Reliable Mixed H∞ and Passivity-Based Control for Fuzzy Markovian Switching Systems With Probabilistic Time Delays and Actuator Failures

Design of robust tracking and disturbance attenuation control for stochastic control systems

The focus of current research is to address the problem of robust output tracking, input delay compensation and disturbance attenuation performance for a family of stochastic systems by implementing the improved-equivalent-input-disturbance (IEID) estimator and the extended Smith predictor (ESP) technique. By integrating the observer and IEID-estimator together with ESP, a new closed-loop configuration is presented. Then, Lyapunov based mean-square asymptotic stability criterion is obtained. According to attained stability criterion, an IEID and ESP based-controller is designed, which ultimately guarantees the exact output tracking. Simulation studies of numerical examples are offered to expose the authenticity of IEID and ESP-based controller. Further, the proposed outcomes in comparison with existing results are presented to demonstrate the efficaciousness of the established control procedure.

Fuzzy SMC for Quantized Nonlinear Stochastic Switching Systems With Semi-Markovian Process and Application

This article is concerned with the issue of quantized sliding-mode control (SMC) design methodology for nonlinear stochastic switching systems subject to semi-Markovian switching parameters, T-S fuzzy strategy, uncertainty, signal quantization, and nonlinearity. Compared with the previous literature, the quantized control input is first considered in studying T-S fuzzy stochastic switching systems with a semi-Markovian process. A mode-independent sliding surface is adopted to avoid the potential repetitive jumping effects. Then, by means of the Lyapunov function, stochastic stability criteria are proposed to be dependent of sojourn time for the corresponding sliding-mode dynamics. Furthermore, the fuzzy-model-based SMC law is proposed to ensure the finite-time reachability of the sliding-mode dynamics. Finally, an application example of a modified series dc motor model is provided to demonstrate the effectiveness of the theoretical findings.

Nonsynchronized State Estimation for Fuzzy Markov Jump Affine Systems With Switching Region Partitions

This article investigates the state estimation issue of discrete-time Takagi-Sugeno fuzzy Markov jump affine systems that cover both traditional fuzzy Markov jump systems and fuzzy affine systems as two special cases. The original system is transformed into a Markov jump piecewise-affine system that varies with different operating regions. The fuzzy rules are dependent on the system mode, and accordingly, the partition of the state space is mode dependent. To analyze the stochastic stability of the estimation error system, a novel mode-dependent piecewise Lyapunov function is constructed, in which the region indices of both the plant state and the estimator state are mode dependent. Then, the existence for a simultaneously mode-dependent and region-dependent fuzzy affine estimator is investigated by virtue of the S -procedure and ellipsoidal outer approximation such that the estimation error system is stochastically stable with a prescribed H_∞ performance. In the end, an illustrative example of a tunnel diode circuit is adopted to showcase the effectiveness and practicability of the developed state estimation strategy.

Further Study on Stabilization for Continuous-Time Takagi-Sugeno Fuzzy Systems With Time Delay

In the recently published paper, a switching method has been proposed to deal with the time derivative of the membership functions and less conservative results can be obtained due to this method; however, this method is based on the assumption that the switching times are finite. In this article, this method is further studied and the average dwell-time (ADT) switching technique is applied to ensure the stability if there is no such assumption. In addition, an algorithm is proposed to find the switching controller gains. The final simulation demonstrates the effectiveness of the developed new results.

H∞ and Passive Fuzzy Control for Non-Linear Descriptor Systems with Time-Varying Delay and Sensor Faults

In this paper, the problem of reliable control design with mixed H∞ /passive performance is discussed for a class of Takagi–Sugeno TS fuzzy descriptor systems with time-varying delay, sensor failure, and randomly occurred non-linearity. Based on the Lyapunov theory, firstly, a less conservative admissible criterion is established by combining the delay decomposition and reciprocally convex approaches. Then, the attention is focused on the design of a reliable static output feedback (SOF) controller with mixed H∞ /passive performance requirements. The key merit of the paper is to propose a simple method to design such a controller since the system output is subject to probabilistic missing data and noise. Using the output vector as a state component, an augmented model is introduced, and sufficient conditions are derived to achieve the desired performance of the closed-loop system. In addition, the cone complementarity linearization (CCL) algorithm is provided to calculate the controller gains. At last, three numerical examples, including computer-simulated truck-trailer and ball and beam systems are given to show the efficacy of our proposed approach, compared with existing ones in the literature.

