Observer-based adaptive fuzzy-neural control for a class of uncertain nonlinear systems with unknown dead-zone input

Prescribed Performance Bipartite Consensus Control for Stochastic Nonlinear Multiagent Systems Under Event-Triggered Strategy

In this article, the event-triggered bipartite consensus problem for stochastic nonlinear multiagent systems (MASs) with unknown dead-zone input under the prescribed performance is studied. To surmount the influence of the dead-zone input, the dead-zone model is transformed into a linear term and a disturbance term. Meanwhile, the prescribed tracking performance is realized by developing a speed function, which means that all tracking errors of MASs can converge to a predefined set in a given finite time. Moreover, the unknown nonlinear dynamics are approximated by fuzzy-logic systems. By combining the dynamic surface approach and the Lyapunov stability theory, we design an adaptive event-triggered control algorithm, such that the bipartite consensus problem of stochastic nonlinear MASs can be achieved, and all signals are semiglobally uniformly ultimately bounded in probability of the closed-loop systems. Finally, simulation examples are proposed to verify the feasibility of the algorithm.

Command Filter-Based Adaptive Neural Control Design for Nonstrict-Feedback Nonlinear Systems With Multiple Actuator Constraints

This article proposes an adaptive neural-network command-filtered tracking control scheme of nonlinear systems with multiple actuator constraints. An equivalent transformation method is introduced to address the impediment from actuator nonlinearity. By utilizing the command filter method, the explosion of complexity problem is addressed. With the help of neural-network approximation, an adaptive neural-network tracking backstepping control strategy via the command filter technique and the backstepping design algorithm is proposed. Based on this scheme, the boundedness of all variables is guaranteed and the output tracking error fluctuates near the origin within a small bounded area. Simulations testify the availability of the designed control strategy.

Event-based adaptive fuzzy control design for nonstrict-feedback nonlinear time-delay systems with state constraints

This article considers the issue of event-triggered adaptive fuzzy control for state-constrained nonstrict-feedback nonlinear time-delay systems. The adverse effect of time-delay is effectively overcome by choosing the approximate Lyapunov-Krasovskii functional. The fuzzy logic systems are utilized to address unknown dynamics. The computation complexity is reduced by taking the norm of fuzzy weight vector as estimation. The barrier Lyapunov function is employed to ensure the prescribed constraints. To decrease the update frequency of control signal, event-triggered mechanism is fused into backstepping design process. The semi-globally uniformly ultimately bounded (SGUUB) of the closed-loop system is proved by virtue of Lyapunov stability analysis. Two simulation examples are given to account for the usefulness of the developed method.

Cooperative Adaptive Dynamic Surface Control for a Class of High-Order Stochastic Nonlinear Multiagent Systems

This article investigates the consensus tracking problem for high-order stochastic pure-feedback nonlinear multiagent systems (MASs) with dead zones. It should be pointed out that each follower's virtual and actual control items are the power-exponential functions with positive odd numbers instead of linear items. Because of the structural characteristics of the followers' dynamics, a technique called adding a power integrator is used, which effectively overcomes the difficulties of states and dead zone with power-exponential functions. Furthermore, radial basis function neural networks are employed to estimate unknown nonlinear functions and solve the problem of algebraic loop caused by the pure-feedback structure of MASs. Meanwhile, the problems of "explosion of complexity" caused by repeated differentiations of the virtual controller are solved by using the tracking differentiators. Based on the Lyapunov stability theorem, it is proved that all signals of the closed-loop systems are semiglobally uniformly ultimately bounded in probability, and the tracking errors can converge to a small neighborhood of the origin. Finally, simulation results are presented to verify the effectiveness of the proposed approach.

Adaptive Fuzzy Control of Stochastic Nonlinear Systems With Fuzzy Dead Zones and Unmodeled Dynamics

This paper focuses on an input-to-state practical stability problem for a class of stochastic nonlinear systems with unmodeled dynamics and fuzzy dead zones. A feasible adaptive fuzzy control method is proposed for the developed stochastic system with the slope of dead zone being certain or fuzzy. Based on stochastic small-gain theorem and backstepping technique, the closed-loop system is guaranteed to be input-state-practically stable in probability. The main contributions of this paper lie in that the considered system is more general, and the modified Lemma 2 makes the presentation of the formulas in lemma consistent with their application forms. Finally, two simulation examples are provided to demonstrate the effectiveness of the proposed approach.

Adaptive output feedback tracking of nonlinear systems with uncertain nonsymmetric dead-zone input

In this paper, the problem of adaptive practical tracking is investigated by output feedback for a class of uncertain nonlinear systems subject to nonsymmetric dead-zone input nonlinearity with parameters of dead-zone being unknown. Instead of constructing the inverse of dead-zone nonlinearity, an adaptive robust control scheme is developed by designing an output compensator including two dynamic gains based respectively on identification and non-identification mechanism. With the aid of dynamic high-gain scaling approach and Backstepping method, stability analysis of the closed-loop system is proceeded using non-separation principle, which shows that the proposed controller guarantees that all closed-loop signal is bounded while the output of system tracks a broad class of bounded reference trajectories by arbitrarily small error prescribed previously. Finally, two examples are given to illustrate our controller effective.

