Discrete-time Fuzzy Systems Research Articles

Observer-based preview control for T-S fuzzy systems

PurposeConsidering the unmeasurable states of the systems and the previewed reference signal, a novel fuzzy observer-based preview controller, which is a mixed controller of the fuzzy observer-based controller, fuzzy integrator and preview controller, is considered to address the tracking control problem.Design/methodology/approachThe authors employ an augmentation technique to construct an augmented error system for uncertain T-S fuzzy discrete-time systems with time-varying uncertainties. Additionally, the authors obtain the corresponding linear matrix inequality (LMI) conditions for designing the preview controller.FindingsThis paper discusses the preview tracking problem for nonlinear systems. First, considering the unmeasurable states of the systems and the previewed reference signal, a novel fuzzy observer-based preview controller, which is a mixed controller of the fuzzy observer-based controller, fuzzy integrator, and preview controller, is considered to address the tracking control problem. Then, using the fuzzy Lyapunov functional with the linear matrix inequality (LMI) technique, new sufficient conditions for the asymptotic stability of the augmented system are derived by applying the LMI technique. The preview controller and fuzzy observer can be designed in one step. Finally, a numerical example is used to illustrate the effectiveness of the results.Originality/valueAn augmented error system is successfully constructed by the state augmentation approach. A novel preview controller is designed to address the tracking control problem. The preview controller and fuzzy observer can be designed in one step.

Convex Stability Analysis of Mamdani-Like Fuzzy Systems With Singleton Consequents

We study the stability of a class of discrete-time fuzzy systems with singleton consequents, called Mamdani-like fuzzy systems. The parametric expressions, specific to this class of fuzzy systems, are leveraged to derive stability analysis conditions via Finsler's lemma and Lyapunov stability tools. This allows avoiding the major challenge in dealing with high-dimensional cases, encountered in the related literature when using the classical state-space representation. Moreover, the information of the piecewise region partition can be fully taken into account in the stability analysis with the well-known <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$S-$</tex-math></inline-formula> procedure to further reduce the stability conservatism. The stability of Mamdani-like fuzzy systems can be checked by solving a set of linear matrix inequalities (LMIs), that is numerically tractable with a suitable semidefinite programming software. Several numerical and physically motivated examples are provided to illustrate the effectiveness of the proposed stability analysis results.

Fuzzy optimal tracking control for nonlinear underactuated unmanned surface vehicles

In this paper, a reinforcement Q-learning fuzzy optimal tracking control method is investigated for nonlinear underactuated unmanned surface vehicles (USVs) with external disturbances. Firstly, the motion dynamics of USVs are described by the Takagi–Sugeno (T–S) fuzzy discrete-time systems. Secondly, by applying parallel distributed compensation (PDC) method and constructing cost function, the existence condition of optimal solutions is derived and reduced to the algebraic Riccati equations (AREs). To solve the solutions of the GAREs, a Q-learning value iteration (VI) algorithm is further developed, which can be implemented by eliminating the demand of initial allowable control policy and system information. The developed strategy has the advantage that the optimal control policy can ensure the USV to be stable and the desired reference signal can also be well tracked by the USV output. Finally, the proposed fuzzy optimal control algorithm is applied to control the USV, the simulation results verify the feasibility of the proposed optimal control algorithm.

Multi-Instant Observer Design of Discrete-Time Fuzzy Systems via An Enhanced Gain-Scheduling Mechanism.

This article is concerned with developing a featured multi-instant Luenberger-like observer of discrete-time Takagi-Sugeno fuzzy systems with unmeasurable state variables, that is, not only to reduce the conservatism but also (at the same time) to alleviate the computational complexity over the recent approach reported in the literature. Contrary to previous approaches, an enhanced gain-scheduling mechanism is proposed for constructing much abundant working modes by online evaluating the updated variation information of normalized fuzzy weighting functions across two adjacent sampling instants and, thus, a different group of observer gain matrices with less conservatism is designed in order to employ the exclusive features for each working mode. Moreover, all the redundant terms containing both surplus and unknown system information are discriminated and removed in this study and, thus, the required computational complexity is reduced to a certain extent than the counterpart one. Finally, numerical examples are provided to illustrate the superiority of the developed approach.

