On stochastic receding horizon control with bounded control inputs

This paper is concerned with the problem of receding horizon control of discrete-time systems subject to possibly unbounded random noise inputs, while satisfying hard bounds on the control inputs. We use a nonlinear feedback policy with respect to noise measurements and show that the resulting mathematical program has a tractable convex solution. Moreover, under the assumption that the zero-input and zero-noise system is asymptotically stable, we show that the variance of the state, under the resulting receding horizon control policy, is bounded. Finally, we provide some numerical examples on how certain matrices in the underlying mathematical program can be calculated off-line.