Anti-disturbance dynamic surface control scheme for a class of uncertain nonlinear systems with asymmetric dead-zone nonlinearity

This study proposes anti-disturbance dynamic surface control scheme for nonlinear strict-feedback systems subjected simultaneously to unknown asymmetric dead-zone nonlinearity, unmatched external disturbance and uncertain nonlinear dynamics. Radial basis function-neural network (RBF-NN) is invoked to approximate the uncertain dynamics of the system, and the dead-zone nonlinearity is represented as a time-varying system with a bounded disturbance. The nonlinear disturbance observer (NDO) is proposed to estimate the unmatched external disturbance which further will be used to compensate the effect of the disturbance. Then, by integrating RBF-NN, NDO and dynamic surface control (DSC) approaches, the proposed anti-disturbance control scheme is designed. Stability analysis of the closed-loop system shows that all signals of the closed-loop system are semi-globally uniformly ultimately bounded and the tracking error can be made arbitrarily small by proper selection of the design parameters. In comparison with the existing methods, the proposed scheme deals with the unmatched external disturbance, uncertain dynamics and unknown asymmetric dead-zone nonlinearity, simultaneously; it avoids the "explosion of complexity" problem and develops the simple control law without singularity concern. Furthermore, some imposed assumptions to the dead-zone input and disturbances are relaxed. Simulation and comparison results verify the effectiveness of the proposed approach.

Adaptive variable structure hierarchical fuzzy control for a class of high-order nonlinear dynamic systems

In this paper, a novel adaptive hierarchical fuzzy control system based on the variable structure control is developed for a class of SISO canonical nonlinear systems in the presence of bounded disturbances. It is assumed that nonlinear functions of the systems be completely unknown. Switching surfaces are incorporated into the hierarchical fuzzy control scheme to ensure the system stability. A fuzzy soft switching system decides the operation area of the hierarchical fuzzy control and variable structure control systems. All the nonlinearly appeared parameters of conclusion parts of fuzzy blocks located in different layers of the hierarchical fuzzy control system are adjusted through adaptation laws deduced from the defined Lyapunov function. The proposed hierarchical fuzzy control system reduces the number of rules and consequently the number of tunable parameters with respect to the ordinary fuzzy control system. Global boundedness of the overall adaptive system and the desired precision are achieved using the proposed adaptive control system. In this study, an adaptive hierarchical fuzzy system is used for two objectives; it can be as a function approximator or a control system based on an intelligent-classic approach. Three theorems are proven to investigate the stability of the nonlinear dynamic systems. The important point about the proposed theorems is that they can be applied not only to hierarchical fuzzy controllers with different structures of hierarchical fuzzy controller, but also to ordinary fuzzy controllers. Therefore, the proposed algorithm is more general. To show the effectiveness of the proposed method four systems (two mechanical, one mathematical and one chaotic) are considered in simulations. Simulation results demonstrate the validity, efficiency and feasibility of the proposed approach to control of nonlinear dynamic systems.

Output feedback adaptive fuzzy control of uncertain MIMO nonlinear systems with unknown input nonlinearities

An adaptive fuzzy output feedback controller is proposed for a class of uncertain MIMO nonlinear systems with unknown input nonlinearities. The input nonlinearities can be backlash-like hysteresis or dead-zone. Besides, the gains of unknown input nonlinearities are unknown nonlinear functions. Based on universal approximation theorem, the unknown nonlinear functions are approximated by fuzzy systems. The proposed method does not need the availability of the states and an observer based on strictly positive real (SPR) theory is designed to estimate the states. An adaptive robust structure is used to cope with fuzzy approximation error and external disturbances. The semi-global asymptotic stability of the closed-loop system is guaranteed via Lyapunov approach. The applicability of the proposed method is also shown via simulations.

Singularity-free neural control for the exponential trajectory tracking in multiple-input uncertain systems with unknown deadzone nonlinearities

The trajectory tracking for a class of uncertain nonlinear systems in which the number of possible states is equal to the number of inputs and each input is preceded by an unknown symmetric deadzone is considered. The unknown dynamics is identified by means of a continuous time recurrent neural network in which the control singularity is conveniently avoided by guaranteeing the invertibility of the coupling matrix. Given this neural network-based mathematical model of the uncertain system, a singularity-free feedback linearization control law is developed in order to compel the system state to follow a reference trajectory. By means of Lyapunov-like analysis, the exponential convergence of the tracking error to a bounded zone can be proven. Likewise, the boundedness of all closed-loop signals can be guaranteed.

On observer-based controller design for Sugeno systems with unmeasurable premise variables

This paper considers the design of observer-based controller for a class of continuous-time nonlinear systems presented by Takagi-Sugeno (T-S) model with unmeasurable premise variables. This T-S structure can represent a larger class of nonlinear systems as compared to the measurable premise variable case but its analysis is more complicated. To reduce the design complexity, a common output model for subsystems is employed by the use of local nonlinear rules. As a result, the proposed T-S structure reduces the number of rules in the Sugeno model as well as the analysis complexity. The proposed controller guarantees exponential convergence of states based on the fuzzy Lyapunov function analysis and Linear Matrix Inequality (LMI) formulation. Simulation results illustrate effectiveness of the proposed method.

Design of adaptive fuzzy wavelet neural sliding mode controller for uncertain nonlinear systems

This paper proposes novel adaptive fuzzy wavelet neural sliding mode controller (AFWN-SMC) for a class of uncertain nonlinear systems. The main contribution of this paper is to design smooth sliding mode control (SMC) for a class of high-order nonlinear systems while the structure of the system is unknown and no prior knowledge about uncertainty is available. The proposed scheme composed of an Adaptive Fuzzy Wavelet Neural Controller (AFWNC) to construct equivalent control term and an Adaptive Proportional-Integral (A-PI) controller for implementing switching term to provide smooth control input. Asymptotical stability of the closed loop system is guaranteed, using the Lyapunov direct method. To show the efficiency of the proposed scheme, some numerical examples are provided. To validate the results obtained by proposed approach, some other methods are adopted from the literature and applied for comparison. Simulation results show superiority and capability of the proposed controller to improve the steady state performance and transient response specifications by using less numbers of fuzzy rules and on-line adaptive parameters in comparison to other methods. Furthermore, control effort has considerably decreased and chattering phenomenon has been completely removed.