Unknown Time Delay Research Articles

Adaptive decentralised dynamic surface control for non‐linear large‐scale systems against actuator failures

This study presents an adaptive decentralised dynamic surface control (DSC) approach for a class of large-scale non-linear systems with unknown non-linear functions, unknown control gains, time-varying delays and in the presence of unknown actuator failures. The considered actuator failures are modelled to cover both loss of effectiveness and stuck at some time-varying values where the values, patterns and time occurrences of the failures are unknown. With the help of neural networks to approximate the unknown non-linear functions, a novel adaptive actuator failure compensation controller is developed based on the backstepping method and the DSC approach. The appropriate Lyapunov–Krasovskii functionals are introduced to design new adaptive laws to compensate the unknown actuator failures as well as uncertainties from unknown non-linearities and time delays. The proposed design method does not require a priori knowledge of the bounds of the unknown time delays and actuator failures. The boundedness of all the closed-loop signals is guaranteed and the tracking errors are proved to converge to a small neighbourhood of the origin. The proposed approach is employed for a double inverted pendulums benchmark and a chemical reactor system. The simulation results show the effectiveness of the proposed method.

Time-Delayed Vibration Control of a Rotating Flexible Manipulator Based on Model Output Prediction Feedback

AbstractThis paper is concerned with vibration control of a single-link flexible beam structure. The proposed beam is controlled by a servo motor through a harmonic gear reducer. After obtaining the models by system identification, a time-delayed optimal controller based on model output prediction and optimal control theory was designed to compensate the unknown time delay in the controlled system. Then, experiments on the proposed control scheme were conducted in a set-point vibration control process. The experimental results demonstrate that the performance of vibration suppression can be improved substantially when applying the proposed method in the presence of time delay compensation, as compared to the traditional proportional and derivative (PD) controller. The accuracy of models was validated according to experimental results, and the factors that influence the output prediction accuracy are analyzed in this paper.

Delay-dependent adaptive dynamic surface control for nonlinear strict-feedback delayed systems with unknown dead zone

In this paper, delay-dependent adaptive dynamic surface control (DSC) is developed for a class of uncertain nonlinear time-delay systems. The considered system is in strict-feedback form with unknown dead zone. Compared with the existing results, a novel adaptive fuzzy memory state feedback controller is constructed, which relaxes the restrictions on the unknown time-delay functions and avoids the singularity problem in controller design. The unknown time delays are adaptively estimated. Design difficulties from unknown time-delay functions are overcome by using mean value theorem for differential, fuzzy logic time-delay systems, appropriate nonnegative function, and the desirable property of adaptive laws of delay parameters. A modified DSC technique is incorporated into backstepping to avoid “the explosion of complexity” problem and simplify the adaptive design procedure. By Barbalat׳s lemma, it is shown that the proposed controller can ensure that the closed-loop system is semi-globally uniformly ultimately bounded, and all the state tracking errors converge to a priori known accuracy. Finally, two simulation examples are given for showing the effectiveness of the proposed approach.

Adaptive fuzzy decentralized control for uncertain large-scale nonlinear time-delay systems with virtual control functions

In this paper, the adaptive fuzzy decentralized tracking control problem is investigated for a class of uncertain large-scale nonlinear systems, interacted through their outputs with completed unknown time-varying delays. The novel contribution is to remove the common assumptions on the unknown time delays by the proposed delay replacement technique, so that the controller design is not dependent on these assumptions any more, and thus, added flexibility in decentralized control design is achieved. Furthermore, the approximation and replacement errors are handled by the adaptive technique. All closed-loop signals are proved to be semiglobal uniform ultimate boundedness, and the tracking errors are guaranteed to converge to a small residual set around the origin. The simulation studies illustrate the effectiveness of the control scheme.

Distributed memoryless detection and accommodation of unknown time-delayed interaction faults in a class of interconnected nonlinear systems

This paper addresses a memoryless design problem for the distributed fault detection and accommodation (FDA) of a class of large-scale nonlinear systems in the presence of nonlinear interaction faults with unknown time delays. Existing works designed distributed FDA schemes without considering interaction delays. However, we consider these delays, design distributed memoryless detection estimators and time-varying thresholds for detecting unknown time-delayed interaction faults, and analyze the distributed fault detectability. Then, an approximation-based distributed fault accommodation scheme which is independent of time delays is constructed via Lyapunov stability theorem. Thus, it is shown that all signals of the total controlled closed-loop system are uniformly ultimately bounded and tracking errors of subsystems converge to an adjustable neighborhood of the origin. Finally, a simulation example is presented to show the effectiveness of the proposed methodology.

