On finite time optimal control for discrete-time linear systems with parameter variation

In this paper, we propose a method of finite time optimal control for discrete time linear systems with parameter variation. This paper introduces the stochastic parameters independent of time to describe variations among products and derive optimal control law to cope with them. The optimal control input is derived by minimizing the expectation of cost function with respect to system parameters. Moreover, the sample size of parameters which is needed in the calculation of the optimal input is given by the Matrix Bernstein inequality. It is further applied to model predictive control for the infinite time horizon case. In the end, numerical simulations show the effectiveness of the proposed method.