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A quasi-sequential approach to large-scale dynamic optimization problems

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Abstract

A novel sequential approach for solving dynamic optimization problems containing path constraints on state variables is presented and its performance analyzed. As in the simultaneous approach, we discretize both state and control variables using collocation on finite elements, so that path constraints can be guaranteed inside each element. The state variables are solved in a manner similar to that in the sequential approach; this eliminates the discretized differential-algebraic equations and state variables, so that the problem is reduced to a smaller problem only with inequality constraints and control variables. Therefore, it possesses advantages of both the simultaneous and the sequential approach. Furthermore, the elimination of the equality constraints substantially simplifies the line search problem and thus larger steps can be taken by successive quadratic programming (SQP) toward the optimum. We call this dynamic optimization method a quasi-sequential approach. We compare this new approach with the simultaneous approach in terms of computational cost and by analyzing the solution path. A highly nonlinear reactor control and the optimal operation of a heat-integrated column system are used to demonstrate the effectiveness of this approach. As a result, it can be concluded that this quasi-sequential approach is well suited for solving highly nonlinear large-scale optimal control problems. © 2005 American Institute of Chemical Engineers AIChE J, 2006

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