Time-varying State Delays Research Articles

Finite-time resilient control for uncertain periodic piecewise polynomial time-varying systems

This study explores the problem of finite-time resilient control for periodic piecewise polynomial time-varying systems in the face of parameter uncertainties, time-varying state delays and external disturbances. Particularly, the considered system is characterized by dividing the fundamental period of periodic systems into numerous subintervals, each of which can be expressed by using matrix polynomial functions. The foremost intention of this work is to lay out a resilient controller such that the resulting closed-loop system is finite-time bounded and satisfies a mixed [Formula: see text] and passivity performance index. Furthermore, by constructing a periodic piecewise time-varying Lyapunov–Krasovskii functional, a delay-dependent sufficient condition is established in line with Wiritinger’s inequality and matrix polynomial lemma to guarantee the needed outcomes of the system under study. Following this, the gain matrix of the devised controller can be calculated by solving the established constraints. As a final step, we conclude with a numerical example that validates the potential and importance of the theoretical discoveries and the developed control scheme.

Exponential stabilization of the class of the switched systems with mixed time varying delays in state and control

This paper presents the problem of exponential stabilization of switched systems with mixed time-varying delays in state and control. Based on the partitioning of the stability state regions into convex cones, a constructive geometric design for switching laws is put forward. By using an improved Lyapunov–Krasovskii functional in combination with matrix knowledge, we design a state feedback controller that guarantees the closed-loop system to be exponentially stable. The obtained conditions are given in terms of linear matrix inequalities (LMIs), which can be effectively decoded in polynomial time by various computational tools such as the LMI tool in MATLAB software. A numerical example is proposed to illustrate the effectiveness of the obtained results.

Improved Criteria for Controllability of Markovian Jump Boolean Control Networks with Time-Varying State Delays

Improved Criteria for Controllability of Markovian Jump Boolean Control Networks with Time-Varying State Delays

Event-triggered anti-windup strategy for time-delay systems subject to saturating actuators

<p>This paper investigates the anti-windup synthesis problem for linear control systems subject to time-varying state delay and saturating actuators. To alleviate the redundant data transmission, the dynamic event-triggered mechanism is adopted. Moreover, to abate the inherent conservatism, novel delay-dependent sector conditions containing double integral terms are explored. Then, using augmented Lyapunov-Krasovskii functionals and several less conservative inequalities, delay-dependent anti-windup synthesis criteria are obtained in accordance with the feasibility of linear matrix inequalities. Subsequently, the optimization of the initial condition set is addressed. Finally, a simulation example illustrates the availability and technique advantages of the proposed results.</p>

Adaptive Regulation of a Chain of Integrators under Unknown and Time-Varying Individual State Delays

In this letter, we study the adaptive regulation problem for a chain of integrators in which there are different individual delays in measured feedback states for a controller. These delays are considered to be unknown and time-varying, and they can be arbitrarily fast-varying. We analytically show that a feedback controller with a dynamic gain can adaptively regulate a chain of integrators in the presence of unknown individual state delays. A simulation result is given for illustration.

Observer and fault reconstruction-based control design for interval type-2 fuzzy systems

In this study, the finite-time stabilization and multiple faults reconstruction issues are scrutinized for nonlinear control systems in the presence of time-varying state delay, actuator faults and sensor faults in which the underlying system is approximated by dint of fuzzy approach. To be specific, the interval type-2 (IT2) fuzzy technique is deployed in tandem with a non-parallel distribution compensation scheme to linearize such a faulty system. Further, the existence of unknown inputs in both the system and its output are effectively reconstructed with the aid of IT2 fuzzy-based observer, namely the IT2 fuzzy unknown input (UI) observer. Simultaneously, the designed observer also ensures the reconstruction of system state vectors that are not able to be measured. With the help of this reconstruction information, a fault-tolerant control scheme is established to maintain the performance of the addressed system even in the occurrence of unknown faults. Particularly, in this work, the sampling strategy is incorporated with the developed controller design. Overall, the proposed IT2 fuzzy UI observer-based sampled fault-tolerant controller guarantees the stability of the resulting system within a finite-time duration. Furthermore, the Lyapunov stability theory enables to formulate the delay-dependent adequate constraints in the framework of linear matrix inequalities. On the grounds of established criteria, the relations are also constructed for obtaining the controller and observer gain matrices. Eventually, the simulation study is conducted with two numerical examples to validate the theoretical and practical significance of the developed control procedure.

