Absolute-Stability-Based Closed-Loop Stability Analysis of Adaptive Model Predictive Control for Self-Excited Lur’e Systems
Published in Proceedings of the American Control Conference, 2025
This paper presents a numerical investigation of the ability of predictive cost adaptive control (PCAC) to stabilize self-excited systems modeled by discrete-time Lur’e systems. The closed-loop Lur’e system is comprised of the positive feedback interconnection of the Lur’e system and the PCAC controller. This work presents a numerical investigation of the circle and Tsypkin absolute stability criteria to evaluate the stability of the closed-loop Lur’e system at each step. An exogenous input is used to increase persistency and thus enhance the ability of the closed-loop system to satisfy the absolute stability criteria. A numerical example illustrates the effect of exogenous persistency on the stability of the closed-loop Lur’e system. These numerical results show the potential value of absolute stability criteria for assessing the ability of adaptive model predictive control to stabilize a class of nonlinear systems.
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Recommended citation: J. A. Paredes Salazar and D. S. Bernstein, "Absolute-Stability-Based Closed-Loop Stability Analysis of Adaptive Model Predictive Control for Self-Excited Lur’e Systems," in Proc. Amer. Contr. Conf. (ACC), IEEE, 2025, pp. 2477-2482.