Unknown Time-varying State Delays Research Articles

Adaptive delay dependent sliding mode fault-tolerant controller design for nonlinear systems with unknown time-varying input and state delays

This paper presents a novel adaptive delay-dependent fault-tolerant sliding mode control (SMC) strategy for the class of nonlinear Lipschitz systems with time-varying unknown delays in system states and inputs. A modified integral sliding surface (ISS) based on which the SMC approach is developed using a linear matrix inequality. Lyapunov-Krasovskii stability theory is employed to guarantee asymptotic stability of the closed-loop system such that system states starting from any arbitrary initial conditions with time-varying delays reach the predefined sliding surface in a finite time. It is also proved that states stay on the surface for all subsequent time, and the effects of the actuator’s faults are simultaneously attenuated. Adaptive tuning laws are used to adjust controller parameters and estimate actuators’ faults. The controllers’ structures are more straightforward than the most existing recent fault-tolerant control methods. Simulation results of practical nonlinear inverted pendulum system verified the outstanding merits and capabilities of the proposed scheme in the presence of actuators’ faults and multiple delays in the system states and inputs.

Fast fixed-time vertical plane motion control of autonomous underwater gliders in shallow water

In this paper, a fast fixed-time vertical plane motion controller is proposed for autonomous underwater gliders (AUGs) gliding in shallow water. The influence of speed-sensorless conditions, model uncertainties, unknown time-varying external disturbances, input saturations, and state delay are taken into account. To improve control performance, a fast fixed-time stable system is first presented. Based on the system, an adaptive extended state observer (ESO) is developed for estimating speed, model uncertainties, and external disturbances. A fast fixed-time controller is designed for improving the gliding efficiency and reducing the risk of hitting the ocean floor. Moreover, an input saturation auxiliary system and an advance compensation method are presented to cope with input saturations and state delay. According to Lyapunov theory, it is proved that the AUG states can converge into a small neighborhood within a fixed time. Finally, simulation results demonstrate the rapidity and effectiveness of the designed control method.

Observer-Based Control Design for Nonlinear Systems With Unknown Delays

In this brief, we study the problem of designing observer-based controller for nonlinear system subject to unknown time-varying state delay. The unknown delay is assumed to be upper bounded, but nevertheless the bound is not required to be known. In order to tackle this interesting problem, we utilize a Halanay-inequality-based criterion which can guarantee exponential stability of the closed-loop system as well as the estimation error system. This exponential stability criterion allows us to design observer-based controller for the nonlinear time-delay system without invoking differentiability assumption on the unknown delay. A robotic system is considered to illustrate the efficiency of the new results.

Mixed control of delayed Markov jump linear systems

This study investigates the state feedback control laws for Markov jump linear systems with state and mode-observation delays. An assumption in this study is that the delay of the mode observation obeys an exponential distribution. Also, the authors raise an unknown time-varying state delay applied in the composition of the state feedback controller. A method of remodelling the closed-loop system as a standard Markov jump linear system with state delay is shown. Furthermore, on the basis of this remodelling, several linear matrix inequalities for designing feedback gains for stabilisation and mixed control are proposed. Finally, the authors apply a numerical simulation for examining the effectiveness of the proposed mixed controller designing method.

Delay-Dependent Functional Observer Design for Linear Systems With Unknown Time-Varying State Delays.

Partial state estimation has numerous applications in practice. Nevertheless, designing delay-dependent functional observers (FOs) for systems with unknown time delays is rigorous and still an open dilemma. This paper addresses the problem for linear time-invariant systems with state time-varying delays. The delay is assumed to be bounded in an interval with a bounded derivative. A sliding mode FO structure that is robust against the delay uncertainties is established to this aim. The structure employs an auxiliary delay function that can be defined based on the existing knowledge on the actual delay values. Delay-dependent sufficient conditions for the stability of the observer are obtained using the Lyapunov Krasovskii approach, and are expressed in terms of a linear matrix inequality and two rank conditions. The delay-free observer structure is additionally studied and the necessary and sufficient conditions for its stability are obtained. Two descriptive numerical examples and simulation results demonstrate the design procedure and emphasize the effectiveness of the proposed observer design algorithm.

Adaptive iterative learning reliable control for a class of non‐linearly parameterised systems with unknown state delays and input saturation

An adaptive iterative learning reliable control (AILRC) strategy is developed in this study for a class of non-linearly parameterised systems subject to unknown time-varying state delays and input saturation as well as actuator faults. In regard to non-linearly parameterised uncertainties, not only the non-linearly parameterised controlled object, but also the non-linearly parameterised input distribution matrix is investigated in this technical note. Without the need for precise system parameters or analytically estimating bound on actuator faults variables, the novel data-driven AILRC is constructed by a non-linear feedback term and a robust term. The non-linear influence brought by actuator faults, input saturation and state delays can be compensated with the resultant algorithms. It is shown that the L [ 0 , T ] 2 convergence of single-input–single-output and multiple-input–multiple-output systems is proved through a new time-weighted Lyapunov–Krasovskii-like composite energy function. The validity of the proposed AILRC is further verified by simulation.

MRAC of systems subject to actuator nonlinearities and unknown time-varying state delays: tube reference approach

In this contribution, a tube based model reference adaptive architecture is developed for a class of nonlinear dynamic systems with unknown time-varying state delay and nonlinear actuator which not only guarantees closed loop stability, asymptotically tracking and robustness to a nonlinear perturbation, and to an external disturbance with unknown bounds, but also diminishes the control cost with respect to some criterion.

