Robust Constrained Model Predictive Control for Discrete‐Time Uncertain System in Takagi‐Sugeno's Form

Abstract

In this paper, we investigate a robust constrained model predictive control synthesis approach for discrete-time Takagi-Sugeno's (T-S) fuzzy system with structured uncertainty. The key idea is to determine, at each sampling time, a state feedback fuzzy predictive controller that minimizes the performance objective function in the infinite time horizon by solving a class of linear matrix inequalities (LMIs) optimization problem. To do this, the fuzzy predictive controller is designed on the basis of non-parallel distributed compensation (non-PDC) control law, relaxed stability conditions of the closed-loop fuzzy system are developed by employing an extended nonquadratic Lyapunov function and introducing additional slack and collection matrices. In addition, the presented approach is capable of ensuring the robust asymptotic stability as well as the recursive feasibility of the closed-loop fuzzy system. Simulations on a highly nonlinear continuous stirred tank reactor (CSTR) are eventually presented to demonstrate the effectiveness of the developed theoretical approach.

Robust H∞ static output‐feedback control for discrete‐time fuzzy systems with actuator saturation via fuzzy Lyapunov functions

“…where u (k) is the control input,ū ∈ ℜ m denotes the saturation level function. In the saturation function (5), each component of the vector (k) can be represented as:…”

“…To avoid this drawback and enlarge the feasibility set of solutions, extended Lyapunov functions have been investigated such as: piecewise Lyapunov functions (PLF) [8] and fuzzy weighting-dependent Lyapunov functions (FWDLF) [9][10][11][12][13][14][15]. Moreover, for nonlinear systems subjected to model uncertainties, robust stability analysis methods for T-S fuzzy systems with uncertainties have been developed in recent years [5,8,[15][16][17][18][19][20][21]. The control of T-S models generally uses the so-called state feedback parallel distributed compensation (PDC) scheme.…”

“…For the latter, static output feedback (SOF) control has attracted the attention of researchers from the control community [12,19,21]. Especially, for discrete-time T-S fuzzy systems, results devoted to SOF control can be found in [5,12,18,19,21,23,24]; and especially, in [4] and [12], where a fuzzy weighting-dependent Lyapunov function (FWDLF) has been used. At last, some performances are generally to be added, H ∞ attenuation being one of the most widely used for T-S systems [8,[10][11][12][13]17,19,20,22,[25][26][27][28][29][30].…”

An iterative model predictive control algorithm for constrained nonlinear systems

“…In this example, a CSTR for an exothermic, irreversible reaction A → B with constant liquid volume is considered to highlight the quality of the control that can be achieved by ItMPC when both the set point and the optimal trajectory of the states to the set point are within the tighter state constraints obtained by the procedure of tightening the state constraints. The continuous time model is derived from the mass and energy balances and it is given by . where C A is the concentration of A in the reactor, T is the reactor temperature, and T C is the temperature of the coolant stream.…”

“…In this example, a CSTR for an exothermic, irreversible reaction A → B with constant liquid volume is considered to highlight the quality of the control that can be achieved by ItMPC when both the set point and the optimal trajectory of the states to the set point are within the tighter state constraints obtained by the procedure of tightening the state constraints. The continuous time model is derived from the mass and energy balances and it is given by [20,25].…”