Robust stabilization for discrete-time Takagi-Sugeno fuzzy system based on N4SID models

Abstract

Nonlinear systems identification from experimental data without any prior knowledge of the system parameters is a challenge in control and process diagnostic. It determines mathematical model parameters that are able to reproduce the dynamic behavior of a system. This paper combines two fundamental research areas: MIMO state space system identification and nonlinear control system. This combination produces a technique that leads to robust stabilization of a nonlinear Takagi-Sugeno fuzzy system (T-S). Design/methodology/approach The first part of this paper describes the identification based on the Numerical algorithm for Subspace State Space System IDentification (N4SID). The second part, from the identified models of first part, explains how we use the interpolation of Linear Time Invariants (LTI) models to build a nonlinear multiple model system, T-S model. For demonstration purposes, conditions on stability and stabilization of discrete time, Takagi-Sugeno (T-S) model were discussed. Findings Stability analysis based on the quadratic Lyapunov function to simplify implementation was explained in this paper. The LMIs (Linear Matrix Inequalities) technique obtained from the linearization of the BMIs (Bilinear Matrix Inequalities) was computed. The suggested N4SID2 algorithm had the smallest error value compared to other algorithms for all estimated system matrices. Originality The stabilization of the closed-loop discrete time T-S system, using the improved PDC control law (Parallel Distributed Compensation), was discussed to reconstruct the state from nonlinear Luenberger observers.

Discrete-Time Takagi-Sugeno Stabilization Approach Applied in Autonomous Vehicles

“…In this section, we compare between the discrete-time T-S of [21] and our new PDC control law design applied to the lateral control for autonomous vehicles. The results demonstrate the robustness and effectiveness of the improved PDC control law formula.…”

“…In this part, we present the results of the lateral control of autonomous vehicles for T-S presented by [21], the methods used by [5][6][7] and the new formulation of the PDC control law. Based on (49), The F matrix is symmetric and positive definite as we can see below, this form of F applied to the Quadratic Lyapunov function ensures the ellipsoid convex shape with a global minimum which is zero.…”

“…We also computed the true values of the state vector using multiple Luenberger observers. Moreover, in this paper, we compared the lateral control results given by the new formulation of the PDC law with the improved classic one [21]. As shown, the two lateral controllers converge the autonomous vehicles states to the equilibrium point and ensure the lane keeping under various constraints.…”

“…It will be measured, and it contains six real state variables values using Luenberger multiobservers. (4) First time application of Jemmali et al [21]'s technique for the autonomous vehicles.…”

“…So (−1) is made as a common factor in Equation (20) to get the Schur LMI desired form (21) as follows:…”