnections satisfy quadratic constraints with manipulated parameters and the sensor nonlinearities are modeled as sector nonlinearities. The design procedure utilizes a general linear estimator structure and consists of two steps: the first giving a block-diagonal Lyapunov matrix together with the robustness degree and the second determining the filter parameters. A numerical example is provided to illustrate the applicability of the method. Copyright © 2012 John Wiley & Sons, Ltd.

This paper is focused on the problem of stability for linear systems with a time-varying delay. A novel Lyapunov–Krasovskii functional that decomposed the delay in all integral terms is proposed. As a result, some less conservative stability criteria are derived by considering the relationship between time-varying delay and its intervals, which have wider application than the existing ones because independent upper bounds of the delay derivative in the various delay intervals are taken into account. Some numerical examples are finally given to show the effectiveness and the benefits of the proposed method. Copyright © 2012 John Wiley & Sons, Ltd.

This paper addresses the design problem of fault-tolerant H_∞ controller for linear systems with state quantization. By combining linear matrix inequality technique and indirect adaptive method, a new method is proposed to design a fault-tolerant controller against actuator faults via quantized state feedback. The controller gains are updating according to the online estimation of eventual faults, which are dependent on the quantized state signals. Meanwhile, the proposed designs conditions with variable gains can be proved to be less conservative than those of the traditional controller with fixed gains. A numerical example is presented to illustrate the effectiveness of the proposed method. Copyright © 2012 John Wiley & Sons, Ltd.

Because switched system with nonlinear subsystems shows great difficulties in controller design by conventional methodologies, the fuzzy logic theory, which has been proven to be a practical and effective way to deal with the analysis and synthesis problems for complex nonlinear systems, is applied to design a class of hybrid fuzzy controller for switched discrete-time fuzzy system in this paper. On a basis of one step prediction of switching signal, a hybrid parallel distributed compensation (PDC) control strategy is proposed, which includes two necessary parts: the state feedback controllers for subsystems and the update feedback controllers for switching instants. In both arbitrary and dwell-time switching cases investigated, it is proved that the hybrid PDC controller contains less conservativeness than conventional switched PDC controller. Numerical examples are given to illustrate the effectiveness and advantages of the proposed approach. Copyright © 2012 John Wiley & Sons, Ltd.

In clinical intensive care unit practice, sedative/analgesic agents are titrated to achieve a specific level of sedation. The level of sedation is currently based on clinical scoring systems. Examples include the motor activity assessment scale, the Richmond agitation–sedation scale, and the modified Ramsay sedation scale. In general, the goal of the clinician is to find the drug dose that maintains the patient at a sedation score corresponding to a moderately sedated state. This is typically done empirically, administering a drug dose that usually is in the effective range for most patients, observing the patient's response, and then adjusting the dose accordingly. However, the response of patients to any drug dose is a reflection of the pharmacokinetic and pharmacodynamic properties of the drug and the specific patient. In this paper, we use pharmacokinetic and pharmacodynamic modeling to find an optimal drug dosing control policy to drive the patient to a desired modified Ramsay sedation scale score. Copyright © 2012 John Wiley & Sons, Ltd.

This paper presents a new approach for delay-dependent H_∞ stability analysis and control synthesis for singular systems with delay. By constructing an augmented Lyapunov–Krasovskii functional with a triple-integral term, and using the partitioning technique, a bounded real lemma is presented to ensure the singular state-delay system to be regular, impulse free and stable with γ-disturbance rejection. The proposed result leads to significant performance improvement in system analysis and synthesis. Based on the criterion obtained, a homotopy-based iterative LMI algorithm is developed to design a static output feedback controller. The feasibility and the effectiveness of theoretical developments are illustrated through numerical examples.Copyright © 2012 John Wiley & Sons, Ltd.

In this paper, we consider the problem of Nash equilibrium solutions of two players tracking game for bilinear systems. A successive approximation approach is modified to design optimal controllers for bilinear systems. More specifically, a sequence of extended Sylvester differential equations are solved by this modified approach. A simulation example is given to demonstrate the validity of this approach. Copyright © 2012 John Wiley & Sons, Ltd.

The aim of this paper is to propose an improvement of a classical change of variables useful to solve multi-objective control design problems that can be formulated with LMIs. For multi-objective problems, the only approach guaranteed to converge to global optima is to use an iterative approach where the order of the design parameter grows (until no improvement is obtained to some relative decrease). The issue is that the order of the design parameter and the size of associated LMIs may easily grow to unacceptably large values (computationally and/or for implementation in practice). The change of variables considered here was proposed to mitigate that issue, that is, to reduce the inflation of number of variables of the corresponding optimization problems. Here, we propose a method exploiting this change of variables further in order to obtain a sequence of increasing order design parameters converging faster towards the global optimum. Copyright © 2012 John Wiley & Sons, Ltd.