Fault detection for discrete-time fuzzy systems with measurement errors using interval observers

This paper presents an interval observer-based fault detection (FD) strategy for discrete-time T–S fuzzy systems with measurement errors. The system and measurement outputs are selected as the premise variables of plant and observer respectively. The bounds of mismatch items caused by the measurement errors are established by covering matched region, mismatched left adjacent region and right adjacent region. Piecewise Lyapunov function, taking full account of possible transitions, is employed to drive observer design condition. FD is turned into optimization problem with disturbance attenuation, fault sensitivity and nonnegativity constraints. The decision is implemented by judging whether zero is excluded from the residual interval. Finally, simulation is explored to verify the scheme.

An outlier‐resistant approach to observer‐based security control for interval type‐2 T‐S fuzzy systems subject to deception attacks

This article focuses on the outlier-resistant observer-based controller for the interval type-2 T-S fuzzy discrete-time systems with distributed delays under deception attacks. The deception attack takes place between sensor channel and observer channel. A neoteric guidance for safety performance is constructed to explain the randomly happening spoofing offensive on the control structure. The random events of parameter uncertainty and spoofing offensives are controlled via two sets of Bernoulli stochastic variables with foregone probability distributions. One outlier-resistant observer-based security control is constructed to induce an innovation saturation structure in order to alleviate the passive influence on the spoofing offensives about the estimation aspect. The goal of the solution is to design an outlier-resistant observer-based security control that can insure boundedness in estimation error while achieving the ideal level of safety. Ultimately, a quantitative value simulation sample is put forward to justify the practicality and validity of the above-mentioned control project.

LMI-Based Robust Fuzzy Model Predictive Control of Discrete-Time Fuzzy Takagi-Sugeno Large-Scale Systems Based on Hierarchical Optimization and H∞ Performance

This paper studies robust fuzzy model predictive control of discrete-time fuzzy Takagi-Sugeno large-scale systems based on hierarchical optimization and H_[Formula: see text] Performance. The considered system in this paper is a large-scale system. So, the Takagi-Sugeno (T-S) fuzzy approach which uses nonlinear local models is applied to estimate the nonlinear system to reduce the burden of modeling. The model predictive control (MPC) is a practical application that is useful for all systems but the problem is the online computational cost. For large-scale systems, this problem is the online computational burden. Besides, it leads to conservative or even no solution. By the proposed method, more relaxed solutions are achieved. First, the T-S system with nonlinear local models is adopted. Second, the hierarchical optimization scheme is considered for the optimization part of the MPC. Third, by inspiring the [Formula: see text] performance, uncertainties and disturbances that are appeared are reduced. Moreover, the linear matrix inequalities (LMIs) are used to solve the proposed method that the computational burden significantly is reduced at the same time. Simulation results are finally presented to show the effectiveness of the proposed controller.

Design of an Unmatching Observer-Based Controller for Discrete-Time Fuzzy Systems with Time Delay

The problem of an unmatching observer-based controller design for discrete-time fuzzy systems with time delay is investigated, in which the fuzzy controller shares different membership functions from the fuzzy model. The objective is to design a state observer and unmatching fuzzy controller such that the discrete closed-loop system with time delay is asymptotically stable. A sufficient condition that contains the information of the membership functions of fuzzy model and fuzzy controller for the stabilization via an unmatching observer-based output feedback is presented. The proposed control scheme is well capable of enhancing the design flexibility, and the stability condition is less conservative. Three numerical examples are given to illustrate the effectiveness and advantages of the proposed method.

Constrained Output-Feedback Control for Discrete-Time Fuzzy Systems With Local Nonlinear Models Subject to State and Input Constraints.

This article presents a new approach to design static output-feedback (SOF) controllers for constrained Takagi-Sugeno fuzzy systems with nonlinear consequents. The proposed SOF fuzzy control framework is established via the absolute stability theory with appropriate sector-bounded properties of the local state and input nonlinearities. Moreover, both state and input constraints are explicitly taken into account in the control design using set-invariance arguments. Especially, we include the local sector-bounded nonlinearities of the fuzzy systems in the construction of both the nonlinear controller and the nonquadratic Lyapunov function. Within the considered local control context, the new class of nonquadratic Lyapunov functions provides an effective solution to estimate the closed-loop domain of attraction, which can be nonconvex and even disconnected. The convexification procedure is performed using specific congruence transformations in accordance with the special structures of the proposed SOF controllers and nonquadratic Lyapunov functions. Consequently, the fuzzy SOF control design can be reformulated as an optimization problem under strict linear matrix inequality constraints with a linear search parameter. Compared to existing fuzzy SOF control schemes, the new structures of the control law and the Lyapunov function are more general and offer additional degrees of freedom for the control design. Both theoretical arguments and numerical illustrations are provided to demonstrate the effectiveness of the proposed approach in reducing the design conservatism.