Adaptive Event-Triggered Finite-Time Control for Uncertain Time Delay Nonlinear System.

In this article, adaptive event-triggered finite-time control is explored for uncertain nonlinear systems with time delay. First, to handle the time-varying state delays, the Lyapunov-Krasovskii function is used. Fuzzy-logic systems are used to deal with the unknown nonlinearities of the system. Notice that compared to the reporting achievements, our proposed virtual control laws are derivable by using the novel switch function, which avoids "singularity hindrance" problem. Moreover, the dynamic event-triggered controller is designed to reduce the communication pressure and we prove that the controller is Zeno free. Our proposed control strategy ensures that the tracking error is arbitrarily small in finite time and all variables of the closed-loop system remain bounded. Finally, to show the effectiveness of our control strategy, the simulation results are given.

Observer-Based Output-Feedback Control for Nonlinear Time-Delay Systems

In this article, the output feedback control design problem for a class of strict-feedback nonlinear systems with unknown state time-varying delays is addressed. Two output feedback control schemes are considered which are based on full-order and reduced-order observer, respectively. Lyapunov–Krasovskii functionals with static gain are used to develop novel memoryless control strategies. The above work ensures that all the signals in the closed-loop system are bounded and the system is asymptotically stable. Finally, two simulation examples illustrate the effectiveness of the two control schemes we proposed.

H∞ cruise control for high-speed trains with process and data transmission time-varying delay

This paper investigates an H∞ cruise control strategy for uncertain high-speed trains (HSTs) with two time-varying delays. The multibody model of the cascading car is established, taking into account the influence of the flexible coupler and the basic resistance (rolling mechanical resistance + aerodynamic resistance) in the actual operation process. There are many uncertainties in the actual operation of the train, such as disturbances caused by gusts and track irregularities and time-varying delays caused by flexible couplers. Based on the above factors, this paper fully considers and supplements the multibody model. A cruise control strategy based on Lyapunov stability theory and linear matrix inequality (LMI) is proposed. The state feedback control rate with input short time delay is designed, and a cruise control method with double time-varying delays is proposed by sampling data. Constructed Lyapunov–Krasovskii function (LKF) with time-delay parameters for time-delay systems to fully introduce the information of time delays. In view of the disturbance effect, the sufficient condition to suppress the disturbance is given. The proposed H∞ cruise control method controls the fluctuating speed and displacement of the train to quickly converge to the steady state. The HST at equilibrium tracks the desired velocity and ensures a stable relative displacement. The specified H∞ interference attenuation level is achieved to ensure safe and comfortable operation. Two numerical simulations are carried out to illustrate the effect of state time-varying delay and disturbance on train stationarity, which proves the superiority of the proposed method.

Output tracking and disturbance rejection control for switched systems under asynchronous switching

In this article, we discuss the output tracking and disturbance rejection problem for a class of switched systems with state time-varying delay under asynchronous switching. More precisely, proportional–integral control law is implemented to obtain the required tracking performance for the addressed systems. In addition, an improved equivalent-input-disturbance estimator is utilized to estimate and suppress the external disturbances. Further, the asynchronous switching phenomenon is considered between the proposed controller and the system mode. Setting a proper choice of multiple piecewise Lyapunov–Krasovskii functional, a group of required condition is established in the structure of linear matrix inequalities by using an average dwell time approach. At last, two numerical examples and their simulations including the DC motor driving model are displayed to justify the efficiency and applicability of the proposed control synthesis.

