Optimal control of switching surfaces in hybrid dynamical systems.

*(English)*Zbl 1101.93054Summary: This paper concerns an optimal control problem defined on a class of switched-mode hybrid dynamical systems. The system’s mode is changed (switched) whenever the state variable crosses a certain surface in the state space, henceforth called a switching surface. These switching surfaces are parameterized by finite-dimensional vectors called the switching parameters. The optimal control problem is to minimize a cost functional, defined on the state trajectory, as a function of the switching parameters. The paper derives the gradient of the cost functional in a costate-based formula that reflects the special structure of hybrid systems. It then uses the formula in a gradient-descent algorithm for solving an obstacle-avoidance problem in robotics.

##### MSC:

93C85 | Automated systems (robots, etc.) in control theory |

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\textit{M. Boccadoro} et al., Discrete Event Dyn. Syst. 15, No. 4, 433--448 (2005; Zbl 1101.93054)

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