In this work, we design a nonlinear state feedback controller based on the State Dependent Riccati Equation (SDRE) technique to eliminate the tumor. One of the most interesting advantages of the SDRE is that it is possible to consider the specific conditions of patients by defining appropriate weights in the cost function and by limiting the administrated drug. Another advantage of this approach is that there are infinite ways to form the state dependent matrices. For each patient, a suitable drug regimen has been obtained using these advantages. A nonlinear model has been utilized to predict the growth of tumor. The model is a system of ODE with four state variables: normal cells, tumor cells, immune cells, and drug concentration. To use the SDRE controller, all state variables must be available for feedback. But for measuring the tumor size, the professional equipment is needed. So, it is impossible to measure the tumor size any time. We suppose that the number of normal cells could be measured in the presence of the Gaussian white noise. Therefore, we can design a state observer to estimate the immeasurable states from measurements. Extended Kalman Filter (EKF) can be used as a state observer for a nonlinear system, and in this work, we use EKF as a nonlinear state observer. Consequently, we can use the SDRE technique just by measuring the normal cell population. Numerical simulations are given to illustrate the design procedure and to show the flexibility of the method. Copyright © 2012 John Wiley & Sons, Ltd.

This paper studies the stochastic stabilization problem for discrete-time networked control systems with time delay and packet dropout. The message losses and time delay from the sensor to the controller and from the controller to the actuator are considered simultaneously. A two-state Markov chain is used to model the correlated packet dropout process. By introducing free weighting matrices, the sufficient condition on the stochastic stability of such networked control system is obtained. An improved criterion is found by introducing the delay fractioning method and a new Lyapunov–Krasovskii functional. On the basis of the stability condition, the mode-dependent controller is given in terms of linear matrix inequalities. A simulation example is given to show the proposed results. Copyright © 2012 John Wiley & Sons, Ltd.

This paper is concerned with the problem of robust fault detection filter design for a class of neutral-type neural networks with time-varying discrete and unbounded distributed delays. A Luenberger-type observer is designed for monitoring fault. By introducing an appropriate Lyapunov–Krasovskii functional and by using Jensen's inequality techniques to deal with its derivative, a new sufficient condition for the existence of robust fault detection filter is proposed in the form of LMIs with nonlinear constraints. To solve the nonlinear problem, a cone complementarity linearization algorithm is proposed. In addition, several numerical examples are provided to illustrate the applicability of the proposed approach. Copyright © 2012 John Wiley & Sons, Ltd.

This paper mainly studies the problem of the robustly stability analysis for uncertain neutral system with mixed time-varying delays. By constructing an augmented Lyapunov–Krasovskii functional, some new delay-dependent criteria can be established in terms of linear matrix inequalities. Compared with some existing results, our delay-dependent criteria can be shown to be some less conservative ones via some illustrative numerical examples. Copyright © 2012 John Wiley & Sons, Ltd.

By realizing the feedback paths over communication networks, we get a class of networked control systems (NCSs), where the network's quality-of-service (QoS) is commonly characterized by the average dropout rate of feedback data packets. The control performance of an NCS however, is determined not only by the average dropout rate but also by the dropout pattern of feedback data packets. This paper provides a systematic way to determine the optimal dropout pattern (policy) under a given average dropout rate, where the performance is measured by the output signal power under an exogenous white noise. By modeling the finite-memory dropout policies with the general Markov chain, this paper formulates the optimal dropout policy design into the optimization of parameters of a dropout Markov chain. That optimization is first solved by an augmented Lagrangian gradient method, which may be stuck at local optima because of the problem's non-convexity. To compensate this weakness, we apply the branch-and-bound method to the optimization whose constraints are bilinear. The branch-and-bound method can approach the global optimal solution with any desired tolerance in finite steps. The obtained optimal dropout policy may be interpreted as a network's QoS constraint whose enforcement provides a hard guarantee on the control system's performance. An example is used to illustrate the effectiveness of the achieved results. Copyright © 2012 John Wiley & Sons, Ltd.

The finite time horizon singular linear quadratic (LQ) optimal control problem is investigated for singular stochastic discrete-time systems. The problem is transformed into positive LQ one for standard stochastic systems via two equivalent transformations. It is proved that the singular LQ optimal control problem is solvable under two reasonable rank conditions. Via dynamic programming principle, the desired optimal controller is presented in terms of matrix iterative form. One simulation is provided to show the effectiveness of the proposed approaches. Copyright © 2012 John Wiley & Sons, Ltd.

