Uncertain Time-delay Systems Research Articles

Output Feedback Fuzzy Regressive PI Control of Time-Delay Systems with Nonlinear Delay Input/Output

This paper presents the fuzzy regressive proportional-integral (FRPI) control for the output feedback regulation of uncertain time-delay systems subject to both nonlinear delayed input and output. First, the system is represented in a new fuzzy linear regressive model which does not have input/output nonlinearity and input delay in each fuzzy rule. Based on the fuzzy linear regressive model, the output feedback regulation controller is straightforwardly designed by combining the proportional-integral and regressive compensation. Then, the gain design is performed by Lyapunov–Krasovskii stability analysis and Linear matrix inequality (LMI) conversion. The LMI optimization approach is utilized to avoid iteratively solving bilinear gain conditions. Moreover, no observer is used in this paper. In addition, the FRPI controller can be further reduced to a linear regressive PI controller form for easier implementation. Finally, numerical simulations show the expected performance.

Chaotic sliding mode controllers for uncertain time-delay chaotic systems with input nonlinearity

This paper presents a novel robust chaotic controller for stabilizing uncertain time-delay chaotic systems with input nonlinearity. Based on dynamic output sliding mode control (SMC), Lyapunov theory and linear matrix inequality (LMI) technique, the stability of overall uncertain time-delay chaotic system with input nonlinearity under the proposed control scheme is guaranteed without the state predictor. The selection of sliding surface and the design of control law are two important issues, which have been addressed. A priori knowledge of upper bounds of uncertainties is not required. Furthermore, the proposed scheme ensures robustness against input nonlinearity, time-delays, nonlinear real-valued functions, parameter uncertainties and disturbances simultaneously. Finally, simulation results demonstrate the validity of the proposed control methodology.

Design of robust H∞ fault detection filter for uncertain time-delay systems using canonical form approach

In this paper, the problem of fault detection for an uncertain time-delay system is considered. Using a canonical form transformation, original time-delay system is transformed into a delay-free system. The fault detection scheme is devised using H∞ model matching approach for the delay-free system and then implemented on original system. The so-called canonical transformation is found to be less conservative and offers reduced complexity in comparison with bicausal transformation, which can also be employed for the aforementioned purpose. An algorithm is proposed for design of such a fault detection system. Simulation results show the effectiveness of proposed scheme.

Robust stabilisation of uncertain time‐delay dynamical systems with unknown bounds of uncertainties: a non‐linear control method

In this study, the problem of robust stabilisation is considered for a class of uncertain dynamical systems with state delays. Here, it is assumed that the upper bounds of the delayed state perturbations, uncertainties and external disturbances are completely unknown. For such a class of uncertain time-delay dynamical systems, a novel design method is presented in which a class of continuous memoryless robust stabilising controllers is constructed. In particular, by making use of the presented method, it is not required to introduce some adaptive schemes to update the unknown upper bounds, which makes the control schemes simpler than adaptive robust control schemes reported in the control literature. Moreover, such a control scheme proposed in this study will be called adaptation-free robust control scheme. It is also shown that the solutions of the resulting closed-loop time-delay dynamical systems can be guaranteed to be uniformly ultimately bounded. Finally, the simulations of some numerical examples are provided to demonstrate the validity of the theoretical results.

LMI Approach for Robust Control of Interval System with Time Delay

Robust control of uncertain time delay system is a challenging problem for control engineers. The problem becomes more difficult when the system is having interval parameters. This paper proposes a method for solving the problem of robust control of an uncertain time delay system with interval parameters. The interval system with time delay has been transformed to a nominal system with time delay. An LMI controller is designed for the nominal system corresponding to the interval system at different values of parametric uncertainties. Then among all the controllers of different cases of parametric uncertainties, determined the controllers which are suitable for all the cases. Then identified the common controllers which are also suitable for the interval system. From the singular value analysis and the worst case gain analysis, the best suitable controller for the nominal system has been determined. The method is illustrated using examples and is seen providing good control performance. The chosen controller is robust for the range of uncertainty associated with the system

