Variational formalism applied to control of autonomous switching systems
Résumé
The formalism of the calculus of variations is applied to determine an optimal control of a class of Hybrid Dynamical Systems. This class consists of autonomous switching systems where jumps of the state are taken into account. It is shown that model switching involves discontinuities in the adjoint state of the system. The expression of the gradient of the cost function, with respect to the control, allows for the calculation of an optimal control by implementing a descent method. An illustrative linear quadratic example is given, which allows to conclude that the method can be easily implemented.