Perfect tracking control of discrete-time quadratic TS fuzzy systems via feedback linearisation

ABSTRACTPerfect tracking control is an important and frequently encountered requirement in various industries (e.g. robotic control). We developed a novel systematic framework for designing a fuzzy controller via feedback linearisation to control a class of discrete-time Takagi–Sugeno (TS) fuzzy systems with quadratic rule consequents to achieve such tracking. We established a necessary condition for its local stability and a necessary and sufficient condition for the boundedness of the controller. The feedback linearisation is known to fail to work in certain systems due to the unboundedness of the tracking controller output. To address this issue, we developed a method to check whether any given quadratic TS fuzzy system will cause such a failure. We developed a scheme to ensure that the output of the controller designed for any failure-causing system will be bounded and the resulting controller will attain nearly perfect tracking performance. Applying feedback linearisation to the quadratic fuzzy systems is innovative relative to the literature exclusively dealing with the TS fuzzy systems with linear rule consequents (including our previous results), which are now generalised by the new findings. Two numerical examples are provided to illustrate the effectiveness and utility of our new theoretical results.

Control Synthesis of Hidden Semi-Markov Uncertain Fuzzy Systems via Observations of Hidden Modes.

This paper investigates the stability analysis and fuzzy control problems for a class of discrete-time fuzzy systems with hidden semi-Markov stochastic uncertainties. The nonlinear plant is described via the Takagi-Sugeno (T-S) fuzzy model, and the parameter uncertainties are represented by a hidden semi-Markov chain. Owing to the semi-Markov kernel (SMK), the probability density functions (PDFs) of sojourn time for different modes in describing the stochastic uncertainties can address different types of distributions according to different target modes. A novel Lyapunov function that depends on the hidden mode and the observed mode with the elapsed time is proposed to analyze the stability and the H∞ performance of the fuzzy system. Then, the sufficient criteria for the elapsed-time-dependent and observed-mode-dependent fuzzy controller are achieved by exploiting the observations of hidden modes, ensuring that the closed-loop system is σ -error mean square stable with guaranteed H∞ performance. A cart-pendulum system is used to demonstrate the effectiveness and applicability of the proposed theoretical results.

Integrated event-triggered fault estimation and fault-tolerant control for discrete-time fuzzy systems with input quantization and incomplete measurements

This paper addresses the problem of robust integrated fault estimation (FE) and fault-tolerant control (FTC) for a class of discrete-time networked Takagi–Sugeno (T–S) fuzzy systems with two-channel event-triggered schemes, input quantization and incomplete measurements. The incomplete information under consideration includes randomly occurring sensor saturation and randomly occurring quantization. In order to save the limited networked resources, this paper firstly proposed a novel dynamic event-triggered scheme on the sensor side and a static one on the controller side. Secondly, an event-triggered FE observer for the T–S fuzzy model is designed to estimate actuator faults and system states, simultaneously. Then, a specified discrete sliding surface in the state-estimation space is constructed. By using time-delay analysis technique and considering the effects of event-triggered scheme, quantization, networked conditions, actuator fault and external disturbance, the sliding mode dynamics and error dynamics are unified into a new networked time-delay model. Based on this model, sufficient conditions are established such that the resulting augmented fuzzy system is stochastically stable with a prescribed H∞ performance level with a single-step linear matrix inequality (LMI) formulation. Furthermore, an observer-based sliding mode controller for reaching motion is synthesized to guarantee the reachability of the sliding surface. Finally, a single-link flexible manipulator example is present to illustrate the effectiveness of the proposed method.

Fuzzy Output Tracking Control and Filtering for Nonlinear Discrete-Time Descriptor Systems Under Unreliable Communication Links.

In this paper, the problems of output tracking control and filtering are investigated for Takagi-Sugeno fuzzy-approximation-based nonlinear descriptor systems in the discrete-time domain. Especially, the unreliability of the communication links between the sensor and actuator/filter is taken into account, and the phenomenon of packet dropouts is characterized by a binary Markov chain with uncertain transition probabilities, which may reflect the reality more accurately than the existing description processes. A novel bounded real lemma (BRL), which ensures the stochastic admissibility with H∞ performance for fuzzy discrete-time descriptor systems despite the uncertain Markov packet dropouts, is presented based on a fuzzy basis-dependent Lyapunov function. By resorting to the dual conditions of the obtained BRL, a solution for the designed fuzzy output tracking controller is given. A design method for the full-order fuzzy filter is also provided. Finally, two examples are finally adopted to show the applicability of the achieved design strategies.