This paper investigates the robust quantized feedback stabilization problem for a class of single-input linear uncertain systems on the basis of sliding mode control schemes. It is assumed that the system signals including the system state and control input are quantized before being transmitted through digital communication channels. A static adjustment policy of the quantization parameter for dynamic quantizers is developed. With the adjustment of the quantization parameter, a sliding mode control strategy is designed to ensure the reachability of the sliding manifold, and then, the system is induced into the stable sliding motion thereafter. Finally, an example is provided to illustrate the effectiveness of the proposed approach. Copyright © 2012 John Wiley & Sons, Ltd.

A design framework of the observer-based robust fault estimation for continuous-time/discrete-time systems is presented in this paper. Firstly, a multiconstrained fault estimation observer under the H_∞ performance specification with the regional pole constraint is proposed to achieve robust fault estimation. Then, the existence conditions for both continuous-time/discrete-time systems are derived explicitly. Furthermore, by introducing slack variables, improved results on the multiconstrained fault estimation observer design are obtained such that different Lyapunov functions can be separately designed for each constraint. Finally, simulation results of a vertical takeoff and landing aircraft are presented to illustrate our contributions. Copyright © 2012 John Wiley & Sons, Ltd.

The quasi-average mean square consensus problem for wireless sensor networks is studied in this paper. The related networks considered are time continuous and linear, and possess the leader–follower structures in which some sensors act as leaders and the others act as followers, with the locale information controlled. Three different leader–follower structures are proposed in this paper. The first one is the topology with fixed leaders and varying followers which arrives at a quasi-average mean square consensus by applying the sleeping-awaking method to all cliques of the followers. The second one is the topology with fixed leaders and fixed followers which arrives at a quasi-average value consensus via the general protocol. The third one is the topology with varying leaders and fixed followers which arrives at a quasi-average mean square consensus by applying the sleeping-awaking method to all cliques of the leaders. For mentioned three topologies, some necessity and sufficiency conditions of the related consensus are obtained, respectively. To illustrate the effectiveness of the obtained results, some numerical examples are presented finally. Copyright © 2012 John Wiley & Sons, Ltd.

The robust guaranteed cost control problem for uncertain discrete-time delay system is considered in this paper. Sufficient conditions for the existence of the robust guaranteed cost controllers via memoryless state feedback and static output feedback are expressed as bilinear matrix inequality (BMI). Furthermore, the design methods of optimal robust guaranteed cost controllers, which minimize the upper bound of a given quadratic cost function are presented. Alternate iterative algorithms are proposed to solve the nonconvex optimization problems with BMI constrains. A numerical example is given to illustrate the effectiveness of the proposed methods.Copyright © 2012 John Wiley & Sons, Ltd.

This paper first develops a discrete-time multi-period mean-variance portfolio selection model under the assumption that return of a risky asset depends on the states of a stochastic market with a bankruptcy state. When bankruptcy happens, the investor can only retrieve a random fraction δ of the wealth that she or he should acquire and then invests her or his retrieved money in a risk-free asset until the terminal time. Then, by dynamic programming approach and induction method, explicit closed-form expressions for the optimal strategy and efficient frontier are derived. Analysis of the optimal results is also provided. Finally, some numerical examples are presented to illustrate the effects of bankruptcy probability and fraction δ on the efficient frontier and optimal strategy. Specially, (i) our results under the mean-variance model have quite different properties compared with those under power-utility criterion, and (ii) our model generalizes the existing mean-variance portfolio selection with regime switching without bankruptcy state. Copyright © 2012 John Wiley & Sons, Ltd.

In this paper, we present an inexact sequential quadratic programming method in the context of a direct multiple shooting approach for differential algebraic equations. For the case that a numerical integration routine is used to compute the states of a relaxed differential algebraic equation, the computation of sensitivities, with respect to a large number of algebraic states, can become very expensive. To overcome this limitation, the inexact sequential quadratic programming method that we propose in this paper requires neither the computation of any sensitivity direction of the differential state trajectory, with respect to the algebraic states, nor the consistent initialization of the differential algebraic equation. We prove the locally quadratic convergence of the proposed method. Finally, we demonstrate the numerical performance of the method by optimizing a distillation column with 82 differential and 122 algebraic states. Copyright © 2012 John Wiley & Sons, Ltd.

In this paper, a composite Chebyshev finite difference method is introduced and applied for finding the solution of optimal control of time-delay systems with a quadratic performance index. This method is an extension of the Chebyshev finite difference scheme. The proposed method can be regarded as a nonuniform finite difference scheme and is based on a hybrid of block-pulse functions and Chebyshev polynomials using the well-known Chebyshev–Gauss–Lobatto points. Various types of time-delay systems are included to demonstrate the validity and the applicability of the technique. The method is easy to implement and provides very accurate results. Copyright © 2012 John Wiley & Sons, Ltd.

