This paper presents an idea to simplify and relax the stability conditions of Takagi–Sugeno (T–S) fuzzy systems based on the membership function extrema1. By considering the distribution of ...membership functions in a unified membership space, a graphical approach is provided to analyze the conservativeness of membership-dependent stability conditions. Membership function extrema are used to construct a simple and tighter convex polyhedron that encloses the membership trajectory and produces less conservative linear matrix inequality (LMI) conditions. The cases of both type-1 and interval type-2 T–S fuzzy systems are considered, and comparison with existing methods is made in the proposed membership vector framework.
This paper investigates the problem of model reduction for interval type-2 (IT2) fuzzy systems subject to D stability constraints. The membership functions and the number of rules can be freely ...chosen and they are different between the original system and the reduced-order system. By introducing some slack matrices and utilizing Lyapunov stability theory, the existence condition of model reduction is obtained to guarantee that the reduced-order model can approximate the original system with an H∞ performance. The parameters of the reduced-order system in the condition can be obtained by standard software. Finally, some simulation results are provided to demonstrate the effectiveness of the proposed results.
This paper endeavors to investigate the output-feedback sliding mode control (SMC) issue of the networked singularly perturbed systems (SPSs) under fast sampling. In order to improve the reliability ...of network communication, a redundant channel transmission protocol is introduced in the SMC design. Based on the measurement outputs, a sliding function is constructed with the consideration of the transmission protocol. With the aid of some appropriate Lyapunov functions, the sufficient conditions are derived to ensure the mean-square exponentially ultimately boundedness of the sliding mode dynamics and the reachability of the specified sliding surface. Moreover, a convex optimization algorithm is formulated to solve the output-feedback SMC law by searching the available upper bound of the singularly perturbed parameter. Finally, an operational amplifier circuit is exploited to explore the influences from the redundant channel transmission protocol to the output-feedback SMC performance and the estimated ε-bound.
In this article, the stability analysis and control synthesis of interval type-2 (IT2) polynomial-fuzzy-model-based networked control systems are investigated under the event-triggered control ...framework. The nonlinear dynamics in the plant is efficiently represented by an IT2 polynomial fuzzy model that the IT2 membership functions are utilized to capture the uncertainties in the plant. An event-triggered IT2 polynomial fuzzy controller is then designed to stabilize the nonlinear model subject to uncertainties. The stability conditions of the closed-loop control system are summarized in the form of sum-of-squares. Under the imperfectly premise matching (IPM) concept, the membership-function-dependent (MFD) approach is applied to endow the polynomial fuzzy controllers with more flexibility in terms of number of rules and premise membership functions. In the MFD approach under the IPM concept, both the number of rules and the shape of membership functions in the fuzzy models and controllers can be different. Also, the information of IT2 membership functions of the polynomial fuzzy model and controller is considered and adopted to further relax the stability conditions. Furthermore, the intrinsic mismatched issue of the premise variables of the fuzzy model and controllers due to the event-triggering mechanism is handled by the MFD approach. A detailed simulation example is provided to verify the effectiveness of the proposed event-based control strategy.
This paper proposes a novel delay-dependent approach to the piecewise-affine H-infinity filter design for discrete-time state-delayed nonlinear systems. The nonlinear plant is expressed by a ...Takagi-Sugeno fuzzy-affine model and the state delay is considered to be time-varying with available lower and upper bounds. The purpose is to design an admissible filter that guarantees the asymptotic stability of the resulting filtering error system (FES) with a prescribed disturbance attenuation level in an H-infinity sense. By applying a new piecewise-fuzzy Lyapunov-Krasovskii functional, combined with a novel summation inequality, improved reciprocally convex inequality and S-procedure, the H-infinity performance analysis criterion is first developed for the FES. Furthermore, the filter synthesis is carried out by some elegant convexification techniques. Finally, simulation examples are employed to confirm the effectiveness and less conservatism of the proposed methods.
This article investigates the sliding-mode control issue for interval type-2 (IT2) T-S fuzzy systems under limited communication resources. An event-triggering weight try-once-discard (ET-WTOD) ...protocol is formulated via two thresholds to determine the transmission of the state signal. The proposed ET-WTOD protocol can dynamically adjust the transmitted nodes and permits only partial components with larger error to be sent at each triggering instant, which is just the key distinction from the existing protocols. Under the imperfect premise matching framework, the controller's membership functions are reconstructed via the received state and the known upper and lower bounds, and then, a new scheduling signal set is established to design the scheduling-signal-dependent fuzzy sliding-mode controller. With the aid of the membership-function-dependent approach, the mismatching premise variables of the fuzzy model and the controller are effectively handled by introducing some slack matrices, while the relaxed stability conditions are derived to ensure the stability of the closed-loop system and the reachability of the specified sliding surface. Moreover, an optimized sliding domain is further obtained via the genetic algorithm (GA). Finally, the proposed control strategy is verified via the mass-spring-damper system.
