STATE VARIANCE CONSTRAINED FUZZY CONTROL VIA OBSERVER-BASED FUZZY CONTROLLERS

An output-feedback fuzzy approach to guaranteed cost control of vehicle lateral motion

This paper investigates the problem of event-triggered dissipative observer-based output feedback control for a class of Takagi-Sugeno (T-S) fuzzy singular systems with unavailable states, time-varying delays, and imprecise membership functions. The considered singular system is presented as a T-S fuzzy singular system which gives a more realistic presentation for a variety of non-linear dynamical systems than conventional state space representation. The general framework we designed is based on a fuzzy observer-based controller with time varying delay along with extended dissipativity, which provides the H∞, L2-L∞ and dissipative performance indices and is robust against the disturbances and time-varying delay. Moreover, a novel Lyapunov-Krasovskii functional is adopted to analyze the closed loop stability of the fuzzy system. The solvability of Lyapunov-Krasovskii functional results in the formation of linear matrix inequalities. The controller and observer gains can be obtained by solving the linear matrix inequalities. Simulations are performed to validate the proposed scheme.

This paper is concerned with the problem of reliable \(\mathrm H_2\) control for discrete-time T-S fuzzy bilinear systems with actuator faults and infinite-distributed delays. A discrete-time homogeneous Markov chain is used to represent the stochastic behavior of actuator faults. Based on a stochastic fuzzy Lyapunov function, the fuzzy observer-based controllers are designed for T-S fuzzy bilinear delay systems, two improved stability conditions are proposed to ensure that the resultant closed-loop system is exponentially stable in the mean-square sense with an \(\mathrm H_2\) performance index. It is shown the fuzzy observer-based controller can be obtained by solving a set of nonlinear minimization problem involving linear matrix inequalities (LMIs) constraints. An iterative algorithm making use of sequential linear programming matrix method (SLPMM) to derive a single-step LMI condition for fuzzy observer-based control design. Finally, an illustrative example is provided to demonstrate the effectiveness of the results proposed in this paper.

This paper introduces a novel observer-based fuzzy tracking controller that integrates disturbance estimation to improve state estimation and path tracking in the lateral control systems of Unmanned Ground Vehicles (UGVs). The design of the controller is based on linear matrix inequality (LMI) conditions derived from a Takagi–Sugeno fuzzy model and a relaxation technique that incorporates additional null terms. The state observer is developed to estimate both the vehicle’s state and external disturbances, such as road curvature. By incorporating the disturbance observer, the proposed approach effectively mitigates performance degradation caused by discrepancies between the system and observer dynamics. The simulation results, conducted in MATLAB and a commercial autonomous driving simulator, demonstrate that the proposed control method substantially enhances state estimation accuracy and improves the robustness of path tracking under varying conditions.

In this article, an observer-based fuzzy adaptive inverse optimal output feedback control problem is studied for a class of nonlinear systems in strict-feedback form. The considered nonlinear systems contain unknown nonlinear dynamics and their states are not measured directly. Fuzzy logic systems are applied to identify the unknown nonlinear dynamics and an auxiliary nonlinear system is constructed. Based on this auxiliary system, a fuzzy state observer is first designed to estimate the immeasurable states. By using the inverse optimal principle and adaptive backstepping design theory, an observer-based fuzzy adaptive inverse optimal output feedback control scheme is then developed. The proposed inverse optimal control scheme need not assume that the states are measurable. It also guarantees that the closed-loop system is semiglobally uniformly ultimately bounded, and achieves the optimal control objective as well. Finally, two simulation examples are provided to check the validity of the presented control method.

This paper investigates the observer-based H∞ fuzzy control problem for a class of discrete-time fuzzy mixed delay systems with random communication packet losses and multiplicative noises, where the mixed delays comprise both discrete time-varying and distributed delays. The random packet losses are described by a Bernoulli distributed white sequence that obeys a conditional probability distribution, and the multiplicative disturbances are in the form of a scalar Gaussian white noise with unit variance. In the presence of mixed delays, random packet losses and multiplicative noises, sufficient conditions for the existence of an observer-based fuzzy feedback controller are derived, such that the closed-loop control system is asymptotically mean-square stable and preserves a guaranteed H∞ performance. Then a linear matrix inequality approach for designing such an observer-based H∞ fuzzy controller is presented. Finally, a numerical example is provided to illustrate the effectiveness of the developed theoretical results.

