Approximate Explicit Model Predictive Controller using Gaussian Processes

Model predictive control is a successful method of regulating the operation of constrained dynamical systems. However, its applicability is limited by the necessity of solving in real-time an optimization problem. Explicit model predictive control techniques aim to precompute the optimal control law off-line for all feasible points in the state space of the system. However, constructing the explicit control law off-line and using it to compute the control inputs on-line can be computationally demanding for medium to large scale systems. Hence, several approaches have been suggested to approximate the explicit control law. This paper proposes the use of Gaussian processes for this purpose. Gaussian processes allow one to define a systematic way of selecting these training data which minimize the uncertainty of the approximation. Unlike other approaches in the literature, domain specific knowledge is exploited here to simplify the training effort, while probabilistic guarantees are provided for the proximity of the derived approximation to the explicit control law. We illustrate, in a number of benchmark systems, the efficacy of the proposed approach which leads to closed-loop operation similar to that of the exact explicit control law, only at a fraction of the computation effort.