Formula omitted] control for singularly perturbed jumping delayed systems and its application in a tunnel diode circuit model

This paper investigates the slow state variable feedback control issue for a group of singularly perturbed Markov jump systems with time-varying state delay in the discrete-time domain. The primary goal of this paper is to propose a slow state controller design approach that ensures the closed-loop dynamics attain stochastic stability with an H∞ performance. First, the time-varying delay is introduced into system state and Markov jump chain is employed to depict system topological change. Secondly, by resorting to the Lyapunov functional theory and matrix analysis method, several necessary criteria are provided to guarantee the desired control performance. The derived conditions rely not only on the size of time-varying state delay and the upper bound of the singular perturbation parameter, but also on the order of the generated Markov jump mode sequence. Based on the established conditions, the gains of the desired slow state controller are obtained by means of the feasibility of a set of linear matrix inequalities. Eventually, a numerical simulation and a tunnel diode circuit model are presented to demonstrate the efficiency of the proposed technique.

A prescribed-performance-based adaptive finite-time tracking control scheme circumventing the dependence on the system initial condition

This paper is concerned with the prescribed finite-time tracking control problem for a class of nonlinear systems with unknown initial condition, state time-varying delays and external disturbances. A new adaptive prescribed finite-time tracking control scheme bypassing system initial condition is proposed via the prescribed performance method. Several nonlinear mapping functions (NMFs) and a new prescribed finite-time performance function (PFTPF) combining finite-time control with prescribed performance control are constructed to obtain the scheme. In this paper, the assumptions on the time-delay terms are removed by means of the designed Lyapunov–Krasovskii functions. In addition, to avoid step impact effect arisen by an overlarge initial control input, a control input with zero initial value is obtained. Aiming at the design of zero initial control input, a new Lyapunov stability criterion form is put forward. Two practical examples are presented to confirm the effectiveness and superiority of the proposed scheme.

Strong stabilisation and decay estimate for distributed semilinear systems with time-varying delay

In this paper we deal with the problem of strong stabilisation for a class of distributed semilinear systems by means of a nonlinear feedback control. The systems under consideration evolve in a Hilbert space and present periodic time-varying state delay. We first give a proof for the existence and uniqueness of the solution for the considered systems. Then, under a null controllability condition, we establish the stabilisation result and provide an explicit optimal decay rate estimate. The particular case of such systems for which the linear part generates a differentiable semigroup is also investigated. Some illustrating applications to hyperbolic and parabolic equations are displayed. Finally, a conclusion and some perspectives are given.

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.

시변지연과 미지 제어 방향과 비억제 성장율을 갖는 피드포워드 비선형 시스템의 안정화

In this study, we investigate the regulation problem of a feedforward nonlinear system with time-varying state delay, an unknown control direction, and an unbounded growth function. The proposed controller was mainly developed using the Nussbaum gain and gain scaling techniques, and a rigorous system analysis was carried out to show that the controller achieved global regulation of the considered system. Numerical simulation results are provided to demonstrate the effectiveness of the proposed controller.

Fraction dynamic-surface-based adaptive neural finite-time control for stochastic nonlinear systems subject to unknown control directions, time-varying input delay and state delay

In this paper, an adaptive neural finite-time tracking control is studied for a category of stochastic nonlinearly parameterized systems with multiple unknown control directions, time-varying input delay, and time-varying state delay. To this end, a novel criterion of semi-globally finite-time stability in probability (SGFSP) is proposed, in the sense of Lyapunov, for stochastic nonlinear systems with multiple unknown control directions. Secondly, a novel auxiliary system with finite-time convergence is presented to cope with the time-varying input delay, the appropriate Lyapunov Krasovskii functionals are utilized to compensate for the time-varying state delay, Nussbaum functions are exploited to identify multiple unknown control directions, and the neural networks (NNs) are applied to approximate the unknown functions of nonlinear parameters. Thirdly, the fraction dynamic surface control (FDSC) technique is embedded in the process of designing the controller, which not only the “explosion of complexity” problems are successfully avoided in traditional backstepping methods but also the command filter convergence can be obtained within a finite time to lead greatly improved for the response speed of command filter. Meanwhile, the error compensation mechanism is established to eliminate the errors of the command filter. Then, based on the proposed novel criterion, all closed-loop signals of the considered systems are SGPFS under the designed controller, and the tracking error can drive to a small neighborhood of the origin in a finite time. In the end, three simulation examples are applied to demonstrate the validity of the control method.

