Adaptive MPC under Time Varying Uncertainty: Robust and Stochastic

TL;DR

This paper develops an adaptive Model Predictive Control strategy for linear systems with time-varying uncertainties, ensuring constraint satisfaction and stability through set membership methods and robust/stochastic approaches.

Contribution

It introduces a novel adaptive MPC framework that refines uncertainty sets online and guarantees constraint satisfaction under time-varying uncertainties.

Findings

The proposed algorithms ensure recursive feasibility and stability.

Numerical examples demonstrate effective constraint handling.

The method adapts to changing uncertainties in real-time.

Abstract

This paper deals with the problem of formulating an adaptive Model Predictive Control strategy for constrained uncertain systems. We consider a linear system, in presence of bounded time varying additive uncertainty. The uncertainty is decoupled as the sum of a process noise with known bounds, and a time varying offset that we wish to identify. The time varying offset uncertainty is assumed unknown point-wise in time. Its domain, called the Feasible Parameter Set, and its maximum rate of change are known to the control designer. As new data becomes available, we refine the Feasible Parameter Set with a Set Membership Method based approach, using the known bounds on process noise. We consider two separate cases of robust and probabilistic constraints on system states, with hard constraints on actuator inputs. In both cases, we robustly satisfy the imposed constraints for all possible values of the offset uncertainty in the Feasible Parameter Set. By imposing adequate terminal conditions, we prove recursive feasibility and stability of the proposed algorithms. The efficacy of the proposed robust and stochastic Adaptive MPC algorithms is illustrated with detailed numerical examples.