Markov跳跃非线性系统逆最优增益设计

证明了一类严格反馈Markov跳跃系统是依概率输入–状态可稳定的.其次,证明了逆最优增益设计问题可解的一个充分条件是存在一组满足小控制量的依概率输入–状态稳定控制李雅普诺夫函数.最后,利用积分反推方法,给出了严格反馈Markov跳跃系统逆最优增益设计问题的一个构造性解.其中,为了克服由于Markov跳跃引起的耦合项所带来的困难,所设计的李雅普诺夫函数以及控制器是与模态无关的.

Inverse optimal gain assignment control for Markovian jump nonlinear systems

The concept of input-to-state stability in probability is introduced and an input-to-state stabilization protocol is proposed for a class of strict feedback Markovian jump nonlinear systems. It is shown that the existence of a group of input-to-state stable control Lyapunov function with small control is a sufficient condition for the solvability of the inverse optimal gain assignment problem. Finally, using backstepping method, we construct a smooth feedback control law for a class of strict feedback nonlinear systems. To deal with the coupling item caused by Markovian jump, the Lyapunov function and the controller are designed independently of the operation mode.