Decentralized continuous MRAC with local asymptotic sliding modes of nonlinear delayed interconnected systems

In this contribution, we develop continuous completely decentralized state-feedback adaptive controllers with sliding mode for a class of large-scale interconnected systems with nonlinear interconnections with unknown time-varying state delays. The novel contribution of this paper is that asymptotically exact tracking within the framework of completely decentralized direct continuous adaptive control is possible also for a class of nonlinear plants with matched interconnections and disturbances.

Output‐feedback sliding‐mode control of multivariable systems with uncertain time‐varying state delays and unmatched non‐linearities

An output-feedback sliding-mode controller is proposed for multivariable uncertain systems with unknown time-varying state delays and unmatched non-linear terms. The non-linearities are allowed to depend not only on the system output, but also on its unmeasurable state, and can be polynomial. This scheme is based on model-reference unit vector control under a mild Hurwitz condition for the high-frequency gain matrix. To achieve global stability properties, the amplitude of the control signal is given by a norm observer for the unmeasured state. For the first time, the design of norm observers is applied to a class of time-delay systems. This approach guarantees finite-time convergence of the output-tracking error to zero. Simulation results illustrate the application of the developed control scheme.

Multivariable output feedback robust adaptive tracking control design for a class of delayed systems

In this paper, we develop a model reference adaptive control scheme for a class of multi-input multi-output nonlinearly perturbed dynamic systems with unknown time-varying state delays which is also robust with respect to an external disturbance with unknown bounds. The output feedback adaptive control scheme uses feedback actions only, and thus does not require a direct measurement of the command or disturbance signals. A suitable Lyapunov–Krasovskii type functional is introduced to design the adaptation algorithms and to prove stability.

An output-feedback adaptive actuator failure compensation controller for systems with unknown state delays

This paper presents an output-feedback adaptive controller for a class of linear systems with unknown time-varying state delay and in the presence of actuator failures. We consider a common type of actuator failure in which some unknown system inputs may be stuck at some unknown fixed values and at unknown time instants. The adaptive controller is designed based on SPR–Lyapunov approach for relative degree one and two cases. Closed-loop system stability and asymptotic output tracking are proved using suitable Lyapunov–Krasovskii functional for each case. Simulation results are provided to demonstrate the effectiveness of the proposed results.

Output-Feedback MRAC with Reference Model Tolerance of Nonlinearly Perturbed Delayed Plants

AbstractA novel approach within the conventional MRAC framework for solving the problem of robust adaptive output tracking for a class of uncertain nonlinear dynamical systems with unknown time-varying state delays is proposed. A MRAC problem formulation in addition to the traditional asymptotic zero error tracking specification makes the problem statement contain an additional explicit requirement, namely the tracking objective is described by a set of admissible reference trajectories which is called a performance tube. As the design parameter which specifies the size of the performance tube, we select the reference model input signal than can be changed within specified bounds. An additional optimization task is formulated to find the best trajectory with a cost function that penalizes the deviation of the control signal from a given signal.

Continuous Decentralized MRAC with Sliding Mode of Nonlinear Delayed Dynamic Systems

AbstractIn this contribution, we develop continuous totally decentralized state-feedback adaptive controllers with sliding mode for a class of large-scale interconnected systems with nonlinear interconnections with unknown time-varying state delays. The novel contribution of this paper is that asymptotically exact tracking within the framework of totally decentralized direct continuous adaptive control is possible also for the class of nonlinear plants considered here.

Tracking for nonlinear plants with multiple unknown time‐varying state delays using sliding mode with adaptation

AbstractIn this paper, we develop a sliding mode model reference adaptive control (MRAC) scheme for a class of nonlinear dynamic systems with multiple time‐varying state delays, which is robust with respect to unknown plant delays, to a nonlinear perturbation, and to an external disturbance with unknown bounds. An appropriate Lyapunov–Krasovskii‐type functional is introduced to design the adaptation algorithms, and to prove stability. Copyright © 2009 John Wiley & Sons, Ltd.

Lyapunov-based Adaptive Output-Feedback Control of MIMO Nonlinear Plants with Unknown, Time-varying State Delays

Abstract In this paper, we develop a model reference adaptive control (MRAC) scheme for a class of multi-input-multi-output (MIMO) non-linear dynamic systems with unknown time-varying state delay which is also robust with respect to an external disturbance with unknown bound. An output feedback adaptive control scheme uses feedback actions only, and thus does not require a direct measurement of the command or disturbance signals. A suitable Lyapunov-Krasovskii type functional is introduced to design the adaptation algorithms and to prove stability.

Robust discrete-time sliding mode control for uncertain systems with time-varying state delay

A robust discrete-time sliding mode control (DT-SMC) for uncertain linear systems with unknown time-varying state delay is analysed, in which uncertainties consist of mismatched uncertain parameters and unknown bounded nonlinear function. By using the linear matrix inequality approach, a sufficient condition for the existence of stable sliding surfaces depending on the lower and upper delay bounds is established. On the basis of this existence condition, the synthesised DT-SMC can guarantee the sliding mode reaching condition of the specified discrete-time sliding surface. Two examples verify the effectiveness of the proposed method.