Uncertain Nonlinear Time-delay Systems Research Articles

A new fuzzy sliding mode controller design for delta operator time-delay nonlinear systems

ABSTRACTThis paper investigates the sliding mode control (SMC) problem for a class of delta operator uncertain time-delay nonlinear systems through Takagi–Sugeno fuzzy models. Some new sufficient conditions for asymptotic stability analysis of the sliding motion are obtained in terms of linear matrix inequalities with some convexification techniques. Then two new dynamic SMC design methods are synthesised to force the resulting closed-loop system states onto the sliding surface in finite time. Two simulation examples are finally given to illustrate the effectiveness of the proposed approaches.

Further Results on Output Tracking for a Class of Uncertain High-Order Nonlinear Time-Delay Systems

Further Results on Output Tracking for a Class of Uncertain High-Order Nonlinear Time-Delay Systems

Event-triggered output-feedback tracking of a class of nonlinear systems with unknown time delays

A single function approximation (SFA) approach for event-triggered output-feedback tracker design is presented for uncertain nonlinear time-delay systems in lower-triangular form. Contrary to the existing event-triggered output-feedback control methods dependent on multiple function approximators in the presence of lower-triangular nonlinearities, the proposed SFA approach provides the following advantages: (i) the simple observer structure independent of function approximators; (ii) one event-triggering condition based on only a tracking error; and (iii) the simple control scheme using one function approximator. Thus, the structural simplicity is allowed for implementing the observer and the event-triggering law in the sensor part and the adaptive tracker in the control part. Under the proposed SFA-based event-triggered control scheme, it is shown that the boundedness of closed-loop signals and the existence of a minimum inter-event time are guaranteed regardless of unknown time-delay nonlinearities and unmeasurable state variables.

Finite-time adaptive neural control for uncertain nonlinear time-delay systems with actuator delay and full-state constraints

ABSTRACTThis paper investigates finite-time adaptive neural tracking control for a class of nonlinear time-delay systems subject to the actuator delay and full-state constraints. The difficulty is to consider full-state time delays and full-state constraints in finite-time control design. First, finite-time control method is used to achieve fast transient performances, and new Lyapunov–Krasovskii functionals are appropriately constructed to compensate time delays, in which a predictor-like term is utilized to transform input delayed systems into delay-free systems. Second, neural networks are utilized to deal with the unknown functions, the Gaussian error function is used to express the continuously differentiable asymmetric saturation nonlinearity, and barrier Lyapunov functions are employed to guarantee that full-state signals are restricted within certain fixed bounds. At last, based on finite-time stability theory and Lyapunov stability theory, the finite-time tracking control question involved in full-state constraints is solved, and the designed control scheme reduces learning parameters. It is shown that the presented neural controller ensures that all closed-loop signals are bounded and the tracking error converges to a small neighbourhood of the origin in a finite time. The simulation studies are provided to further illustrate the effectiveness of the proposed approach.

Neural Networks-Based Adaptive Tracking Control for a Class of High-Order Stochastic Nonlinear Time-Delay Systems

In this paper, neural networks (NNs)-based adaptive backstepping control problem is investigated for uncertain high-order stochastic nonlinear time-delay systems in nonstrict-feedback form. The control design problems appeared in our considered system are (1) high-order nonstrict-feedback structure; (2) completely unknown nonlinear functions; (3) full-state time delays; and (4) stochastic disturbances. The NNs are directly utilized to cope with the completely unknown nonlinear functions and stochastic disturbances existing in systems. The problem raised by full-state time delays is addressed by combining the appropriate Lyapunov-Krasovskii functional with hyperbolic tangent functions. In addition, the variable separation technique is employed to handle the nonstrict-feedback structure of the system. At last, on the basis of stochastic Lyapunov function method, an adaptive neural controller is developed for the considered system. It is shown that the designed adaptive controller can guarantee that all the signals remain semi-globally uniformly ultimately bounded (SGUUB) and the desired signal can be tracked with a small domain of the origin. The simulation results are offered to illustrate the feasibility of the newly designed control scheme.

