Control Of Time-varying Delay Systems Research Articles

Security Control for Time-Varying Delay Systems Based on Random Switching Moving Defense Method in Cyber-Physical Environment

With the high digitization, informatization, and networking of practical complex systems, the security and reliability issue of systems control in the cyber-physical environment is becoming more and more critical, especially under the background of rampant network attacks nowadays. The security control for time-varying delay systems based on random switching moving defense method in a cyber-physical environment is studied in this paper. First, the security control model of one class of time-varying delay dynamic systems considering the actuator and controller attack problem is presented; second, controller design based on switching strategy for moving defense is studied; and then the security control scheme for time-varying delay systems based on random switching moving defense is presented for dealing with cyber attacks from malicious adversaries. Finally, multiple simulation results are presented to show the effectiveness of the proposed scheme.

Adaptive fault tolerant control for time-varying delay system with actuator fault and mismatched disturbance

In this paper, the fault tolerant control (FTC) problem for a class of continuous Lipschitz nonlinear systems with actuator fault, mismatched disturbance, and time-varying delay is investigated. An adaptive integral sliding mode fault tolerant control (AISMFTC) technique is proposed. First, a composite observer is designed to estimate the states and disturbance simultaneously, by introducing a sliding mode observer, the actuator fault is reconstructed. Then, in accordance with the estimated information, an AISMFTC method is designed. In the AISMFTC scheme, two adaptive laws and compensators are contained to compensate the observer errors, deal with the effects of actuator fault and attenuate the disturbance. Furthermore, the H∞performance is considered for the robustness of the system. Finally, the effectiveness of the proposed method is illustrated by two examples.

Gain-scheduled control of time-varying delay systems with input constraint

ABSTRACTThis paper investigates gain-scheduled control design for linear systems with time-varying state delays subject to actuator saturation and external disturbance. Assuming the disturbance is peak bounded, a sufficient delay-dependent condition is established to guarantee that a family of level sets, corresponding to a novel parameter-dependent Lyapunov–Krasovskii functional, are nested and invariant to the closed-loop system. The invariant sets are then used to obtain nested reachable sets (ellipsoids) to bound the closed-loop states. A family of continuous controllers are designed based on these nested ellipsoids. The controller with the best performance is selected, each time, based on the closed-loop state vector, while complying with the saturation bound, and the resulting closed-loop system is locally input-to-state stable. All conditions are represented in the form of linear matrix inequalities (LMIs) by the linear spline method. Finally, the benefit of the control method is illustrated by two examples.

A new approach for the optimal control of time-varying delay systems with external persistent matched disturbances

The aim of this study is to develop an efficient iterative approach for solving a class of time-delay optimal control problems with time-varying delay and external persistent disturbances. By using the internal model principle, the original time-delay model with disturbance is first converted into an augmented system without any disturbance. Then, we select a quadratic performance index for the augmented system to form an undisturbed time-delay optimal control problem. The necessary optimality conditions are then derived in terms of a two-point boundary value problem involving advance and delay arguments. Finally, a fast iterative algorithm is designed for the latter advance-delay boundary value problem. The convergence of the new iterative technique is also investigated. Numerical simulations verify that the proposed approach is efficient and provides satisfactory results.

Constrained model predictive control for time-varying delay systems: Application to an active car suspension

This study investigates the problem of robust model predictive control (RMPC) for active suspension systems with time-varying delays and input constraints. The uncertainty is of convex polytopic type. Based on the Lyapunov-Krasovskii functional method, sufficient stability conditions of the time-varying delays systems are derived by linear matrix inequalities (LMIs) terms. At each time set, a feasible state feedback is obtained by minimizing an upper bound of the ‘worst-case’ quadratic objective function over an infinite horizon subject to constraints on inputs. Finally, a quarter-vehicle model is exploited to demonstrate the effectiveness of the proposed method.

