Stochastic disturbance rejection in model predictive control by randomized algorithms

In this paper we consider model predictive control with stochastic disturbances and input constraints. We present an algorithm which can solve this problem approximately but with arbitrary high accuracy. The optimization at each time step is a closed loop optimization and therefore takes into account the effect of disturbances over the horizon in the optimization. Via an example it is shown that this gives a clear improvement of performance although at the expense of a large computational effort

Optimal control of linear, stochastic systems with state and input constraints

In this paper we extend the work presented in our previous papers (2001) where we considered optimal control of a linear, discrete time system subject to input constraints and stochastic disturbances. Here we basically look at the same problem but we additionally consider state constraints. We discuss several approaches for incorporating state constraints in a stochastic optimal control problem. We consider in particular a soft-constraint on the state constraints where constraint violation is punished by a hefty penalty in the cost function. Because of the stochastic nature of the problem, the penalty on the state constraint violation can not be made arbitrary high. We derive a condition on the growth of the state violation cost that has to be satisfied for the optimization problem to be solvable. This condition gives a link between the problem that we consider and the well known $H_\infty$ control problem

Feedback model predictive control by randomized algorithms

In this paper we present a further development of an algorithm for stochastic disturbance rejection in model predictive control with input constraints based on randomized algorithms. The algorithm presented in our work can solve the problem of stochastic disturbance rejection approximately but with high accuracy at the expense of a large computational effort. The algorithm described here uses a predefined controller structure in the optimization and it is significantly less computationally demanding but with a price of some performance loss. Via an example it is shown that the algorithm gives considerable reduction in the computational time and that performance loss is rather small compared to the algorithm in our earlier work

Certainty equivalence in constrained linear systems subject to stochastic disturbances

A sufficient condition is provided under which the optimal controller of a constrained optimization problem can be synthesized by combining an optimal state estimator with an optimal static state feedback. An application of a model predictive controller is considered that involves both input and state constraints in a system that is subject to stochastic disturbances