具有Markov跳跃参数的一类随机非线性系统逆最优增益设计

研究了一类随机非线性系统的逆最优增益设计问题，系统中除了方差未知的Wiener噪声之外，还含有Markov跳跃参数. 首先，给出此类系统逆最优增益设计问题可解的一个充分条件. 其次，针对一类具有严格反馈形式的随机非线性系统，利用积分反推法，给出了依概率全局渐近稳定和逆最优控制策略的设计方法. 其中，所设计的Lyapunov函数和控制策略与模态显式无关，克服了由于Markov跳跃模态引起的耦合项所带来的设计困难. 最后，通过仿真验证了控制策略的有效性.

Inverse Optimal Gain Assignment Control for a Class of Stochastic Nonlinear Systems with Markovian Jump Parameters

In this paper, the inverse optimal gain assignment problem for a class of stochastic nonlinear systems with Markovian jump parameters is investigated. Firstly, a sufficient condition to solve this problem for Markovian jump nonlinear systems with bounded indefinite Wiener noises is given. Then, the control strategies of global asymptotic stability and inverse optimal stabilization in probability are presented for a class of strict feedback nonlinear systems. To avoid dealing with the "interconnected" term caused by Markovian jump, the Lyapunov function and the controller are designed to be independent of the regime. Finally, simulation verifies the effectiveness of the control algorithm.