Adaptive fuzzy reliable tracking control for a class of uncertain nonlinear time-delay systems with abrupt non-affine faults

This paper investigates the problem of approximation-based adaptive reliable tracking control for a class of uncertain nonlinear strict-feedback systems. The considered system is with unknown time delays and abrupt non-affine nonlinear faults. To eliminate the effect of unknown time delays, the finite covering lemma and fuzzy logic systems are utilized, and the traditional Lyapunov–Krasovskii function is abandoned. With the help of mean-value theorem, the non-affine nonlinear faults are decoupled for the strictness of system. Based on the property of Nussbaum function, the problem of unknown control directions and control gains is solved. Finally, a novel adaptive fault-tolerant control scheme with the feedback information of not only the current states but also the past states is designed. It is guaranteed that all the signals in the closed-loop system are semi-global uniformly bounded and the tracking error converges to a small neighborhood of the origin. Simulation results from a practical example of isothermal continuous stirred tanks reactors are given to demonstrate the effectiveness of the proposed control scheme.

On Reduced-Order Linear Functional Interval Observers for Nonlinear Uncertain Time-Delay Systems with External Unknown Disturbances

In this paper, we consider the problem of designing reduced-order linear functional interval observers for nonlinear uncertain time-delay systems with external unknown disturbances. Given bounds on the uncertainties, we design two reduced-order linear functional state observers in order to compute two estimates, an upper one and a lower one, which bound the unmeasured linear functions of state variables. Conditions for the existence of a pair of reduced-order linear functional observers are presented, and they are translated into a linear programming problem in which the observers’ matrices can be effectively computed. Finally, the effectiveness of the proposed design method is supported by four examples and simulation results.

Approximation-based decentralized output-feedback control for uncertain stochastic interconnected nonlinear time-delay systems with input delay and asymmetric input saturation

This paper proposes an adaptive observer-based neural controller for a class of uncertain large-scale stochastic nonlinear systems with actuator delay and time-delay nonlinear interactions, where drift and diffusion terms contain all state variables of their own subsystem. First, a state observer is established for estimating the unmeasured states, and a predictor-like term is utilized to transform the input delayed system into the delay-free system. Second, novel appropriate Lyapunov–Krasovskii functionals are used to compensate the time-delay terms, and neural networks are employed to approximate unknown nonlinear functions. At last, an output-feedback adaptive neural control scheme is constructed by using Lyapunov stability theory and backstepping technique. It is shown that the designed neural controller can ensure that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded (SGUUB) and the tracking error is driven to a small neighborhood of the origin. The simulation results are presented to further show the effectiveness of the proposed approach.

Adaptive control for uncertain nonlinear time-delay systems in a lower-triangular form

In the presence of uncertain time-varying control coefficients, structuring parameter uncertainty and unknown state time delay, this paper proposes a continuous feedback control scheme for highly nonlinear systems without extra nonlinear growth restriction. An expansion of the backstepping method is presented based on dynamic gains and tuning functions. By Lyapunov–Krasovskii functionals, a delay-free controller is designed to regulate the original system states to zero with the other states being globally bounded.

Decentralized adaptive neural control for high-order interconnected stochastic nonlinear time-delay systems with unknown system dynamics

This paper is concerned with the problem of decentralized adaptive backstepping state-feedback control for uncertain high-order large-scale stochastic nonlinear time-delay systems. For the control design of high-order large-scale nonlinear systems, only one adaptive parameter is constructed to overcome the over-parameterization, and neural networks are employed to cope with the difficulties raised by completely unknown system dynamics and stochastic disturbances. And then, the appropriate Lyapunov–Krasovskii functional and the property of hyperbolic tangent functions are used to deal with the unknown unmatched time-delay interactions of high-order large-scale systems for the first time. At last, on the basis of Lyapunov stability theory, the decentralized adaptive neural controller was developed, and it decreases the number of learning parameters. The actual controller can be designed so as to ensure that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded (SGUUB) and the tracking error converges in the small neighborhood of zero. The simulation example is used to further show the validity of the design method.

Practical output tracking for a class of uncertain nonlinear time-delay systems via state feedback

In this paper, the problem of global practical output tracking is investigated by state feedback for a class of uncertain nonlinear time-delay systems. Under mild conditions on the system nonlinearities involving time delay, we construct a homogeneous state feedback controller with an adjustable scaling gain. By a homogeneous Lyapunov-Krasovskii functional, the scaling gain is adjusted to dominate the time-delay nonlinearities bounded by homogeneous growth conditions and render the tracking error can be made arbitrarily small while all the states of the closed-loop system remain to be bounded.

