Development of offset-free Koopman Lyapunov-based model predictive control and mathematical analysis for zero steady-state offset condition considering influence of Lyapunov constraints on equilibrium point. (October 2022)

• Record Type: Journal Article
• Authors: Son, Sang Hwan; Narasingam, Abhinav; Kwon, Joseph Sang-Il
• Is Part Of: Journal of process control. Volume 118(2022)
• Page Start: 26
• Page End: 36
• Publication Date: 2022-10
• Subjects: Koopman operator -- Extended dynamic mode decomposition -- Koopman Lyapunov-based model predictive control -- Offset-free tracking; Process control -- Periodicals; Fabrication -- Contrôle -- Périodiques; Process control; Periodicals; Electronic journals; 660.281
• DOI: 10.1016/j.jprocont.2022.08.005
• Languages: English
• ISSNs: 0959-1524

Abstract

Abstract: Koopman operator theory enables a global linear representation of a given nonlinear dynamical system. However, since an approximation to the Koopman operator cannot fully represent a nonlinear dynamical system, plant-model mismatch inherently exists and negatively influences the performance of control systems. To this end, we present a new approach called offset-free Koopman Lyapunov-based model predictive control (KLMPC) that augments disturbance dynamics to a Koopman-based model to consider the plant-model mismatch in the optimal control problem. The zero steady-state offset condition of the developed framework is also mathematically examined by rigorously investigating the influence of Lyapunov constraints on the equilibrium point of the offset-free KLMPC system. Highlights: An offset-free Koopman Lyapunov-based model predictive control scheme is developed. The zero steady-state offset condition is mathematically investigated. Influence of the Lyapunov constraints on the equilibrium point is considered. Developed Koopman-based controller shows proper offset-free tracking performance.