乘性/加性噪声Markov跳变系统线性均方最优控制

Linear Quadratic Optimal Control for Discrete-Time Markov Jump System with Multiplicative and Additive Noise

针对具有乘性/加性噪声的离散时间Markov跳变线性系统,运用Bellamn随机动态规划法,对于噪声相互独立和相关两种情形推导了有限终止时间和无限终止时间的随机LQ最优控制算法,控制器的求解归结为求一组代数R iccati方程解。与不含有乘性噪声的系统相比较,此R iccati方程中多了包含噪声强度的项,反映了噪声对控制器的影响,从而改善了系统的性能。仿真结果与名义系统相比较,表明了本文所设计的控制器使系统具有更优的性能。

The finite and infinite horizon stochastic linear quadratic optimal control algorithms for discrete -time Markov jump with muhiplicative and additive noise system are presented based on Bemllman stochastic dynamic programming. And an optimal control is studied when the noises are correlated. The solution to the controller boils down to solving a set of algebra Riccati equations. The algebra Riccati equations include the noise covariance matrix which describes the effect of the noise on the controller, so the performance of the system is improved. Finally, the simulation results show that the performance of the system with the controller in this paper is better than that of the nominal system.