Distributed adaptive consensus control of heterogeneous multi‐agent chaotic systems with unknown time delays

In this study, the distributed consensus tracking problem for heterogeneous multi-agent chaotic delayed non-linear systems is addressed. Each follower is modelled as a chaotic system with non-identical and unknown time delays, non-linear dynamics, and disturbances. The general case of directed communication graphs is considered and the graph structure is taken into account in the control protocol design. Distributed controllers with an adaptive learning feature based on neural network approximations are designed to guarantee that all agents synchronise to the leader's state with bounded synchronisation error. A graph-dependent Lyapunov proof provides error bounds that depend on the maximum time delays, the graph topology, and the agent dynamics properties. Special cases of the dynamics considered here cover many examples in the literature, including master–slave synchronisation of two chaotic delayed systems. A simulation with multiple non-identical chaotic agents is given to verify the effectiveness of the proposed method.

A CS Recovery Algorithm for Model and Time Delay Identification of MISO-FIR Systems

This paper considers identifying the multiple input single output finite impulse response (MISO-FIR) systems with unknown time delays and orders. Generally, parameters, orders and time delays of an MISO system are separately identified from different algorithms. In this paper, we aim to perform the model identification and time delay estimation simultaneously from a limited number of observations. For an MISO-FIR system with many inputs and unknown input time delays, the corresponding identification model contains a large number of parameters, requiring a great number of observations for identification and leading to a heavy computational burden. Inspired by the compressed sensing (CS) recovery theory, a threshold orthogonal matching pursuit algorithm (TH-OMP) is presented to simultaneously identify the parameters, the orders and the time delays of the MISO-FIR systems. The proposed algorithm requires only a small number of sampled data compared to the conventional identification methods, such as the least squares method. The effectiveness of the proposed algorithm is verified by simulation results.

Neural identifier for unknown discrete-time nonlinear delayed systems

This work proposes a discrete-time nonlinear neural identifier based on a recurrent high-order neural network trained with an extended Kalman filter-based algorithm for discrete-time deterministic multiple-input multiple-output systems with unknown dynamics and time-delay. To prove the semi-globally uniformly ultimately boundedness of the proposed neural identifier, the stability analysis based on the Lyapunov approach is included. Applicability of the proposed identifier is shown via simulation and experimental results, all of them performed under the presence of unknown external and internal disturbances as well as unknown time-delays.

Adaptive Fuzzy Control of Strict-Feedback Nonlinear Time-Delay Systems With Unmodeled Dynamics.

In this paper, an approximated-based adaptive fuzzy control approach with only one adaptive parameter is presented for a class of single input single output strict-feedback nonlinear systems in order to deal with phenomena like nonlinear uncertainties, unmodeled dynamics, dynamic disturbances, and unknown time delays. Lyapunov-Krasovskii function approach is employed to compensate the unknown time delays in the design procedure. By combining the advances of the hyperbolic tangent function with adaptive fuzzy backstepping technique, the proposed controller guarantees the semi-globally uniformly ultimately boundedness of all the signals in the closed-loop system from the mean square point of view. Two simulation examples are finally provided to show the superior effectiveness of the proposed scheme.

Parameter estimation for nonlinear time-delay systems with noisy output measurements

This paper considers the problem of using noisy output data to estimate unknown time-delays and unknown system parameters in a general nonlinear time-delay system. We formulate the problem as a dynamic optimization problem in which the unknown quantities are decision variables to be chosen optimally, with the cost function penalizing the mean and variance of the least-squares error between actual and predicted system output. Since the time-delays and system parameters influence the cost function implicitly through the governing time-delay system, the cost function’s gradient–which is required to solve the problem using gradient-based optimization techniques–cannot be computed analytically using standard differentiation rules. We instead develop two computational methods for evaluating this gradient: one involves solving an auxiliary time-delay system forward in time; the other involves solving an auxiliary time-advance system backward in time. On this basis, we propose an efficient optimization algorithm for determining optimal estimates for the time-delays and system parameters. We conclude the paper by examining the performance of this algorithm on a dynamic model of a continuously-stirred tank reactor.

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.

Global output feedback regulation of uncertain nonlinear systems with unknown time delay

This paper investigates the problem of global output feedback regulation for a class of nonlinear systems with unknown time delay. It is also allowed to contain uncertain functions of all the states and input as long as the uncertainties satisfying certain bounded condition for the considered systems. In this paper, a constructive control technique has been proposed for controlling the systems. By using dynamic high-gain scaling approach and choosing an appropriate Lyapunov-Krasovskii functional, a delay-independent robust adaptive output feedback controller is constructed such that the states of the considered systems achieve global regulation. Two simulation examples are provided to demonstrate the effectiveness of the proposed design scheme.