Asymptotic stabilization of a class of uncertain nonlinear time-delay fractional-order systems via a robust delay-independent controller

This paper studies the robust stabilization for a class of nonlinear time-delay fractional order (FO) systems in the presence of some practical aspects. The considered aspects in the FO system include: nonlinear Lipschitz functions; time-varying norm-bounded uncertain terms; and time-delays in the state variables. A major challenge in the control of time-delay systems is that the value of delay is usually not perfectly known or it may be even time-varying. In this paper, a novel asymptotic stabilizing control law is proposed which is delay independent and also has a robust manner in the presence of uncertain terms in the model which may be due to model uncertainties (parameter uncertainties or model simplification) and/or external disturbances. The proposed controller is a FO sliding mode controller that is designed such that the closed-loop system is asymptotically delay-independent stable. For this purpose, a FO sliding manifold is introduced and the occurrence of the reaching phase in a finite time is proved. Finally, in order to validate the theoretical results, an example is given and simulation results confirm the appropriate performance of the proposed controller.

Simple adaptive robust control schemes of uncertain strict‐feedback non‐linear time‐delay systems

The main purpose of this study is to present a simple design method to synthesise the adaptive robust controllers for a class of uncertain strict-feedback non-linear systems with delayed state perturbations and external disturbances. In this study, such a simple design method is presented so that (i) the presented design method is easy to understand for the system designers; (ii) it is not necessary to know any information on the upper bound functions of non-linear delayed state perturbations and the non-linear functions due to the derivatives of the fictitious control functions to construct some state feedback control schemes; and (iii) the resulting adaptive robust control schemes are simple and easy to implement in practical engineering control problems. The adaptive robust controllers synthesised by the presented design method have a rather simple structure, and can guarantee the uniform exponential boundedness of the considered uncertain strict-feedback non-linear time-delay systems. A numerical example is provided to illustrate the authors' simple design procedure and the corresponding simulations are made to demonstrate the validity of the theoretical results.

Memoryless disturbance-observer-based adaptive tracking of uncertain pure-feedback nonlinear time-delay systems with unmatched disturbances

This paper presents a delay-independent nonlinear disturbance observer (NDO) design methodology for adaptive tracking of uncertain pure-feedback nonlinear systems in the presence of unknown time delays and unmatched external disturbances. Compared with all existing NDO-based control results for uncertain lower-triangular nonlinear systems where unknown time delays have been not considered, the main contribution of this paper is to develop a delay-independent design strategy to construct an NDO-based adaptive tracking scheme in the presence of unknown time-delayed nonlinearities and non-affine nonlinearities unmatched in the control input. The proposed delay-independent scheme is constructed by employing the appropriate Lyapunov-Krasovskii functionals and the same function approximators for the NDO and the controller. It is shown that all the signals of the closed-loop system are semi-globally uniformly ultimately bounded and the tracking error converges to an adjustable neighborhood of the origin.

Neural-network-based adaptive fault-tolerant tracking control of uncertain nonlinear time-delay systems under output constraints and infinite number of actuator faults

In this paper, the problem of NN-based adaptive fault-tolerant tracking control for a class of uncertain nonlinear time-varying delay systems under output constraints and infinite number of actuator faults is considered. By constructing Lyapunov–Krasovskii functions, introducing a bound estimation approach and using dynamic surface control technique, a novel adaptive fault-tolerant control scheme is designed to compensate actuator faults and unknown time-delay uncertain functions as well as the output constraint is not violated. Compared with the existing results, the proposed controller can be implemented easily. Furthermore, via Lyapunov theory, it is proven that all the signals of the closed-loop system are semi-globally uniformly ultimately bounded. Finally, two illustrative examples are used for verifying effectiveness of the proposed approach.