Adaptive Event-Triggered Synchronization of Reaction-Diffusion Neural Networks

This article focuses on the design of an adaptive event-triggered sampled-data control (ETSDC) mechanism for synchronization of reaction-diffusion neural networks (RDNNs) with random time-varying delays. Different from the existing ETSDC schemes with predetermined constant thresholds, an adaptive ETSDC mechanism is proposed for RDNNs. The adaptive ETSDC mechanism can be promptly adaptively adjusted since the threshold function is based on the current sampled and latest transmitted signals. Thus, the adaptive ETSDC mechanism can effectively save communication resources for RDNNs. By taking the influence of uncertain factors, the random time-varying delays are considered, which belongs to two intervals in a probabilistic way. Then, by constructing an appropriate Lyapunov-Krasovskii functional (LKF), new synchronization criteria are derived for RDNNs. By solving a set of linear matrix inequalities (LMIs), the desired adaptive ETSDC gain is obtained. Finally, the merits of the adaptive ETSDC mechanism and the effectiveness of the proposed results are verified by one numerical example.

HMM-Based Asynchronous H∞ Filtering for Fuzzy Singular Markovian Switching Systems With Retarded Time-Varying Delays

This article reports our study on asynchronous H_∞ filtering for fuzzy singular Markovian switching systems with retarded time-varying delays via the Takagi-Sugeno fuzzy control technique. The devised parallel distributed compensation fuzzy filter modes are described by a hidden Markovian model, which runs asynchronously with that of the original fuzzy singular Markovian switching delayed system. The fuzzy asynchronous filtering dealt with in this article contains synchronous and mode-independent filtering as special cases. Novel admissibility and filtering conditions are derived in terms of linear matrix inequalities so as to ensure the stochastic admissibility and the H_∞ performance level. Simulation examples including a single-link robot arm are employed to demonstrate the correctness and effectiveness of the proposed fuzzy asynchronous filtering technique.

Synchronization of Coupled Time-Delay Neural Networks With Mode-Dependent Average Dwell Time Switching

In the literature, the effects of switching with average dwell time (ADT), Markovian switching, and intermittent coupling on stability and synchronization of dynamic systems have been extensively investigated. However, all of them are considered separately because it seems that the three kinds of switching are different from each other. This article proposes a new concept to unify these switchings and considers global exponential synchronization almost surely (GES a.s.) in an array of neural networks (NNs) with mixed delays (including time-varying delay and unbounded distributed delay), switching topology, and stochastic perturbations. A general switching mechanism with transition probability (TP) and mode-dependent ADT (MDADT) (i.e., TP-based MDADT switching in this article) is introduced. By designing a multiple Lyapunov-Krasovskii functional and developing a set of new analytical techniques, sufficient conditions are obtained to ensure that the coupled NNs with the general switching topology achieve GES a.s., even in the case that there are both synchronizing and nonsynchronizing modes. Our results have removed the restrictive condition that the increment coefficients of the multiple Lyapunov-Krasovskii functional at switching instants are larger than one. As applications, the coupled NNs with Markovian switching topology and intermittent coupling are employed. Numerical examples are provided to demonstrate the effectiveness and the merits of the theoretical analysis.

Disturbance rejection in fuzzy systems based on two dimensional modified repetitive-control

This paper concerns with the issues of designing an improved-equivalent-input-disturbance (IEID) based robust two dimensional modified repetitive control (2D MRC) for a class of fuzzy systems in the presence of aperiodic disturbances. Specifically, IEID-estimator is implemented to the 2D MRC systems that estimates all types of disturbances and compensates them for assuring robust stability. In particular, the proposed 2D MRC system has two different type of behaviours such as continuous control and discrete learning independently. To obtain gains of the observer and the controller, an adequate set of robust stability conditions is derived in the form of a linear-matrix-inequalities. Finally, simulation results for three numerical examples are provided to depict the efficacy of the proposed control technique.

Forward and backward motions path following controls of a truck-trailer with references on the head-truck and on the trailer

This paper presents new control designs and implementations of truck-trailer path following in forward and backward motions. The path following controls are designed in two modes, which are the controls with reference on the head-truck (RH-control) and with reference on the trailer (RT-control). Both modes aim to converge the distance and orientation errors of the head-truck as well as the trailer with respect to the desired path to zero. Using the designed controls, the asymptotic stabilities of the equilibrium points (i.e., error points equal to zeros) are analyzed using the Lyapunov method. The performances of RH-and RT-controls in controlling the truck-trailer are compared for forward and backward motions. The simulation results show that the RT-controls perform better than the RH-controls and the RT-controls can be applied for a curve-path following in both forward and backward directions. The experimental results of a prototype truck-trailer show the effectiveness of the proposed controls.

