Stabilizing Model Predictive Control Synthesis using Integral Quadratic Constraints and Full-Block Multipliers*

Abstract

In this paper, we discuss how to synthesize stabilizing Model Predictive Control (MPC) algorithms based on convexly parameterized Integral Quadratic Constraints (IQCs), with the aid of general multipliers. Specifically, we consider Lur’e systems subject to sector-bounded and slope-restricted nonlinearities. As the main novelty, we introduce point-wise IQCs with storage in order to accordingly generate the MPC terminal ingredients, thus enabling closed-loop stability, strict dissipativity with regard to the nonlinear feedback, and recursive feasibility of the optimization. Specifically, we consider formulations involving both static and dynamic multipliers, and provide corresponding algorithms for the synthesis procedures. The major benefit of the proposed approach resides in the flexibility of the IQC framework, which is capable to deal with many classes of uncertainties and nonlinearities. Moreover, for the considered class of nonlinearities, our method yields larger regions of attraction of the synthesized predictive controllers (with reduced conservatism) if compared to the standard approach to deal with sector constraints from the literature.

Robust Differential Dynamic Programming

“…is bounded by the Rayleigh coefficient y ⊺ k y k . Hence, multiplying by c 2 k yields the requirement c k ≥ c k+1 + y ⊺ k y k , which implies both (26) and (27). Applying a similar left/right multiplication to (7d) results in the condition…”

“…Furthermore, optimizing robust performance and incorporating model uncertainty descriptions from robust control is challenging in tube-based MPC. In recent publications, the integration of classical robust control tools, like dynamic IQCs [27], [34], into MPC is explored. In addition, optimizing tube parameters online to reduce conservatism has gained interest [28].…”