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.

Input–Output Finite-Time Stabilization of T–S Fuzzy Systems Through Quantized Control Strategy

The issues of input–output finite-time stability and stabilization of Takagi–Sugeno (T–S) fuzzy systems with time-varying state delay and exogenous input signal are studied in this article. For the stabilization process, a controller that does not share the same membership functions as the system is considered and the state feedback is quantized by using a logarithmic quantizer. The desired stability criterion for the addressed fuzzy system is first derived without the control term. It is then extended to the case in which the proposed controller is present. The stability criteria are given in the form of matrix inequalities, which are supported by the augmented Lyapunov–Krasovskii functional, generalized free-weighting-matrix approach and Finsler’s lemma. Moreover, as a special case, an asymptotic stability criterion is obtained and used in a comparative study. As a result, the time-delay interval is much larger than some of the works published very recently, which is due to the augmented Lyapunov–Krasovskii functional construction. In addition, the effectiveness and practicability of the theoretical findings are validated with simulation examples.

Distributed adaptive dynamic event-based consensus control for nonlinear uncertain multi-agent systems

In order to tackle the real network constraints such as unknown state time-varying delays and limited communication resources, this article proposes a dynamic event-triggered control framework to satisfy the distributed consensus of heterogeneous strict-feedback multi-agent systems. Each follower agent is subject to nonlinear-in-parameter uncertainties regardless of satisfying the Lipschitz condition. Having considered the follower’s uncertainties, the adaptive neural network strategy is used to approximate uncertain functions. To further simplify the controller form, the minimal learning parameter technique is introduced to evade the updated information of the neural network weight vectors. Graph-based Lyapunov–Krasovskii functionals are utilized to handle the unknown state time-delays. A command filter dynamic event-triggered control scheme is then introduced to remove the complexity explosion regardless of global information of network. Different from the existing triggering strategies for the strict-feedback multi-agent systems, the proposed triggering mechanism is proved to include a positive bounded dynamical variable which results in the exclusion of the Zeno phenomenon and reducing the communication load in the controller to actuator channels. That can lead to the save of energy and communication resources, which are meaningful for employing the proposed scheme in the real practical applications. It is eventually proved that under the proposed approach, all the closed-loop network errors converge to a small neighborhood of the origin. A simulation example is finally given to show the effectiveness of the control scheme.

Adaptive-observer-based consensus tracking with fault-tolerant network connectivity of uncertain time-delay nonlinear multiagent systems with actuator and communication faults

In this study, a distributed output-feedback design approach for ensuring fault-tolerant initial network connectivity and preselected-time consensus tracking performance is proposed for a class of uncertain time-delay nonlinear multiagent systems (TDNMSs) with unexpected actuator and communication faults. It is assumed that time-varying state delays and system nonlinearities in TDNMSs are unknown. The main contribution of this study is to provide a delay-independent output-feedback control strategy to address a fault-tolerant initial connectivity preservation problem in the consensus tracking field. A local delay-independent adaptive state observer using neural networks is designed for each follower, and the boundedness of local observation errors is proved by constructing a Lyapunov–Krasovskii functional and adaptive tuning laws. Then, the local nonlinear relative output errors using a time-varying function with a preselected convergence time are derived to design simple local delay-independent trackers. The stability of the proposed consensus tracking system is analyzed, and simulation comparison results demonstrate the validity of the proposed strategy.