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) - Son, Sang Hwan; Narasingam, Abhinav; Kwon, Joseph Sang-Il
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.