Model predictive control for constrained systems with serially correlated stochastic parameters and portfolio optimization

In this paper, we consider MPC for constrained discrete-time systems with stochastic parameters which are assumed to be a set of serially correlated time series. A generalized performance criterion is composed of a weighted sum of a linear combination of the (a) expected value of quadratic forms of state and control vectors, (b) quadratic forms of the expected value of the state vector, and (c) the linear component of the expected value of the state vector. The purpose of the present paper is to design optimal control strategies that are independent of distributional assumptions on the stochastic parameters and subject to hard constraints on the input manipulated variables and to provide a numerically tractable algorithm for practical applications. All expressions are presented in terms of the first- and second-order conditional moments. The results are applied to a problem of investment portfolio optimization with serially correlated returns. We present the numerical modelling results, based on stocks traded on the Russian Stock Exchanges MICEX.