Adaptive MPC with Chance Constraints for FIR Systems
It provides a method for adaptive control under uncertainty with probabilistic constraints, but is incremental as it builds on prior work [1],[2] and is limited to FIR systems.
The paper proposes an adaptive stochastic MPC strategy for stable LTI systems with bounded disturbances, using RLS estimation and distributionally robust optimization to handle hard input and probabilistic output constraints, achieving persistent feasibility and demonstrated efficacy in a numerical example.
This paper proposes an adaptive stochastic Model Predictive Control (MPC) strategy for stable linear time invariant systems in the presence of bounded disturbances. We consider multi-input multi-output systems that can be expressed by a finite impulse response model, whose parameters we estimate using a linear Recursive Least Squares algorithm. Building on the work of [1],[2], our approach is able to handle hard input constraints and probabilistic output constraints. By using tools from distributionally robust optimization, we formulate our MPC design task as a convex optimization problem that can be solved using existing tools. Furthermore, we show that our adaptive stochastic MPC algorithm is persistently feasible. The efficacy of the developed algorithm is demonstrated in a numerical example and the results are compared with the adaptive robust MPC algorithm of [2].