Model predictive control for nonlinear systems with time‐varying dynamics and guaranteed Lyapunov stability

Abstract

This article focuses on model predictive control (MPC) of nonlinear systems in the case that the system parameters are inaccurate due to equipment wear or environmental changes. An MPC where the parameters of the predictive model are recursive estimated is proposed for nonlinear continuous time systems. The range of initial state that is able to guarantee the state always bounded in an allowable stability region, even when there does not exist any robust control law designed based on the mismatched initial model, is deduced. The corresponding optimization problem is designed based on Lyapunov controller techniques and includes parameter estimation parts. By this method, the state will eventually converge to a small neighborhood of the desired set-point. Stability analysis is performed and an application of the proposed method to the chemical process is presented to show the effectiveness of the proposed method.

Economic Lyapunov‐based model predictive control with event‐triggered parametric identification

“…In this article, we extended the result in Reference 18, an ELMPC with an event‐triggered parametric identification is designed for systems with slow time‐varying dynamics. In the proposed method, a condition that the ELMPC being required to identify the system model is designed to supervise if the feasibility of closed‐loop systems will be violated.…”

“…In literature, 17 to further decrease the affection of the tight constraints to optimize the performance, the terminal invariant set and the constraints are online updated and relaxed based on the increasingly accurate model. Moreover, Reference 18 proposes an adaptive LMPC where the state of closed‐loop system is able to be regulated within a certain bound and eventually converges to a small region if the state starts from a predefined region and the model parameters are recursively updated through the real‐time measurement. The Lyapunov controller which constrains the MPC control law is also updated according to new arrival data.…”

A distributed model predictive control with neighborhood state feedback invariant set for reconfigurable networked systems

“…5,6,8 These local optimization problems work together to get the solution of the constrained optimization problem to be solved in centralized MPC. Compared with the centralized MPC, DMPC not only inherits MPC's abilities to obtain good optimization performance, explicitly accommodate constraints, [9][10][11][12][13][14][15][16] but also can reduce the computational complexity and improve the flexibility and robustness of the overall networked system. 7,12,[17][18][19][20] For the control of reconfigurable networked systems, one problem is how to improve the performance of the entire closed-loop system with feasibility guaranteed even when the network topology changes.…”

“…These local optimization problems work together to get the solution of the constrained optimization problem to be solved in centralized MPC. Compared with the centralized MPC, DMPC not only inherits MPC's abilities to obtain good optimization performance, explicitly accommodate constraints, 9‐16 but also can reduce the computational complexity and improve the flexibility and robustness of the overall networked system 7,12,17‐20 …”

Nonlinear disturbance observer‐based adaptive feedback linearized model predictive controller design for a class of nonlinear systems

“…Further, in [6], authors have designed a nonlinear model predictive control (NMPC) with an adaptive neural network (NN) predictor for a highly nonlinear system. Moreover, in [10][11][12], an NMPC with control Lyapunov functions has been used for achieving optimal control performance and ensuring stability guarantees for a uncertain system. Recently, a learning-based adaptive MPC has been developed by a researcher in [13], where a modified extended Kalman filter (EKF) is used to perform the joint state and parameter estimation.…”