Adaptive Control of Nonlinear Semi-Markovian Jump T-S Fuzzy Systems With Immeasurable Premise Variables via Sliding Mode Observer

The issue of observer-based adaptive sliding mode control of nonlinear Takagi-Sugeno fuzzy systems with semi-Markov switching and immeasurable premise variables is investigated. More general nonlinear systems are described in the model since the selections of premise variables are the states of the system. First, a novel integral sliding surface function is proposed on the observer space, then the sliding mode dynamics and error dynamics are obtained in accordance with estimated premise variables. Second, sufficient conditions for stochastic stability with an H_∞ performance disturbance attenuation level γ of the sliding mode dynamics with different input matrices are obtained based on generally uncertain transition rates. Third, an observer-based adaptive controller is synthesized to ensure the finite time reachability of a predefined sliding surface. Finally, the single-link robot arm model is provided to verify the control scheme numerically.

Robust H∞ Adaptive Fuzzy Tracking Control for MIMO Nonlinear Stochastic Poisson Jump Diffusion Systems

Recently, stochastic Poisson jump diffusion system has attracted much attention in stochastic control. Poisson jump process has been used to model the random discontinuous jump behavior of the intrinsic discontinuous perturbation in stochastic system. Wiener process also called diffusion process represents the continuous random fluctuation to the system. In this paper, a robust adaptive control is introduced for multi-input multi-output (MIMO) nonlinear stochastic Poisson jump diffusion system with continuous and discontinuous random fluctuations to achieve the H_∞ tracking performance with a prescribed disturbance attenuation level. The system structure is of a strict-feedback form. Based on the backstepping design technique and H_∞ control theory, a robust adaptive control law is constructed for MIMO nonlinear stochastic Poisson jump diffusion system to achieve the H_∞ tracking performance with a prescribed attenuation level of external disturbance, despite of fuzzy approximation error and the effect of continuous and discontinuous random fluctuations. The proposed H_∞ adaptive control law combines both merits of H_∞ tracking control and adaptive control scheme to sufficiently solve the robust H_∞ adaptive tracking control problem for MIMO stochastic nonlinear systems with continuous and discontinuous random fluctuations. In addition, the uniformly positive definite assumption of control coefficient matrix is relaxed for the proposed MIMO adaptive control as well. A stochastic quadrotor trajectory tracking control simulation is provided to show the effectiveness of the proposed H_∞ robust adaptive control law.

New Stability Criterion for Continuous-Time Takagi-Sugeno Fuzzy Systems With Time-Varying Delay

In this technical paper, a new Lyapunov-Krasovskii functional (LKF) is designed to study the stability of continuous-time Takagi-Sugeno fuzzy systems with time-varying delay. The integrand of the LKF depends on integral variable and time t which can help to reduce the number of linear matrix inequalities (LMIs). Then, a new stability criterion is derived by analyzing the sign of the time derivatives of membership functions. Compared with the existing results, larger delay bounds can be obtained by applying the new criterion. In the end, two examples show the effectiveness of the conclusions.

Networked Estimation of a Class of Fuzzy Stochastic Hybrid Systems With Variable Rates of Packet Losses

This paper focuses on the state estimator design problem for a class of Takagi-Sugeno fuzzy stochastic hybrid systems with intermittent measurements in discrete-time domain. The hybrid systems are characterized with the stochastic switching among a set of subsystems, and the switching is supposed to be governed by a semi-Markov process with finite sojourn time. The random packet dropouts are modeled by a Bernoulli distributed sequence, and the packet dropout rate, which is considered to be variable, is described by the semi-Markov stochastic process that governs the switching dynamics of the fuzzy stochastic hybrid system. A more general class of Lyapunov functions that not only depends on the system modes, but also on the time that the current mode has been in since the last mode switching, is employed to analyze the stability and H_∞ performance of the estimation error system. Then, numerically testable conditions on the existence of a desired fuzzy mode-dependent state estimator are presented such that the estimation error system approaches to be mean square stable to an adjustable level and achieves a prescribed H_∞ disturbance attenuation index. Finally, an illustrative example of a single-link robotic arm system is provided to demonstrate the effectiveness and the superiority of the design method of state estimator.

