The Optimal Control Of Systems With Impulse And Switching

This paper discusses the optimal control of the hybrid systems with impulses andswitchings in the free terminal state. Using the maximum principle and the spikemethod, the global optimal control of the hybrid systems is solved. Specially, a adjointequation with impulses is given to contruct its Hamiltonian function. As a result, themaximum principle for such system is delivered.Then with this method we discussedthe optimal control of a linear systems with impulses and switchings, and we get theoptimal control with a Ricatti equation. Second, the optimal control of time-delayswitched nonlinear system control problem is discussed, the necessary conditions forthe system optimization are found out, and similar maximum principle is also laid out.