New Results for Robust Stability of Discrete Bilinear Uncertain Time-Delay Systems

In this paper, new results for the problem of the robust stability of discrete homogeneous bilinear time-delay systems subjected to nonlinear or parametric uncertainties are addressed. Applying a concise upper bound to the Lyapunov equation approach and then associating some linear algebraic techniques, several delay-independent conditions are presented to assure the robust stability of the aforementioned systems. One of the features of the present criteria is that they are independent of any Lyapunov equation, although the Lyapunov equation approach is adopted. Comparing to an existing work, it is shown that the obtained results are sharper. Finally, all obtained results are applied to solve the same problem of discrete bilinear uncertain systems and discrete time-delay systems with/without uncertainties. Concise criteria for the robust stability of the mentioned systems are developed, and comparisons between the obtained results and those appeared in the literature are also made. It is shown that all obtained results in this work are either tighter or more concise.

Decentralised robust stabilisation of uncertain large-scale interconnected time-delay systems with unknown upper bounds of uncertainties

The problem of decentralised robust stabilisation is considered for a class of uncertain large-scale time-delay interconnected dynamical systems. In the paper, the upper bounds of delayed state perturbations, uncertainties, interconnection terms, and external disturbances are assumed to be completely unknown, and the delays are assumed to be any non-negative constants. For such a class of uncertain large-scale time-delay interconnected systems, a new method is presented whereby a class of adaptation-free decentralised local robust state feedback controllers can be constructed. In addition, it is also shown that the solutions of uncertain large-scale time-delay interconnected systems can be guaranteed to be uniformly ultimately bounded. Finally, as an application to the practical mechanical systems, some simulations of a numerical example are provided to demonstrate the validity of the theoretical results.

Adaptive fuzzy observer-based stabilization of a class of uncertain time-delayed chaotic systems with actuator nonlinearities

An observer-based output feedback adaptive fuzzy controller is proposed to stabilize a class of uncertain chaotic systems with unknown time-varying time delays, unknown actuator nonlinearities and unknown external disturbances. The actuator nonlinearity can be backlash-like hysteresis or dead-zone. Based on universal approximation property of fuzzy systems the unknown nonlinear functions are approximated by fuzzy systems, where the consequent parts of fuzzy rules are tuned with adaptive schemes. The proposed method does not need the availability of the states and an observer based output feedback approach is proposed to estimate the states. To have more robustness and at the same time to alleviate chattering an adaptive discontinuous structure is suggested. Semi-global asymptotic stability of the overall system is ensured by proposing a suitable Lyapunov–Krasovskii functional candidate. The approach is applied to stabilize the time-delayed Lorenz chaotic system with uncertain dynamics amid significant disturbances. Analysis of simulations reveals the effectiveness of the proposed method in terms of coping well with the modeling uncertainties, nonlinearities in actuators, unknown time-varying time-delays and unknown external disturbances while maintaining asymptotic convergence.

Robust output feedback control of uncertain time-delay systems with actuator saturation and disturbances

This paper investigates the problem of robust output feedback control of uncertain continuous-time time-delay systems with both external disturbances and saturating actuators. Both the system uncertainties and the external disturbances are assumed to be time-varying and bounded, and the states of the system under consideration are not available but detectable. First, in the absence of external disturbances, some delay-dependent conditions for designing observer-based output feedback controller are derived which ensure that the system without perturbations on its input matrices can be stabilized together with the domain of attraction. To obtain a maximal estimate of the domain of attraction, an iterative optimization algorithm is proposed. When the system input matrices are subject to perturbations, new stabilization conditions are obtained to adjust the gain of the observer on the basis of the above-mentioned controller design rules. Second, in the presence of external disturbances, the robust observer-based output feedback controller is designed to guarantee that the corresponding closed-loop system converges uniformly exponentially to a ball with an initial admissible domain. Finally, numerical results are given to demonstrate the effectiveness of the proposed method.