Dissipativity-based non-fragile sampled-data control design of interval type-2 fuzzy systems subject to random delays

This paper investigates the β-dissipativity-based reliable non-fragile sampled-data control problem for a class of interval type-2 (IT2) fuzzy systems. In particular, it is allowed to have randomly occurring time-varying delays in the controller design, which are modeled by Bernoulli distributed white noise sequences. Precisely, the IT2 fuzzy model and the non-fragile sampled-data controller are formulated by considering the mismatched membership functions. By constructing an appropriate Lyapunov-Krasovskii functional, a set of delay-dependent conditions is derived to guarantee that the closed-loop IT2 fuzzy system is strictly <Q,S,R>-β-dissipative. Moreover, the gain matrices of feedback reliable non-fragile sampled-data controller are derived in terms of linear matrix inequalities (LMIs), which can be solved by using existing LMI solvers. Two numerical examples are eventually given to illustrate the applicability and effectiveness of the proposed controller design technique.

A Piecewise-Markovian Lyapunov Approach to Reliable Output Feedback Control for Fuzzy-Affine Systems With Time-Delays and Actuator Faults

This paper addresses the problem of delay-dependent robust and reliable $\mathscr {H}_{\infty }$ static output feedback (SOF) control for a class of uncertain discrete-time Takagi-Sugeno fuzzy-affine (FA) systems with time-varying delay and actuator faults in a singular system framework. The Markov chain is employed to describe the actuator faults behaviors. In particular, by utilizing a system augmentation approach, the conventional closed-loop system is converted into a singular FA system. By constructing a piecewise-Markovian Lyapunov-Krasovskii functional, a new $\mathscr {H}_{\infty }$ performance analysis criterion is then presented, where a novel summation inequality and S-procedure are succeedingly employed. Subsequently, thanks to the special structure of the singular system formulation, the piecewise-affine SOF controller design is proposed via a convex program. Lastly, illustrative examples are given to show the efficacy and less conservatism of the presented approach.

Adaptive Backstepping-Based Neural Tracking Control for MIMO Nonlinear Switched Systems Subject to Input Delays

This brief proposes a new neural-network (NN)-based adaptive output tracking control scheme for a class of disturbed multiple-input multiple-output uncertain nonlinear switched systems with input delays. By combining the universal approximation ability of radial basis function NNs and adaptive backstepping recursive design with an improved multiple Lyapunov function (MLF) scheme, a novel adaptive neural output tracking controller design method is presented for the switched system. The feature of the developed design is that different coordinate transformations are adopted to overcome the conservativeness caused by adopting a common coordinate transformation for all subsystems. It is shown that all the variables of the resulting closed-loop system are semiglobally uniformly ultimately bounded under a class of switching signals in the presence of MLF and that the system output can follow the desired reference signal. To demonstrate the practicability of the obtained result, an adaptive neural output tracking controller is designed for a mass-spring-damper system.

Fault Detection for Nonlinear Process With Deterministic Disturbances: A Just-In-Time Learning Based Data Driven Method

Data-driven fault detection plays an important role in industrial systems due to its applicability in case of unknown physical models. In fault detection, disturbances must be taken into account as an inherent characteristic of processes. Nevertheless, fault detection for nonlinear processes with deterministic disturbances still receive little attention, especially in data-driven field. To solve this problem, a just-in-time learning-based data-driven (JITL-DD) fault detection method for nonlinear processes with deterministic disturbances is proposed in this paper. JITL-DD employs JITL scheme for process description with local model structures to cope with processes dynamics and nonlinearity. The proposed method provides a data-driven fault detection solution for nonlinear processes with deterministic disturbances, and owns inherent online adaptation and high accuracy of fault detection. Two nonlinear systems, i.e., a numerical example and a sewage treatment process benchmark, are employed to show the effectiveness of the proposed method.

Reachable Set Estimation for Markovian Jump Neural Networks With Time-Varying Delays

In this paper, the reachable set estimation problem is investigated for Markovian jump neural networks (NNs) with time-varying delays and bounded peak disturbances. Our goal is to find a set as small as possible which bounds all the state trajectories of the NNs under zero initial conditions. In the framework of Lyapunov-Krasovskii theorem, a newly-found summation inequality combined with the reciprocally convex approach is used to bound the difference of the proposed Lyapunov functional. A new less conservative condition dependent on the upper bound, the lower bound and the delay range of the time delay is established to guarantee that the state trajectories are bounded within an ellipsoid-like set. Then the result is extended to the case with incomplete transition probabilities and a more general condition is derived. Finally, examples including a genetic regulatory network are given to demonstrate the usefulness and the effectiveness of the results obtained in this paper.

