Regulation and look-ahead disturbance rejection receding horizon control

We consider the control of systems which are driven by exogenous influences such as disturbances or tracking signals. We assume there exists a nominal stabilizing controller which achieves a finite worst-case cost for the closed-loop system. We also assume that a finite horizon preview of the disturbance is available. The receding horizon strategy optimizes a differential game cost under the assumption that the worst-case disturbance ‘plays’ at the end of each finite horizon. We show that a receding horizon control algorithm that uses information about the disturbance preview results in a controller that achieves closed-loop stability and reduces the overall cost when compared to the cost of using the nominal controller alone. Since we optimize in the face of a known disturbance preview, this is not disturbance rejection in the usual sense.; Wherever optimization is required, the optimization need only satisfy an ‘improvement property’. This property is important since any optimization routine we use will likely only be able to find local minima, or may terminate early due to limited computational resources. We show that we can prove stability and performance results when using a control Lyapunov function (CLF) in place of the terminal cost function. This is important because the computation of the terminal cost function requires, in principal, that the system be simulated on the interval [k, ∞).; Since a CLF is often unavailable, we present examples showing that significant performance improvement can be obtained by using these methods in an ad hoc manner, by using lower bound estimates of the terminal cost function.; We also restate, in discrete time, some important results in receding horizon control theory from the recent works by Jadbabaie, Yu, and Hauser.