Delayed Feedback Asymptotic Stabilization of Rigid Body Attitude Motion for Large Rotations

The delayed feedback control of rigid body attitude motion is addressed where there is an unknown time delay in the feedback measurement. The attitude motion is described on the tangent bundle TSO(3) to globally and uniquely represent the orientation of the rigid body, while a continuous nonlinear delayed feedback control law is proposed for local asymptotic stabilization on TSO(3). For this purpose, we introduce a notion based on the Lyapunov technique, which combines the Morse-Lyapunov method with Lyapunov-Krasovskii technique to yield a suitable Morse-Lyapunov-Krasovskii (M-L–K) functional, from which the stability conditions and proper control gain matrices are obtained in terms of linear matrix inequalities (LMIs). Simulations illustrate the performance of the proposed control scheme.

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.

PARAMETER ESTIMATION FOR NOISY CHAOTIC SYSTEMS BASED ON AN IMPROVED PARTICLE SWARM OPTIMIZATION ALGORITHM

It is of great importance to estimate the unknown parameters and time delays of chaotic systems in control and synchronization. This paper is concerned with the uncertain parameters and time delays of chaotic systems corrupted with random noise. Parameters and time delays of such chaotic systems are estimated based on the improved particle swarm optimization algorithm for its global searching ability. Numerical simulations are given to show satisfactory results.

Adaptive Synchronization of Fractional Neural Networks with Unknown Parameters and Time Delays

In this paper, the parameters identification and synchronization problem of fractional-order neural networks with time delays are investigated. Based on some analytical techniques and an adaptive control method, a simple adaptive synchronization controller and parameter update laws are designed to synchronize two uncertain complex networks with time delays. Besides, the system parameters in the uncertain network can be identified in the process of synchronization. To demonstrate the validity of the proposed method, several illustrative examples are presented.

The Butterfly-Shaped Feedback Loop in Networked Control Systems for the Unknown Delay Compensation

Available model-based networked control system (NCS) design approaches are basically formulated from the known system model and the information of the networked-induced delay time. Because the delay in remote control systems is significant and time-varied as commercial networks involved, available model- based NCS design approaches may thus become impractical. The increase of time delay due to the limited communication bandwidth usually induces data dropout to make NCS design even more difficult.Inthispaper,theschemeoftheperfectdelaycompensation (PDC) is proposed by introducing the butterfly-shaped inner feed- back loop in NCS to deal with the unknown network-induced time delay. Furthermore, analytical results indicate that the controller obtained in general control systems can be directly implemented on NCS with the proposed PDC scheme. Both simulation and experi- mental results were successfully carried out on an ac servo motor at a distance of 15 km through Ethernet to maintain a stable remote control system.

Adaptive Consensus Control for a Class of Nonlinear Multiagent Time-Delay Systems Using Neural Networks

Because of the complexity of consensus control of nonlinear multiagent systems in state time-delay, most of previous works focused only on linear systems with input time-delay. An adaptive neural network (NN) consensus control method for a class of nonlinear multiagent systems with state time-delay is proposed in this paper. The approximation property of radial basis function neural networks (RBFNNs) is used to neutralize the uncertain nonlinear dynamics in agents. An appropriate Lyapunov-Krasovskii functional, which is obtained from the derivative of an appropriate Lyapunov function, is used to compensate the uncertainties of unknown time delays. It is proved that our proposed approach guarantees the convergence on the basis of Lyapunov stability theory. The simulation results of a nonlinear multiagent time-delay system and a multiple collaborative manipulators system show the effectiveness of the proposed consensus control algorithm.

Markovian jump guaranteed cost congestion control strategies for large scale mobile networks with differentiated services traffic

In this paper, two novel congestion control strategies for mobile networks with differentiated services (Diff-Serv) traffic are presented, namely (i) a Markovian jump decentralized guaranteed cost congestion control strategy, and (ii) a Markovian jump distributed guaranteed cost congestion control strategy. The switchings or changes in the network topology are modeled by a Markovian jump process. By utilizing guaranteed cost control principles, the proposed congestion control schemes do indeed take into account the associated physical network resource constraints and are shown to be robust to unknown and time-varying network latencies and time delays. A set of Linear Matrix Inequality (LMI) conditions are obtained to guarantee the QoS of the Diff-Serv traffic with a guaranteed upper bound cost. Simulation results are presented to illustrate the effectiveness and capabilities of our proposed strategies. Comparisons with centralized and other relevant works in the literature focused on Diff-Serv traffic and mobile networks are also provided to demonstrate the advantages of our proposed solutions.

Robust adaptive control of switched non-linear systems in strict feedback form with unknown time delay

Robust adaptive control of switched non-linear systems in strict feedback form with unknown time delay