Variable structure adaptive fuzzy control for a class of nonlinear time-delay systems

The problem of variable structure adaptive fuzzy control for a class of nonlinear time delay systems is investigated. Sliding surface dependent of the time delay is constructed based on the Lyapunov-Krasovskii method. Two adaptive fuzzy logic systems are proposed to approximate two unknown continuous nonlinear functions containing the current state and the delayed state respectively. The corresponding reaching law is designed, which can drive the state trajectory of the closed-system onto the sliding surface within limited time.

An observer-based adaptive neural-network robust control for a class of nonlinear time-delay systems with unmodeled dynamics. It is presented for a class of nonaffine nonlinear time-delay systems with external disturbance and unavailable states. By the implicit function theorem, Taylor’s formula and mean theorem, the form of the non-affine nonlinear systems is transformed into the form of affine nonlinear systems. The controller designed to attenuate the effect of external disturbance and approximation errors of the neural networks on tracking. The unknown time-delay is compensated by using appropriate Young inequality, the weight update laws based on Lyapunov stability theory can guarantee the system stability and asymptotic convergence of the tracking error to zero. Theoretical analysis and simulation results demonstrate the effectiveness of the approach.

The accessibility of the class of driftless single-input nonlinear time-delay systems is fully characterized for the first time. This result is obtained through the introduction of new tools within a geometric approach recently introduced in the literature. Moreover, all those possible autonomous elements, which can depend on the variables with time-delay, are also characterized when the system is not accessible and in consequence, a canonical form of those systems is deduced.

In this paper, we determine the delay-dependent conditions of global asymptotic stability for a class of multi-dimensional nonlinear time-delay systems with application to computer communication networks. A nonlinear delayed model is considered for a rate-based congestion control system of a heterogeneous network with arbitrary topology and time-varying delays. We propose a Lyapunov-based method to obtain a sufficient condition under which global asymptotic stability of the equilibrium is guaranteed. The main contribution of the paper lies in considering time variations of delays in a heterogeneous network which may be applicable in actual networks. Moreover, we obtain conditions for Internet-style networks with multi-source multi-link topology. We first prove the stability for a class of nonlinear time-delay systems. Then, we apply the results to a Kelly’s rate-based approximation of the congestion control system.

This paper is devoted to design of observer for a class of Lipschitz nonlinear state delay systems with, or without parameter uncertainty. The nonlinearities are assumed to appear in both state and measured output equations. For both the cases with and without norm-bounded time-varying parameter uncertainties, a design method is proposed, in which linear matrix inequalities (LMIs) are solved. When certain LMIs are satisfied, the explicit expression of a desired nonlinear observer is presented. A numerical example and the simulating results are provided to demonstrate the applicability of the proposed approach.

This paper presents a Variable Structure Adaptive Backstepping Controller (VS-ABC) for linear plants with arbitrary relative degree, using only input/output measurements. In order to improve the transient response, switching laws are proposed in the adaptive backstepping approach via modular design, instead of the integral adaptive laws. Furthermore, simplified algorithms are presented for the VS-ABC, motivating applications on industrial environments. Simulation results for an unstable system with relative degree three are shown.

This paper investigates the fusion of unknown dead-zone nonlinearity with adaptive fuzzy control techniques in face of nonlinear time-delayed systems. Control design achieved by using the backstepping recursive method and Fuzzy logic systems in Mamdani type is used to approximate the unknown nonlinear functions, and Lyapunov-Krasovskii functionals are used to compensate the effect of delay term. Based on Lyapunov stability theory and Theorem 1, the proposed adaptive fuzzy controller guarantees that all the closed-loop signals are semi-globally uniformly ultimately bounded. Finally, a simulation example is provided to illustrate the Validity of the theoretical results.

Motivated by the recent advance in adaptive output feedback control of affine nonlinear systems [8-10], an adaptive variable structure controller is proposed in this paper for solving the model reference adaptive control of nonlinear time-varying systems. Asymptotic output tracking performance can be achieved for relative degree one case. When the relative degree of the nonlinear system is greater than one, a systematic design procedure is given under a modified sector-type condition so that the closed-loop stability and the tracking performance are achieved similar to that in relative degree one case.

This article aims at proposing an adaptive neural control strategy for a class of nonlinear time-delay systems with input delays and unknown control directions. Different from previous researches that investigated delays and constraints separately, the novelty of this article lies in that it simultaneously considers delays (state and input delays) and input constraints (magnitude and rate constraints) for a class of uncertain nonlinear systems. In this article, the uncertain states and input delays are handled by integrating a constructed auxiliary system that functions as an observer with neural networks (NNs), with which the adverse effects caused by the uncertain states and input delays can be approximated and compensated. By involving smooth hyperbolic tangent functions in the designed auxiliary system, the problem of magnitude and rate constraints of the control input is fully addressed. Then, the backstepping technique runs through the entire control designing process, which allows the designed adaptive neural control strategy to handle the input constraints and delays at the same time. Furthermore, Nussbaum functions are employed to resolve the problem of unknown control directions. Due to the introduction of an input-driven filter, only the output of the system is required to be measured as the control feedback, which promotes the applicability of the designed controller. Under the proposed control scheme, semiglobal, uniform, and ultimate boundedness of all signals of the closed-loop system is realized with uncertain control directions, input and state delays, and guaranteed magnitude and rate constraints of control inputs. Finally, simulation results are illustrated to verify the effectiveness of the presented control method.

Adaptive iterative learning control of a class of nonlinear time-delay systems with unknown backlash-like hysteresis input and control direction

In this article, the output-feedback control problem for a class of nonlinear time-delay systems has been considered. Unmeasured system states and the time-varying delays which appear in all state variables bring great challenges to the controller design. Novel Lyapunov–Krasovkii functionals with control gains are proposed for a delay-independent controller. The system is proved to be asymptotically stable driven by the controller with suitable design parameters. Finally, we apply the new control scheme to a two-stage chemical reactor system and the time-delay tension leg platform system, the effectiveness of the control scheme is illustrated in the simulation results.

This paper investigates adaptive fuzzy output feedback fault-tolerant optimal control problem for a class of single-input and single-output nonlinear systems in strict feedback form. The considered nonlinear systems contain unknown nonaffine nonlinear faults and unmeasured states. Fuzzy logic systems are used to approximate cost function and unknown nonlinear functions, respectively. It is assumed that the states of the systems to be controlled are unmeasurable, thus an adaptive state observer is developed. To solve the nonaffine nonlinear fault control design problem, filtered signals are introduced into the adaptive backstepping control design procedures, and in the framework of adaptive critic technique and fault-tolerant control technique, a novel adaptive fuzzy fault-tolerant optimal control scheme is developed. The stability of the closed-loop system is proved by using Lyapunov stability theory. The simulation results verify the effectiveness of the proposed control strategy.

Adaptive control for uncertain nonlinear systems with state-function constraints and input delay

Stability of time-delay systems with impulsive control involving stabilizing delays

Robust fault detection for a class of nonlinear time-delay systems