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

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

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.

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.

Quantized output feedback control for nonlinear Markovian jump distributed parameter systems with unreliable communication links

For nonlinear space-varying parabolic partial differential equation systems (PPDESs) with random time-varying delay, this article introduces a dynamic fuzzy boundary output feedback (DFBOF) control under noncollocated boundary measurement (NCBM). Initially, the nonlinear delayed PPDESs are represented by Takagi–Sugeno (T–S) fuzzy models and random time-varying delay is considered by taking the influence of uncertain factors, which belongs to two intervals in a probabilistic way. Since the system state is not fully available and NCBM makes the boundary control design very difficult, a fuzzy observer under NCBM is presented to surmount the design difficulty. Subsequently, an observer-based fuzzy boundary controller is proposed and spatial linear matrix inequality (SLMI)-based sufficient conditions to ensure mean-square exponential stability are obtained for closed-loop delayed PPDESs by utilizing the Lyapunov direct method and Wirtinger inequality. Then, to solve the SLMIs, the feasibility conditions of DFBOF controller design for nonlinear delayed PPDES are expressed in LMIs. Finally, two examples are offered to demonstrate the validity of the presented dynamic fuzzy boundary control approach.

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 article proposes a fault diagnosis method for closed-loop satellite attitude control systems based on a fuzzy model and parity equation. The fault in a closed-loop system is propagated with the feedback loop, increasing the difficulty of fault diagnosis and isolation. The study uses a Takagi-Sugeno (T-S) fuzzy model and parity equation to diagnose and isolate a fault in a closed-loop satellite attitude control system. A fully decoupled parity equation is designed for the closed-loop satellite attitude control system to generate a residual that is sensitive only to a specific actuator and sensor. A T-S fuzzy model is used to describe the nonlinear closed-loop satellite attitude control system. With the combination of the T-S fuzzy model and fully decoupled parity equation, the fuzzy parity equation (FPE) of the nonlinear system can be obtained. Then this article uses a parameter estimator based on a Kalman filter to identify deviations and scale factor changes from information contained in the residuals generated by the FPE. The actuator and sensor fault detection and isolation simulation of the three-axis stable satellite attitude control system is provided for illustration.

In this paper, a state variance constrained design method is developed to deal with the observer-based fuzzy control problem for continuous Takagi-Sugeno (T-S) fuzzy stochastic models. The stability problem considered in this paper is a standard feasibility problem with several Linear Matrix Inequalities (LMIs), which can be solved numerically using the interior-point method. The purpose of this paper aims at finding observer-based fuzzy controllers such that the closed-loop system is asymptotically stable and the state variance performance constraints are satisfied. Finally, a numerical example is included to demonstrate the effectiveness of the proposed controller design method.

Event-triggered fault detection filter design for nonlinear networked systems via fuzzy Lyapunov functions

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 presents the design of a state convergence (SC)-based bilateral controller for a nonlinear teleoperation system, which has been approximated by a Takagi–Sugeno (TS) fuzzy model. The selection of SC is made due to the advantages offered by this scheme both in the modeling and control design stages. The modeling stage considers master/slave systems, which can be represented by the $n$ th order differential equations, while the control design stage offers an easy way to determine the control gains required for assigning desired closed loop dynamics to teleoperation system. After the master/slave systems are represented by TS fuzzy models, a stabilizing fuzzy law is adopted which allows deploying the SC scheme with all its benefits to design the fuzzy bilateral controller. In this way, not only the simplicity of the design scheme is ensured but also the existing SC scheme is able to control a nonlinear teleoperation system based on its TS fuzzy model description. As an additional advantage, the SC-based existing linear bilateral controller can be easily derived from the SC-based proposed fuzzy bilateral controller. Various cases of master/slave systems originally reported in terms of their linear model representation and communication in the absence/presence of time delay are all discussed in the corresponding fuzzy framework. The MATLAB simulations, considering a one-degree-of-freedom teleoperation system, are performed to validate the proposed methodology for controlling a nonlinear teleoperation system.

