Inverse optimal control for continuous-time nonlinear systems
Control óptimo inverso para sistemas no lineales en tiempo continuo
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Optimization theory applied to automatic control allows governing actions reaching desired conditions but minimizing a given performance index. Such optimization tasks imply to solve complicated mathematical expressions. The inverse optimal control appears as alternative to find the optimal control law without the explicit solution for the Hamilton-Jacobi-Bellman equation. To show the potential of the inverse optimal control for solving complex optimization problems in control theory. A general description of the optimal control problem is performed, followed by the justification of an inverse optimal approach. Examples for illustration are properly selected. Mathematical formulations given are applied to solve analytically the cases of a linear optimal quadratic regulator (LQR) and a nonlinear inverse optimal Lyapunov-based control problem (CLF). It is posible to solve optimal control problems for nonlinear systems, without explicitly facing the Hamilton-Jacobi-Bellman equation, by means of the inverse optimal control approach.
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