In this note, state-estimator-based adaptive control is under consideration for a sort of nonlinear stochastic switched systems by Takagi-Sugeno (T-S) fuzzy modeling and sliding mode technique. A new ...fuzzy sliding surface is established by a reformed state estimator, and a novel adaptive fuzzy reaching motion controller synthesis is carried out to force the state trajectories onto the designated sliding surface in limited moments. A new mean-square exponential stability of the resultant plant with passivity is ensured under the average dwell time method and stochastic stability theory. The key challenge overcome here is that one conditional assumption involved in the previous sliding mode control-based strategies for the considered systems is no longer required despite the unavailable states, unknown perturbations, and specified switching signal. At last, a practical data communication network model (DCNM) with simulation is offered to verify the feasibility of the theoretical result.
This paper focuses on the predefined-time adaptive neural tracking control problem for nonlinear multiagent systems (MASs). In contrast to the existing results of the predefined-time control methods, ...this paper introduces a lemma for achieving predefined-time stability within the framework of backstepping, and the primary distinguishing feature is the ability to predefine the convergence time according to user specifications and the controller design process being influenced by a singular parameter. Meanwhile, a numerical example is presented by using the proposed lemma such that the convergence performance can be ensured by the user practical specification. Moreover, by using the neural networks (NNs) and the finite time differentiators, an adaptive approach to predefined-time tracking control is presented for nonlinear MASs. This method ensures the predefined-time stability of all signals within the MASs, while also enabling the followers' outputs to accurately track the desired trajectory with the predefined time. The effectiveness and merits of the proposed scheme are substantiated through simulation results. Note to Practitioners - This paper aims to address the predefined-time control problem for MASs, which can be widely used in practice, such as vehicular platoon systems control, teleoperation systems control, etc. The existing predefined-time methods only guarantee system convergence within the predefined-time interval, and achieving predefined-time convergence with an exact convergence time <inline-formula> <tex-math notation="LaTeX">t</tex-math> </inline-formula> remains a challenge. Moreover, the existing predefined-time methods contain many control parameters, which complicates the process of the parameter tuning. To address the aforementioned challenges, a predefined-time adaptive neural control method for MASs is developed, which can guarantee that all signals within MASs are predefined-time stable while enabling the followers to accurately track the desired trajectory with predefined time. Moreover, only one parameter and a pair of the finite time differentiators designed constants are involved in the controller design process, which simplifies the process of the parameter tuning.
This paper investigates the problem of sampled-data H ∞ control of uncertain active suspension systems via fuzzy control approach. Our work focuses on designing state-feedback and output-feedback ...sampled-data controllers to guarantee the resulting closed-loop dynamical systems to be asymptotically stable and satisfy H ∞ disturbance attenuation level and suspension performance constraints. Using Takagi-Sugeno (T-S) fuzzy model control method, T-S fuzzy models are established for uncertain vehicle active suspension systems considering the desired suspension performances. Based on Lyapunov stability theory, the existence conditions of state-feedback and output-feedback sampled-data controllers are obtained by solving an optimization problem. Simulation results for active vehicle suspension systems with uncertainty are provided to demonstrate the effectiveness of the proposed method.
This article addresses the event-triggered asynchronous fault detection (FD) problem of fuzzy-model-based nonlinear Markov jump systems (MJSs) with partially unknown transition probabilities. For ...this objective, the nonlinear plant is modeled as an interval type-2 (IT2) fuzzy MJS with the aid of the IT2 fuzzy sets capturing the uncertainties of the membership functions. An adaptive event-triggered scheme is introduced to bring down the costs of the communication network from the system to the fuzzy fault detection filter (FDF), in which the triggering parameter can be adaptively tuned with the system dynamics. A hidden Markov model (HMM) is employed to characterize the asynchronous phenomenon between the system and the FDF. Unlike the existing results, the transition probabilities of the plant and the FDF are allowed to be partially known. By using the Lyapunov and the membership-function-dependent methods, the existence conditions of the FDF are derived. Finally, the proposed FD methods are verified by a numerical simulation.
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