Dissipative based adaptive reliable sampled-data control of time-varying delay systems

This paper is concerned with the problem of dissipative based adaptive reliable controller for a class of time delay systems subject to actuator failures and time-varying sampling with a known upper bound on the sampling intervals. By constructing a proper Lyapunov-Krasovskii functional which fully uses the available information about the actual sampling pattern and time delays, a new set of sufficient conditions is derived to obtain the required result. Then, a dissipative based adaptive sampled-data controller is designed such that the resulting closed-loop system is reliable in the sense that it is asymptotically stable and has the prescribed dissipative performance under given constraints. The existence condition of the desired dissipative based adaptive reliable sampled-data controller is obtained in terms of linear matrix inequalities. Further, the performance of the proposed controller is implemented on a liquid propellant rocket motor with a pressure feeding system model. The simulation results show the effectiveness and better performance of the proposed adaptive reliable sampled-data controller over conventional reliable controller.

Discrete sliding mode control for time-varying delay systems: a multi-delay approach

Owing to its potential for real applications, many researchers have studied the problem of modelling and control of time-varying delay systems. In this paper, we propose a new strategy called multi-delay approach for modelling and control of these systems. In this new strategy, the time-varying delay systems are modelled by a multi-delay model representation in which each elementary model is characterised by a constant delay value varying between the lower and upper bounds of the delay term supposed to be known. A systematic elementary model reproducing the real output evolution is generated. Then, a discrete sliding mode control based on the multi-delay model representation (MD-DSMC) was developed to stabilise such systems. The proposed controller guarantees a finite time convergence of systems under consideration. The controller parameters are selected by solving linear matrix inequalities (LMIs). A comparative study with the classical discrete sliding mode control was also subject of this work.

Robust <i>H</i><sub>∞</sub> Control for Time-Varying Delay Systems with Frequency-Dependent Performance Weights

Robust <i>H</i><sub>∞</sub> Control for Time-Varying Delay Systems with Frequency-Dependent Performance Weights

Fault-distribution-dependent reliable control for time-varying delay system

This paper considers the problem of reliable control for continuous-time systems with interval time-varying delay. By introducing a random matrix, a new practical actuator fault model is established. Using the Lyapunov-Krasovskii approach, a sufficient condition for the existence of reliable controller is expressed by a linear matrix inequality(LMI). An illustrative example is exploited to show the effectiveness of the proposed design procedures.

Static output feedback sliding mode control for time‐varying delay systems with time‐delayed nonlinear disturbances

AbstractIn this paper, a robust stabilization problem for a class of linear time‐varying delay systems with disturbances is studied using sliding mode techniques. Both matched and mismatched disturbances, involving time‐varying delay, are considered. The disturbances are nonlinear and have nonlinear bounds which are employed for the control design. A sliding surface is designed and the stability of the corresponding sliding motion is analysed based on the Razumikhin Theorem. Then a static output feedback sliding mode control with time delay is synthesized to drive the system to the sliding surface in finite time. Conservatism is reduced by using features of sliding mode control and systems structure. Simulation results show the effectiveness of the proposed approach. Copyright © 2009 John Wiley & Sons, Ltd.

Static output feedback sliding mode control for time-varying delay systems with time-delayed nonlinear disturbances

In this paper, a robust stabilization problem for a class of linear time-varying delay systems with disturbances is studied using sliding mode techniques. Both matched and mismatched disturbances, involving time-varying delay, are considered. The disturbances are nonlinear and have nonlinear bounds. A sliding surface is designed and the stability of the corresponding sliding motion is analysed based on the Razumikhin Theorem. Then a static output feedback sliding mode control with time-delay is synthesized to drive the system to the sliding surface in finite time. Simulation results show the effectiveness of the proposed approach.

Robust mixed H 2 /H ∞ control of time-varying delay systems

This paper describes the mixed H 2 /H X controller design method of linear systems with time-varying delays in both state and control input. More specifically, the proposed mixed H 2 /H X controller minimizes the H 2 performance measure when satisfying a prescribed H X norm bound on the closed loop system. The sufficient conditions for the existence of controller, the mixed H 2 /H X controller design method and the upper bound of performance measure are presented using the linear matrix inequality (LMI) technique. Also, all solutions including controller gain and the upper bound of performance measure are obtained simultaneously. Furthermore, the proposed controller design method can be easily extended into the problem of robust mixed H 2 /H X controller design method for parameter uncertain systems with time-varying delays in both state and control input.