This paper addresses the issue of tracking the output of an activated sludge process using fuzzy integral control. First, the dynamics of the nonlinear process are modeled with a dynamic state space fuzzy model integrating the effect of external disturbances, and then an additional integral state of the output tracking error is introduced to obtain an augmented Takagi-Sugeno (TS) fuzzy model. The TS fuzzy model is able to describe the dynamics of complex nonlinear systems with an excellent degree of accuracy. It is formulated by fuzzy if-then rules which can give local linear representation of the overall nonlinear system. Second, the design of the fuzzy integral control is performed, in which the state feedback gains are obtained by solving linear matrix inequalities (LMI). The objective is to ensure trajectory tracking of an activated sludge process (ASP) by controlling two key variables: the substrate concentration and the level of dissolved oxygen. To assess the performance of the proposed control strategy, a comparative analysis is carried out with a gain scheduling PI (GS-PI) controller. Simulation results are provided to illustrate the effectiveness of the proposed approach. Where, the fuzzy integral control reduces the high energy consumption in water treatment plants.

This paper proposes the robust fuzzy fault tolerant control (FTC) problem for the fuzzy Takagi-Sugeno (TS) systems with sensor faults and actuator faults in the presence of parameter uncertainties. The TS fuzzy model is first employed to approximate a nonlinear uncertain system, and then the fuzzy sensor fault, fuzzy actuator fault model and the fuzzy state observer are developed. Sufficient stabilization conditions of the fuzzy FTC systems are given, which are formulated in terms of linear matrix inequalities (LMIs). The LMIs can be efficiently solved using the convex optimization techniques. Finally, fuzzy observer based on fuzzy fault tolerant controller is developed. It is proved that the fuzzy control system is reliable in the sense of that the closed-loop system is asymptotic stability and the all sensor and actuator components can operate well in the presence of some component failures. The control scheme is tested for real profiles of wind speed pattern and provides satisfactory results

This paper presents new stability conditions and LMI (linear matrix inequality) based designs for both continuous and discrete fuzzy control systems. First, Takagi and Sugeno's fuzzy models and some stability results are recalled. To design fuzzy control systems, nonlinear systems are represented by Takagi-Sugeno fuzzy models. The concept of parallel distributed compensation is employed to design fuzzy controllers from the Takagi-Sugeno fuzzy models. New stability conditions are obtained by relaxing the stability conditions derived in previous papers. The stability analysis of the feedback system is reduced to a problem of finding a common Lyapunov function for a set of linear matrix inequalities. Convex optimization techniques involving LMIs are utilized to find a common Lyapunov function. A procedure to design the fuzzy controller is constructed using the parallel distributed compensation and the relaxed stability conditions. Some stability issues are remarked. A simple example demonstrates the effects of the derived stability conditions.

Observer-based fuzzy feedback control for nonlinear systems subject to transmission signal quantization

This study discusses the new stochastic <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">maximum power point tracking</i> control approach toward the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">photovoltaic cells</i> (PCs). A PC generator is isolated from the grid, resulting in a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">direct current</i> microgrid that can provide changing loads. In the course of the nonlinear systems through the time-varying delays, we proposed <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">networked control systems</i> beneath an event-triggered approach basically in the fuzzy system. In this scenario, we look at how random, variable loads impact the PC generator's stability and efficiency. The basic premise of this article is to load changes and the value matching to a Markov chain. PC generators are complicated nonlinear systems that pose a modeling problem. Transforming this nonlinear PC generator model into the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Takagi–Sugeno</i> (T--S) fuzzy model is another option. The T--S fuzzy model is presented in a unified framework, for which 1) the fuzzy observer based on this premise variables can be used for approximately in the infinite states to the present system, 2) the fuzzy observer-based controller can be created using the same premises being the observer, and 3) to reduce the impact of transmission burden, an event-triggered method can be investigated. Simulation in the PC generator model for the real-time climate data obtained in China demonstrates the importance of our method. In addition, by using a new <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Lyapunov–Krasovskii functional</i> for combining with the allowed weighting matrices incorporating mode-dependent integral terms, the developed model can be stochastically stable and achieves the required performances. Based on the tensor-product (T-P) <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">transformation</i> , a new depiction of the nonlinear system is derived in two separate steps in which an adequate controller input is guaranteed in the first step and an adequate vertex polytope is ensured in the second step. To present the potential of our proposed method, we simulate it for PC generators.

