Article:  Kircher, KJ; Zhang, KM; “Sample-Average Model Predictive Control of Uncertain Linear Systems”, 2016 IEEE 55th Conference on Decision and Control (CDC), 6234-6239

Abstract:  We propose a randomized implementation of stochastic model predictive control (MPC). As a proxy for the expected cost, which may not be efficiently computable, the algorithm minimizes the empirical average cost under N random samples of the uncertain influences on the system.

The setting is an imperfectly-observed linear system with multiplicative and additive uncertainty, convex, deterministic control constraints, and convex costs that may include penalties on state constraint violations.

In this setting, each sample-average MPC subproblem is a feasible convex program that, under mild regularity conditions, yields consistent estimators of the stochastic MPC subproblem’s optimal value and minimizers. Under stronger assumptions, the full sample-average MPC control trajectory is asymptotically optimal for stochastic MPC as N -> infinity. A numerical example shows that even for small N, sample-average MPC can significantly improve performance relative to certainty-equivalent MPC.

Funding Acknowledgement:  Hydro Research Foundation; U.S. Department of Energy’s Office of Renewable Energy and Energy Efficiency

Funding Text:  We are grateful to the Hydro Research Foundation and the U.S. Department of Energy’s Office of Renewable Energy and Energy Efficiency for funding. Thanks as well to Professors Eilyan Bitar and Shane Henderson of Cornell University for their valuable suggestions.