A new stability result for nonlinear cascade time-delay system and its application in chaos control

Based on the converse Lyapunov stability theorem and invariant set theory, this paper presents a new theorem for the nonlinear cascade delay system. With this new proposed method, a lot of coupled items can be taken as zero items. So the whole system can be converted to a very simple form. Also, a simple chaos control technique is proposed for the uncertain time-delay Lorenz chaotic system via this new method. The controller designed is linear and easy to be implemented. Simulation results for uncertain chaotic systems are provided to illustrate the effectiveness of the proposed scheme.

Adaptive backstepping control of uncertain linear systems under unknown actuator delay

Trajectory tracking of uncertain time-delay linear systems by output feedback control is of theoretical importance and practical value. In this paper, concentrating on a class of linear plants whose relative degree equals to system dimension, we develop a Lyapunov-based control scheme to achieve trajectory tracking despite some classic difficulties including unmeasurable system state, unknown plant parameters and unknown input time-delay. A comprehensive approach combining adaptive backstepping output feedback with prediction-based boundary control is employed in the design. The stability analysis exhibits the global boundedness of all closed-loop system signals and the tracking performance is also guaranteed.

Sliding Mode Control for A Class of Uncertain Time-Delay Systems

This paper investigates the stability and stabilization pr oblems for a class of uncertain time-delay systems. For exploring the stability problem, the Lyapunov-Krasovskii function (LKF) method and Leibniz-Newton formula are adopted to analyze the stability problems of a class of uncertain time-delay systems. In addition, the proposed delay-dependent stability conditions f or a class of time-delay unforced systems can be formulated by linear matrix inequalities (LMIs). By examining the stabilization pr oblem, based on the sliding mode control scheme, some assumptions, and some transformations, the delay-dependent stabilization condition for uncertain time-delay system is propounded to guarantee the asymptotic stabilization of uncertain time-delay system i n this paper. Moreover, based on the Schur complement formula and some variable transformations, the delay-dependent stabilizatio n conditions of the uncertain time-delay system can be presented in terms of linear matrix inequality (LMI) form. Finally, a numerical example is illustrated to demonstrate the effectiveness and validity of the proposed control scheme.

Robust synchronization of uncertain complex systems with time-varying delays

Synchronization analysis and design problems for uncertain time-delayed high-order complex systems with dynamic output feedback synchronization protocols are investigated. By stating projection on the synchronization subspace and the complement synchronization subspace, synchronization problems are transformed into simultaneous stabilization problems of multiple subsystems related to eigenvalues of the Laplacian matrix of the interaction topology of a complex system. In terms of linear matrix inequalities (LMIs), sufficient conditions for robust synchronization are presented, which include only five LMI constraints. By the changing variable method, sufficient conditions for robust synchronization in terms of LMIs and matrix equalities are given, which can be checked by the cone complementarily linearization approach. The effectiveness of theoretical results is shown by numerical examples.

New Stability Criteria for Uncertain Nonlinear Stochastic Time-Delay Systems

This paper deals with the problem of robust stabilization and non-fragile robust control for a class of uncertain stochastic nonlinear time-delay systems that satisfy a one-sided Lipschitz condition. The parametric uncertainties are assumed to be real time-varying and norm bounded. Based on the one-sided Lipschitz condition including useful information of the nonlinear part, a new stability criterion for this class of nonlinear systems is provided. A memoryless non-fragile state-feedback controller is designed to guarantee robust stochastic stability of closed-loop systems. The approach of linear matrix inequalities is proposed to solve the robust stability for stochastic nonlinear systems with time-varying delay, and to obtain new delay-dependent sufficient conditions. Numerical examples are given to illustrate the validity and advantages of the proposed theoretical results.