Adaptive robust output tracking of uncertain strict-feedback nonlinear time-delay systems via control schemes with simple structure

ABSTRACTThe output tracking control problem is considered for a class of uncertain strict-feedback nonlinear systems with time-varying delays. In the paper, the time-varying delays are assumed to be any non-negative continuous and bounded functions, and it is not necessary for their derivatives to be less than one. It is also assumed that the upper bounds of nonlinear delayed state perturbations and external disturbances are unknown. On the basis of backstepping algorithm, a novel design method is proposed by which some simple adaptive robust output tracking control schemes are synthesised. The proposed design method can avoid the repeated differentiation problem which appears in using the conventional backstepping algorithm, and need not know all the nonlinear upper bound functions of uncertainties, which are repeatedly employed at each step of the backstepping algorithm. In particular, it is not necessary to know any information on the time-varying delays to construct our simple output tracking control schemes. It is also shown that the tracking error can converge uniformly exponentially towards a neighbourhood of the origin. Finally, a numerical example and its simulations are provided to demonstrate the design procedure of the simple method proposed in the paper.

MLP-based adaptive neural control of nonlinear time-delay systems with the unknown hysteresis

ABSTRACTIn this note, the authors study the tracking problem for uncertain nonlinear time-delay systems with unknown non-smooth hysteresis described by the generalised Prandtl–Ishlinskii (P-I) model. A minimal learning parameters (MLP)-based adaptive neural algorithm is developed by fusion of the Lyapunov–Krasovskii functional, dynamic surface control technique and MLP approach without constructing a hysteresis inverse. Unlike the existing results, the main innovation can be summarised as that the proposed algorithm requires less knowledge of the plant and independent of the P-I hysteresis operator, i.e. the hysteresis effect is unknown for the control design. Thus, the outstanding advantage of the corresponding scheme is that the control law is with a concise form and easy to implement in practice due to less computational burden. The proposed controller guarantees that the tracking error converges to a small neighbourhood of zero and all states of the closed-loop system are stabilised. A simulation example demonstrates the effectiveness of the proposed scheme.

Approximation-based adaptive tracking of a class of uncertain nonlinear time-delay systems in nonstrict-feedback form

ABSTRACTThis paper investigates a predefined performance control problem for adaptive tracking of uncertain nonlinear time-delay systems in nonstrict-feedback form. Nonstrict-feedback nonlinearities, time-varying delays and external disturbances are assumed to be unknown. Based on the exponential decaying design functions denoting the preassigned bounds of transient and steady-state tracking errors, some variable separation lemmas are derived to design an approximation-based robust adaptive control scheme in the presence of nonstrict-feedback time-delayed nonlinearities. The proposed control system guarantees that a tracking error remains within a predesigned bound for all t ≥ 0 and converges to a preselected neighbourhood of the origin. Compared with the existing results in the literature, the main contribution of this paper is to provide a solution on the guaranteed performance control in the presence of unknown nonstrict-feedback nonlinearities related to all delayed state variables. Simulation results illustrate the effectiveness of the proposed methodology.

Delay-estimation-based adaptive fuzzy memory control for a class of uncertain nonlinear time-delay systems

This paper is concerned with the problem of adaptive fuzzy memory control for a class of uncertain nonlinear systems with unknown time delays. Compared with the existing results, the restrictions on the time-delayed functions are overcome, and the unknown delay parameters are estimated by establishing the piecewise adaptive laws. Based on the delay estimations and the backstepping technique, a novel adaptive fuzzy memory output feedback controller is designed. For the analysis of stability, the cubic Lyapunov functions with absolute value are constructed. It is proved that the proposed control scheme can guarantee that all the signals in the closed-loop system are bounded and the tracking error converges to a small neighborhood of the origin. Two practical simulation examples are given to demonstrate the effectiveness of the proposed control scheme.

Observer-based fault detection and accommodation for nonlinear time-delay systems with a prescribed performance mechanism

In this paper, delay-independent fault detection and accommodation (FDA) control is developed for a class of uncertain nonlinear time-delay systems with multiple time-delay faults and external disturbances. Compared with the existing results, the system states are unmeasurable and the bounds of model uncertainties and the disturbances only exist but are unknown. A novel parameter-varying observer is designed for fault detection and state estimation. The modified prescribed performance bound (PPB) is used as detection threshold. It is shown that the state estimate error is guaranteed within a PPB before the fault occurs. Then, a backstepping-based adaptive fuzzy fault accommodation controller is designed and activated after the detection, which compensates multiple time-delay faults and guarantees the state estimate error which has violated the performance constraint returns into a new PPB. The effectiveness of the proposed FDA method is illustrated through a simulation example on the robot manipulator system.