The present work is concerned to solve the problem of nonlinear robotic control systems on the basis of Takagi- Sugeno (T-S) fuzzy models. In addition, controllability and observability studies for T-S fuzzy model systems are considered for Single-Input Single-Output (SISO) and Multiple-Input Multiple-Output (MIMO) systems. In particular, the robust pole assignment approach is extended to the fuzzy field. This approach is used to design fuzzy stabilizers and fuzzy observers directly on the overall T-S fuzzy system. The latter one is the representation of the nonlinear robotic system, which is linearized around certain operation regions. The suggested method is considered for either SISO or MIMO systems. Furthermore, the method allows inducing an arbitrary behavior into the fuzzy plant in a relatively easy way. Two examples are used to verify the effectiveness of the proposed approach. The results are compared with the well-known Parallel Distributed Compensation (PDC) method, which is designed on the basis of Linear Matrix Inequalities (LMIs).

This paper proposes new algorithms based on the fuzzy c-regressing model algorithm for Takagi-Sugeno (T-S) fuzzy modeling of the complex nonlinear systems. A fuzzy c-regression state model (FCRSM) algorithm is a T-S fuzzy model in which the functional antecedent and the state-space-model-type consequent are considered with the available input-output data. The antecedent and consequent forms of the proposed FCRSM consists mainly of two advantages: one is that the FCRSM has low computation load due to only one input variable is considered in the antecedent part; another is that the unknown system can be modeled to not only the polynomial form but also the state-space form. Moreover, the FCRSM can be extended to FCRSM-ND and FCRSM-Free algorithms. An algorithm FCRSM-ND is presented to find the T-S fuzzy state-space model of the nonlinear system when the input-output data cannot be precollected and an assumed effective controller is available. In the practical applications, the mathematical model of controller may be hard to be obtained. In this case, an online tuning algorithm, FCRSM-FREE, is designed such that the parameters of a T-S fuzzy controller and the T-S fuzzy state model of an unknown system can be online tuned simultaneously. Four numerical simulations are given to demonstrate the effectiveness of the proposed approach.

Over the past two decades, there has been a rapidly growing interest in approximating a nonlinear system by a Takagi-Sugeno (T-S) fuzzy model (Takagi & Sugeno, 1985). In general, this model is represented by using a set of fuzzy rules to describe a global nonlinear system in terms of a set of local linear models which are smoothly connected by fuzzy membership functions. Based on the T-S fuzzy model, recently, various fuzzy controllers have been developed under the so-called parallel-distributed compensation (PDC) scheme (in which each control rule is distributively designed for the corresponding rule of a T-S fuzzy model) and have been widely and successfully applied in fields ranging from aerospace to process control. The reason is because the fuzzy model-based control method provides a natural, simple and effective design approach to complement other nonlinear control techniques that require special and rather involved knowledge. Below are listed the main features of T-S model-based fuzzy control method: 1. It does not require severe structural assumptions on the plant model. 2. It preserves well-understood linear intuition. 3. It is naturally compatible with decompositions of the overall control problem. The decompositions are typically not hierarchical, and the interactions of sub-problems are captured by physical variables that are typically state variables in a more complete model of the overall system. 4. It enables control systems to respond rapidly to changing operating conditions. For this reason, it is important that the selected physical variables reflect changes in plant dynamics as operating conditions change. In fact, the T-S model-based fuzzy control method (of divide and conquer type) constructs a nonlinear controller, with certain required dynamic properties, by combining, in some sense, the members of appropriate family of linear time-invariant controllers. Here, nonlinear control design task is broken into a number of linear sub-problems, which enable linear design methods to be applied to nonlinear problems. Within the general framework of the T-S fuzzy model-based control method, a flurry of research activities have quickly yielded many important results on the design of fuzzy control systems by means of the following Lyapunov function approaches: 1. Common quadratic Lyapunov function approach (Tanaka & Sugeno, 1992; Tanaka et al, 1996; Wang et al, 1996; Cao & Frank, 2000; Assawinchaichote, 2004).

This paper considers the finite-time stabilization problem for a class of nonlinear systems that can be described by Takagi–Sugeno (T–S) fuzzy models. We propose a novel finite-time switching fuzzy control scheme for T–S fuzzy models, and the scheme is based on the Lyapunov stability theory and the control Lyapunov function technique. It is shown that the finite-time fuzzy controller and the quadratic control Lyapunov function can be obtained at the same time by solving a set of linear matrix inequalities, which can be easily facilitated by available software packages. It is also shown that the potential control law singularity can be avoided with the proposed control scheme. Unlike many existing approaches to finite-time stabilization of general nonlinear systems, the proposed approach does not require the restrictive assumption on the existence of a control Lyapunov function before the corresponding control law is constructed. Furthermore, a finite upper bound on the settling time is estimated, which indicates that within the settling time, the system trajectory would arrive and stay at the origin thereafter. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed approach.