The primary aim of a vehicle's suspension system is to isolate the vehicle's main body from road irregularities, thus improving passenger comfort and ensuring optimal handling stability. This research discusses a stabilizing fuzzy control design for active vehicle suspension systems. The nonlinear model of the active suspension is then represented using a Takagi-Sugeno (TS) fuzzy model. The control approach uses a TS fuzzy controller utilizing an observer to estimate the state while reducing road disturbances. The closed-loop stability requirements of the vehicle utilizing the fuzzy controller and observer are expressed as a Linear Matrix Inequalities (LMI) problem, which can be effectively resolved through convex optimization methods. In this paper, we study the stability of the nonlinear automotive active suspension system with two degrees of freedom represented by a TS fuzzy model, where we will present the stabilization conditions by state feedback via the PDC (Parallel Distributed Compensation) control law and in the last section we introduced the TS fuzzy observer for the case of non-measurable premise variables.

This chapter investigates the problem of stabilization of nonlinear discrete-time networked control systems (NCS) with event-triggering communication scheme in the presence of signal transmission delay. A Takagi–Sugeno (T–S) fuzzy model and parallel-distributed compensation (PDC) scheme are first employed to design a nonlinear fuzzy event-triggered controller for the stabilization of nonlinear discrete-time NCS. The idea of the event-triggering communication scheme (a soft computation algorithm) under consideration is that the current sensor data is transmitted only when the current sensor data and the previously transmitted one satisfy a certain state-dependent trigger condition. By taking the signal transmission delay into consideration and using delay system approach, a T–S fuzzy delay system model is established to describe the nonlinear discrete-time NCSs with event-triggering communication scheme. Attention is focused on the design of fuzzy event-triggered controller which ensures asymptotic stability of the closed-loop fuzzy systems. Linear matrix inequality- (LMI-) based conditions are formulated for the existence of admissible fuzzy event-triggered controller. If these conditions are feasible, a desired fuzzy event-triggered controller can be readily constructed. A nonlinear mass-spring-damper mechanical system is presented to demonstrate the effectiveness of the proposed method.

This paper presents new stability conditions satisfying decay rate for both continuous and discrete fuzzy control systems. Linear matrix inequality (LMI) based designs for decay rate are also considered using the concept of parallel distributed compensation (PDC). To design fuzzy control systems, nonlinear systems are represented by Takagi-Sugeno fuzzy models. The PDC is employed to design fuzzy controllers from the Takagi-Sugeno fuzzy models. The stability analysis discussed here is reduced to a problem of finding a common Lyapunov function for a set of LMIs. Convex optimization techniques involving LMIs are utilized to find a common Lyapunov function and stable feedback gains satisfying decay rate. A simple example demonstrates the utility of the LMI-based designs proposed in this paper.

This paper addresses stability analysis and stabilization for Takagi-Sugeno (T-S) fuzzy systems with parametric uncertainties via a so-called fuzzy Lyapunov function which is a multiple Lyapunov function. The fuzzy Lyapunov function is defined by fuzzily blending quadratic Lyapunov functions. First, the Takagi-Sugeno (T-S) fuzzy model with parametric uncertainties is used as the model for the uncertain nonlinear system. Based on the fuzzy Lyapunov function approach and a parallel distributed compensation (PDC) scheme, we give stabilization conditions for closed-loop fuzzy systems with parametric uncertainties. Second, all the conditions are formulated in the format of linear matrix inequalities (LMIs) and contain upper bounds of the time derivative of premise membership functions as LMI variables. Finally, the T-S fuzzy model of the chaotic Lorenz system, which has complex nonlinearity, is developed as a test bed. A numerical example of the chaotic Lorenz system is given to illustrate the utility of the fuzzy Lyapunov function approach.