• optimal control;
  • region of convergence;
  • subdivision algorithm;
  • attractors of dynamical systems;
  • genetic algorithms;
  • shooting algorithm


We present a novel algorithm for optimal control of nonlinear systems based on a subdivision algorithm. The algorithm presented in this paper is an alternative to a set-oriented approach for optimal feedback stabilization. We compare the proposed algorithm to the set-oriented approach, contrast these two approaches, and use examples to show that the new algorithm produces comparable results. Also, we demonstrate by example that we receive a precomputed optimal solution. The main contribution of the paper is understanding how cost function improves with further subdivision of state space and smaller memory footprint of the final solution in comparison with set-oriented approach. Copyright © 2012 John Wiley & Sons, Ltd.