A Continuous Feedback Optimal Control based on Second-Variations for Problems with Control Constraints

Details A Continuous Feedback Optimal Control based on Second-Variations for Problems with Control Constraints A Continuous Feedback Optimal Control based on Second-Variations for Problems with Control Constraints

2011-09-24

arxiv.org/abs/1109.5240v1

Mathematics

Optimization and Control

17 pages, 3 figures

Scientific paper

The paper describes a continuous second-variation algorithm to solve optimal control problems where the control is defined on a closed set. A second order expansion of a Lagrangian provides linear updates of the control to construct a locally feedback optimal control of the problem. Since the process involves a backward and a forward stage, which require storing trajectories, a method has been devised to accurately store continuous solutions of ordinary differential equations. Thanks to the continuous approach, the method adapts implicitly the numerical time mesh. The novel method is demonstrated on bang-bang optimal control problems, showing the suitability of the method to identify automatically optimal switching points in the control.

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