Global stabilisation for a class of uncertain nonlinear time-delay systems by dynamic state and output feedback

This paper investigates the design problem of constructing the state and output feedback stabilisation controller for a class of uncertain nonlinear systems subject to time-delay. First, a dynamic linear state feedback control law with an adaptive strategy is developed to globally stabilise the uncertain nonlinear time-delay system under a lower-triangular higher-order growth condition. Then, one more challenging problem of the adaptive output feedback stabilisation is addressed, which can globally stabilise the time-delay system when the unmeasurable states linearly grow with rate functions consisting of higher-order output.

Global adaptive neural control for strict-feedback time-delay systems with predefined output accuracy

This paper focuses on the stabilization problem for a class of nonlinear strict-feedback systems with disturbances and time delay. By constructing some nonnegative functionals, a multiswitching-based adaptive backstepping neural state-feedback controller is designed. Compared with all the existing control methodologies for the uncertain time-delay systems, the outstanding merits of the proposed control scheme are presented as follows. First, the controller guarantees that all the signals in the closed-loop system remain globally bounded, meanwhile the system output achieves an accuracy that is given a priori according to the practical requirements. Second, in contrast to the classical adaptive backstepping neural control schemes, we analyze the convergence of the tracking error by using Barbalat’s Lemma instead of Lyapunov stability theory. Third, the main technical novelty is to construct three new nth-order continuously differentiable functions which are used to design the actual controller, the virtual control variables and the adaptive laws. Two simulation examples are provided to illustrate the effectiveness and advantage of the proposed control scheme.

On the design of suboptimal sliding manifold for a class of nonlinear uncertain time-delay systems

This paper proposes a new method to design suboptimal sliding manifolds for a class of nonlinear uncertain systems with state and input delays. A switching control law is obtained based on the designed suboptimal sliding manifold. It is proved that the proposed method is able to guarantee the stability of the closed-loop system in the presence of uncertainty. Three numerical simulations are given to illustrate the effectiveness of the proposed method.

Guaranteed cost control using Lyapunov redesign for uncertain linear time delay systems

In this contribution, we combine the complete type functional approach with the guaranteed cost control strategy to design an optimal controller that stabilizes the system in closed loop and ensures an upper bound of the cost function. Then with the Lyapunov redesign technique, an additional control component is synthesized to robustify the design to a class of uncertainties that satisfy the matching condition.

Robust adaptive control of non‐linear time‐delay systems with saturation constraints

In this study, a robust adaptive control strategy is presented for a class of uncertain time-delay non-linear systems in the presence of non-symmetric saturation constraints. On the one hand, an auxiliary system is constructed to reduce the negative effects cased by possible saturations, and the following stability proof ensures the theoretical strictness; the unknown time delays, on the other hand, are compensated by choosing appropriate Lyapunov–Krasovskii functions. Furthermore, the hyperbolic tangent functions are employed to efficiently avoid the controller singularity problem encountered in Lyapunov synthesis, and it is proved that the proposed controller design method is able to guarantee semi-global uniform ultimate boundedness of all the signals in the closed-loop system. Finally, an example simulation is conducted to verify the effectiveness of theoretic results.

Observer-Based Bounded Control for Discrete Time-Delay Uncertain Nonlinear Systems

A bounded controller is proposed for a class of uncertain discrete time-delay systems with nonlinearity and disturbance based on state estimator and disturbance observer technique. A state estimator is developed to estimate the unmeasured system state vector. Suppose that the disturbance is generated by an exogenous system; a disturbance observer is designed to estimate the unknown disturbance. The parameters of the state estimator and the disturbance observer are calculated by solving linear matrix inequalities (LMIs). By applying the outputs of the state estimator and the disturbance observer, the sufficient condition for the existence of the bounded controller is derived based on an appropriate Lyapunov function candidate. Under the developed bounded controller, the stability of the closed-loop system can be guaranteed. Simulation examples are provided to show the effectiveness of the proposed bounded control scheme.