Unknown Input Observer Design for Interval Type-2 T-S Fuzzy Systems With Immeasurable Premise Variables

This paper deals with the problem of robust unknown input fault detection observers (UIFDOs) design for interval type-2 Takagi-Sugeno (T-S) fuzzy systems with immeasurable premise variables. It has been shown that choosing the system states, which may be immeasurable, as premise variables, will able us to model a larger class of nonlinear systems. Accordingly, the premise variables of underlying system are considered to be immeasurable. However, the design procedure of a stable observer for such systems are more challenging. Furthermore, the system is supposed be affected by time-varying delays and unknown inputs. The UIFDO is exploited so as to generate a residual signal with the most possible sensitivity to fault and the least sensitivity to exogenous signals. In this paper, this issue is investigated thoroughly, in this respect the design procedure consists of two sections: 1) measurable and 2) immeasurable premise variables. Sufficient design conditions are provided in terms of linear matrix inequalities for both cases. The effectiveness of the proposed UIFDO in detection of two different kinds of faults is illustrated during the simulation of a numerical example. Moreover, a fair comparison has been drawn between the proposed UIFDO and an existent reference to indicate that interval type-2 T-S fuzzy model is more superior than type-1. Finally, the faulty behavior of a one-link manipulator is investigated to express the applicability of the proposed method.

An Adaptive NN-Based Approach for Fault-Tolerant Control of Nonlinear Time-Varying Delay Systems With Unmodeled Dynamics

This paper presents an adaptive neural network (NN)-based fault-tolerant control approach for the compensation of actuator failures in nonlinear systems with time-varying delay. The novelty of this paper lies in the fact that both the lock in place and loss of effectiveness faults, unmodeled dynamics, and dynamic disturbances are catered for simultaneously. Furthermore, this is achieved by the adaptation of only one parameter, which simplifies the computation of the control effort, and therefore extends its applicability. In the approach, the Razumikhin lemma and a dynamic signal are employed. It is shown that the output of the system converges to a neighborhood of the reference signal and the semiglobal boundedness of all signals is guaranteed. A simulation example is used to illustrate the validity and efficacy of the approach.

Incremental Passivity and Incremental Passivity-Based Output Regulation for Switched Discrete-Time Systems

This paper investigates incremental passivity and output regulation for switched discrete-time systems. We develop the results in two parts. First of all, a concept of incremental passivity is proposed to describe the overall incremental passivity property of a switched discrete-time system in the absence of the classic incremental passivity property of the subsystems. A condition for incremental passivity is given. A certain negative output feedback is designed to produce asymptotic stability. Incremental passivity is shown to be preserved under feedback interconnection. The second part of this paper is concerned with an application of the incremental passivity theory to the output regulation problem for switched discrete-time systems. The key idea is to construct a switched internal model with incremental passivity, which closely links the solvability of the output regulation problem. A characteristic of the switched internal model is that it does not necessarily switch synchronously with the controlled plant, which greatly increases the freedom of design. Once such a switched internal model is established, the output regulation problem is then solved by construction of the feedback interconnection between the controlled plant and the switched internal model. The main usefulness of the strategy is to get rid of the solvability of the output regulation problem for the subsystems.

A Decentralized Event-Triggered Dissipative Control Scheme for Systems With Multiple Sensors to Sample the System Outputs

This paper is concerned with decentralized event-triggered dissipative control for systems with the entries of the system outputs having different physical properties. Depending on these different physical properties, the entries of the system outputs are grouped into multiple nodes. A number of sensors are used to sample the signals from different nodes. A decentralized event-triggering scheme is introduced to select those necessary sampled-data packets to be transmitted so that communication resources can be saved significantly while preserving the prescribed closed-loop performance. First, in order to organize the decentralized data packets transmitted from the sensor nodes, a data packet processor (DPP) is used to generate a new signal to be held by the zero-order-hold once the signal stored by the DPP is updated at some time instant. Second, under the mechanism of the DPP, the resulting closed-loop system is modeled as a linear system with an interval time-varying delay. A sufficient condition is derived such that the closed-loop system is asymptotically stable and strictly (Q₀,S₀,R₀) -dissipative, where Q₀,S₀ , and R₀ are real matrices of appropriate dimensions with Q₀ and R₀ symmetric. Third, suitable output-based controllers can be designed based on solutions to a set of a linear matrix inequality. Finally, two examples are given to demonstrate the effectiveness of the proposed method.