Observer-Based State Estimation of Discrete-Time Fuzzy Systems Based on a Joint Switching Mechanism for Adjacent Instants.

The problem of observer-based state estimation of discrete-time fuzzy systems is investigated by constructing a joint switching mechanism for adjacent instants. Thanks to the usage of both the proposed spatial partitioning method and a set of new free matrix-valued variables, abundant information about size differences of all the normalized fuzzy weighting functions for adjacent instants can be interactively integrated into the fuzzy observer design for the first time. Compared with the recent result from three important aspects (conservatism level, online computational burden, and offline computational burden), three positive results can be obtained: 1) it provides a chance for reducing the conservatism by a large margin; 2) the required online computational burden remains unchanged as referred ones; and 3) as a tradeoff, the required offline computational burden increases to some extent but is still affordable from the view of complexity analysis. Finally, two numerical simulations have been given to validate the effectiveness of our developed theoretical results.

Regularization and Stabilization for Rectangular T–S Fuzzy Discrete-Time Systems With Time Delay

This paper is concerned with the regularization and stabilization problems for rectangular discrete-time fuzzy systems with time delay. A dynamic compensation is designed to ensure that the close-loop system is square, and a necessary and sufficient condition is proposed to guarantee the existence of a dynamic compensation with which the close-loop system is regular and causal. Moreover, sufficient conditions are derived in terms of bilinear matrix inequalities to guarantee the admissibility of the closed-loop system. We present an efficient algorithm which is proved to be convergent to solve the conditions. Two examples are given to show the effectiveness and efficiency of the proposed method.

Feedback-linearization-based control of discrete-time quadratic TS fuzzy systems with disturbances

Feedback-linearization-based control of discrete-time quadratic TS fuzzy systems with disturbances

Unknown Input Observer Design for Takagi-Sugeno Systems with Fuzzy Output Equation

This paper studies unknown input observer design for discrete-time Takagi-Sugeno fuzzy systems. The proposed unknown input observer has a new structure that can be applied to Takagi-Sugeno fuzzy systems with nonlinear output equation. We derive the design conditions of the proposed unknown input observer based on Lyapunov function and convert them into a set of linear matrix inequalities. Numerical simulations of a vehicle lateral dynamics are given to illustrate the effectiveness of the proposed method.

Dynamic output feedback [formula omitted] control for 2D fuzzy systems

In this paper, the dynamic output feedback H∞ control problem is considered for two-dimensional discrete fuzzy systems described by the second Fornasini–Marchesini state-space model. By introducing novel slacked matrices, sufficient criteria are established to guarantee an H∞ noise attenuation of the resulting closed-loop system. Then the proposed output feedback H∞ controller design method is applied to one-dimensional discrete-time fuzzy systems. It is worth mentioning that there is no rank constraints to system matrices. Moreover, the sufficient criteria are expressed as strict linear matrix inequalities, which can be effectively solved via MATLAB LMI toolbox. Finally, the effectiveness and advantage of the proposed approach are shown through two simulation examples.

Observer Design of Discrete-Time Fuzzy Systems Based on an Alterable Weights Method

This paper proposes an improvement on observer design of discrete-time fuzzy systems based on an alterable weights method. Different from the recent result, a more effective ranking-based switching mechanism is developed by introducing a bank of alterable weights for the sake of making use of the size difference information of the normalized fuzzy weighting functions more freely than before. Therefore, a positive result can be provided in this paper, that is, less conservative conditions of designing feasible fuzzy observers can be obtained than those existing results, while the computational cost of designing feasible fuzzy observers is even less than the up-to-date one. Finally, two numerical examples are given to show the progressiveness of the proposed method.

Disturbance-observer-based sliding mode control for T–S fuzzy discrete-time systems with application to circuit system

In this paper, the problem of disturbance-observer-based sliding mode control (SMC) is studied for a class of Takagi–Sugeno (T–S) fuzzy discrete-time systems subject to dead-zone input and external disturbance. The disturbance is monitored by a disturbance observer (DO). Then, a DO-based sliding mode controller is derived. By selecting the suitable gain matrices, the DO can approximate the external disturbance effectively, and the stability of the system can be guaranteed. Finally, the validity of the proposed SMC scheme is verified with the simulation results of the tunnel diode circuit system.