Abstract
This paper addresses an approximate version of the optimal control problem with non-convex state constraints via discretization of time and space, where the specific application pursued is the obstacle avoidance problem. First, it is pointed out that the standard continuous-time cost function with the final state fixed is not suitable to the optimal control problem under the non-convex state constraints, and then a new cost function including intermediate target states is proposed. Next, for the optimal control problem with this cost function, where the non-convex state constraints are discretized with respect to time axis and state space, an optimal continuous-time control is given in an explicit form, including the intermediate target states obtained by solving a discrete optimization problem. Efficient algorithms such as the breadth first search algorithm can be applied to this discrete problem. Thus the continuous-time trajectory as well as the discretized state at each discrete time is simultaneously optimized. Finally, we illustrate the effectiveness of the proposed approach with numerical simulations
Original language | English |
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Title of host publication | Proceedings of the 2004 IEEE international conference on control applications : September 2-4, 2004, Taipei, Taiwan |
Place of Publication | Piscataway |
Publisher | Institute of Electrical and Electronics Engineers |
Pages | 878-883 |
ISBN (Print) | 0-7803-8633-7 |
Publication status | Published - 2004 |