Multi‐Step Control Set‐Based Nonlinear Model Predictive Control with Persistent Disturbances

Abstract

A robust model predictive control algorithm is proposed for a constrained nonlinear system with bounded persistent disturbance in this paper. Based on polytopic descriptions that include the initial system, the proposed algorithm computes a series of multi-step control sets offline and the convex combination of them online respectively by solving convex optimization problems described by a few linear matrix inequalities. At each sampling time, the control moves satisfying the control constraint are obtained and implemented in the system. The controller design is illustrated with two examples. The proposed MPC controller achieves closed-loop input-to-state (practical) stability (ISS/ISpS) and strong robustness in respect of bounded persistent disturbances.

Constrained Model Predictive Control for Nonlinear Markov Jump System With Persistent Disturbance via Quadratic Boundedness

“…Assuming that the nonlinear function F (•) is continuous differentiable at the origin and the equilibrium of the system (1) is F (r k , 0, 0, 0) = 0. In the neighborhood of the equilibrium point of the system (1), a polytopic description system including original system can be constructed by use of the Taylor series extension and the extreme value of partial differentiation [32] or the differential inclusion [23]. L vertices are assumed to vary in the set…”

“…Thus the optimization problems of NMPC are nonlinear and nonconvex, which are difficult to solve even for cases involving only few variables [23]. If the nonlinear items can be represented by neural network model [28], T-S fuzzy model [29]- [31] or polyhedral model [23], [32], [33], the linear analytical expressions of original systems can be obtained and the relatively mature results on stability and feasibility of linear MPC can be applied in nonlinear MJSs. Considering the nonlinear MJS with nonhomogeneous process, the constrained MPC design was proposed and avoids solving nonlinear optimization problem through applying a differential-inclusion-based design [23].…”

“…For linear MJSs subjected to the linear combinational constraints of states and input controls, constrained MPC synthesis based on coupled invariant sets can guaranteed the convergence of the closed loop responses [19], [24]. Considered input-to-state stable problems and Lyapunov-like sufficient conditions, MPC scheme was a powerful tool for nonlinear systems subjected to hard constraints and disturbances [28], [29], [32], [33]. Using quadratic boundedness, the receding-horizon estimators were designed for linear systems with bounded disturbances [34], [35].…”

Robust constrained model predictive control design for piecewise non-linear systems with multiple operating points

“…A promising accepted approach to overcome this detriment is to design a robust MPC controller. Robust MPC has received a great deal of attention of the researchers in past years (Ažman and Kocijan, 2008; Cannon and Kouvaritakis, 2005; Ding, 2010; Hu et al, 2004; Kothare et al, 1996; Poursafar et al, 2010), and we can also find further development in the recent papers (Koeln and Alleyne, 2018; Liu et al, 2018; ; Moradi et al, 2019; Shamaghdari and Haeri, 2020; Shi and Mao, 2019; Xu et al, 2019; Zhang et al, 2018).…”

Adaptive predictive path following control based on least squares support vector machines for underactuated autonomous vessels

“…One of difficulties for path following controller design is to satisfy rudder magnitude constraints [5]. Model predictive control (MPC) offers a good choice to handle this challenge because of its advantage of considering constraints explicitly [23,24]. Since MPC relies on a system model for trajectory predictions, prediction models should be updated when system dynamics change.…”