In this paper, we study the trajectory-planning problem for planar underactuated robot manipulators with two revolute joints in the presence of gravity. This problem is studied as an optimal control problem. We consider both possible models of planar underactuated robot manipulators, namely with the elbow joint not actuated, called Pendubot, and with the shoulder joint not actuated, called Acrobot. Our method consists of a numerical resolution of a reformulation of the optimal control problem, as an unconstrained calculus of variations problem, in which the dynamic equations of the mechanical system are regarded as constraints and treated by means of special derivative multipliers. We solve the resulting calculus of variations problem by using a numerical approach based on the Euler–Lagrange necessary condition in integral form. In which, time is discretized, and admissible variations for each variable are approximated using a linear combination of the piecewise continuous basis functions of time. In this way, a general method for the solution of optimal control problems with constraints is obtained, which, in particular, can deal with nonintegrable differential constraints arising from the dynamic models of underactuated planar robot manipulators with two revolute joints in the presence of gravity. Copyright © 2012 John Wiley & Sons, Ltd.

The problem of robust H_∞ control for a class of uncertain singular time-delay systems with Markovian jumping parameters is addressed in this paper. The considered Markovian jump singular systems involve constant time delay and norm-bounded uncertainties. On the basis of LMI approach, a delay-dependent condition is proposed, which ensures the nominal Markovian jump singular system to be regular, impulse-free and stochastically stable. From the delay-dependent condition, a sufficient condition leading to the existence of a state feedback controller that guarantees the robust admissibility and the H_∞ performance is also given. A numerical example is given to demonstrate the applicability of the proposed method. Copyright © 2012 John Wiley & Sons, Ltd.

In this paper, we discuss subprime mortgage design in both a theoretical- and numerical-quantitative framework. In particular, we model mortgages that are able to fully amortize, voluntarily prepay (involving prepayment and possibly refinancing), or default. In this regard, we find that mortgage refinancing is curtailed by high loan-to-value ratios because of house price depreciation, whereas low loan-to-value ratios increase mortgagor house equity. Furthermore, an optimal originator valuation problem under mortgage origination is solved. In this case, optimal mortgage value and rates as well as profit are computed. The paper supports the view that the subprime mortgage crisis was partially caused by the intricacy of design of subprime mortgages that led to information (asymmetry, contagion, inefficiency, and loss) problems, valuation opaqueness, and ineffective risk mitigation. Copyright © 2012 John Wiley & Sons, Ltd.

This paper investigates the state feedback robust H_∞ control problem of a class of discrete-time singular systems with norm-bounded uncertainties and interval time-varying delays in state and input. A new bounded real lemma for discrete-time singular systems with a pair of time-varying interval state delays is first investigated. Mathematical comparisons of the new bounded real lemma and two existing ones are presented. Then, on the basis of the bounded real lemma proposed here, a sufficient condition in the form of nonlinear matrix inequality, such that the considered state feedback robust H_∞ control problem is solvable, is given. In order to solve the nonlinear matrix inequality, a cone complementarity linearization algorithm is offered. Several numerical examples are presented to show the applicability of the proposed approach. Copyright © 2012 John Wiley & Sons, Ltd.

This paper considers a class of nonlinear descriptor systems whose nonlinear terms are time-varying and satisfy a quadratic inequality. An nonlinear observer is constructed and the error system is represented by a Lur'e descriptor system (LDS). Motivated by the basic idea of absolute stability theory, both types of full-order and reduced-order observers are constructed by a unified approach. The proposed method generalizes the existing ones for standard state-space systems, and global convergence of the nonlinear observer is achieved without the usual global Lipschitz restriction. Furthermore, the stability criterion for the error system extends the existing ones for LDS in the sense that the involved interconnected nonlinearities are time-varying and in unbounded sector. Finally, the design methods are reduced to a linear matrix inequality problem and illustrated by two numerical examples. Copyright © 2012 John Wiley & Sons, Ltd.

This paper presents a conjugate gradient-based algorithm for feedback min–max optimal control of nonlinear systems. The algorithm has a backward-in-time recurrent structure similar to the back propagation through time (BPTT) algorithm. The control law is given as the output of the one-layer NN. Main contribution of the paper includes the integration of BPTT techniques, conjugate gradient methods, Adams method for solving ODEs and automatic differentiation, to provide an effective, numerically robust algorithm for solving optimal min–max control problems. The proposed algorithm is evaluated on a robotic system with two DOFs. Copyright © 2012 John Wiley & Sons, Ltd.