Adaptive Robust Output Tracking Control of Uncertain Nonlinear Cascade Systems with Disturbance and Multiple Unknown Time‐Varying Delays

In this paper, an adaptive robust controller is designed for a class of uncertain nonlinear cascade systems with multiple time‐varying delays under external disturbance. It is assumed that multiple time‐varying delays are not exactly known and, therefore, the delayed terms must not appear in the adaptation and control laws. Accordingly, by using a Lyapunov‐Krasovskii function, delays are deleted from the adaptation and control laws. A controller based on an adaptive backstepping approach is designed to assure the global asymptotic tracking of the desired output and boundedness of the other states. The proposed controller is proved to be robust against unknown time‐varying delays and external disturbances applying to the system. Simulation results are provided to show the effectiveness of the proposed approach.     

Robust flow control in data‐communication networks with multiple time‐delays

Robust controller design for a flow control problem where uncertain multiple time‐varying time‐delays exist is considered. Although primarily data‐communication networks are considered, the presented approach can also be applied to other flow control problems and can even be extended to other control problems where uncertain multiple time‐varying time‐delays exist. Besides robustness, tracking and fairness requirements are also considered. To solve this problem, an ??^∞ optimization problem is set up and solved. Unlike previous approaches, where only a suboptimal solution could be found, the present approach allows to design an optimal controller. Simulation studies are carried out in order to illustrate the time‐domain performance of the designed controllers. The obtained results are also compared to the results of a suboptimal controller obtained by an earlier approach. Copyright © 2009 John Wiley & Sons, Ltd.     

Global adaptive stabilization for high‐order uncertain time‐varying nonlinear systems with time‐delays

This paper focuses on the adaptive stabilization problem for a class of high‐order nonlinear systems with time‐varying uncertainties and unknown time‐delays. Time‐varying uncertain parameters are compensated by combining a function gain with traditional adaptive technique, and unknown multiple time‐delays are manipulated by the delicate choice of an appropriate Lyapunov function. With the help of homogeneous domination idea and recursive design, a continuous adaptive state‐feedback controller is designed to guarantee that resulting closed‐loop systems are globally uniformly stable and original system states converge to zero. The effectiveness of the proposed control scheme is illustrated by the stabilization of delayed neural network systems. Copyright © 2016 John Wiley & Sons, Ltd.     

Global output feedback regulation of nonlinear time delay systems subject to sensor measurement faults

This article studied the global output feedback regulation problem for a class of uncertain nonlinear time delay systems subject to unknown measurement faults on sensors. Different from the existing works, we consider the unknown time‐varying delays on the system states and relax their conservative condition on nonlinear functions. By introducing two novel time‐varying gains, a new global output feedback regulation algorithm is proposed, which ensures control parameters can be chosen flexibly. The proposed linear‐like controller is independent of the unknown time‐varying delays. Moreover, it has a simple structure, which is convenient for the implementation in practice. Based on the Lyapunov stability theory, it is strictly proved that all signals of the resulting closed‐loop system are globally bounded with the designed controller. Finally, a simulation example is presented to illustrate the effectiveness of the proposed output feedback regulation algorithm.     

Finite‐Time Stabilization of Coupled Systems on Networks with Time‐Varying Delays via Periodically Intermittent Control

In this paper, finite‐time stabilization of coupled systems on networks with time‐varying delays (CSNTDs) via periodically intermittent control is studied. Both delayed subsystems and delayed couplings are considered; the self‐delays of different subsystems in delayed couplings are not identical. A periodically intermittent controller is designed to stabilize CSNTDs within finite time, and the stabilization duration is closely related to the topological structures of networks. Furthermore, two sufficient criteria are developed to ensure CSNTDs under periodically intermittent control can be stabilized within finite time by using an approach that combines the Lyapunov method with Kirchhoff's Matrix Tree Theorem. Then finite‐time stabilization of coupled oscillators with time‐varying delays is given as a practical application and sufficient criteria is obtained. Finally, a numerical simulation is proposed to support our results and show the effectiveness of the controller.     

ADAPTIVE ROBUST CONTROL OF UNCERTAIN SYSTEMS WITH TIME‐VARYING STATE DELAY

In this paper, a new adaptive robust control scheme is developed for a class of uncertain dynamical systems with time‐varying state delay, unknown parameters and disturbances. By incorporating adaptive techniques into the robust control method, we propose a continuous adaptive robust controller which guarantees the uniform boundedness of the system and at the same time, the regulating error enters an arbitrarily designated zone in a finite time. The proposed controller is independent of the time‐delay, hence it is applicable to a class of dynamical systems with uncertain time delays. The paper includes simulation studies demonstrating the performance of the proposed control scheme.     

Robust exponential stability of uncertain stochastic systems with probabilistic time‐varying delays

This paper is concerned with the problem of delay‐distribution–dependent robust exponential stability for uncertain stochastic systems with probabilistic time‐varying delays. Firstly, inspired by a class of networked systems with quantization and packet losses, we study the stabilization problem for a class of network‐based uncertain stochastic systems with probabilistic time‐varying delays. Secondly, an equivalent model of the resulting closed‐loop network‐based uncertain stochastic system is constructed. Different from the previous works, the proposed equivalent system model enables the controller design of the network‐based uncertain stochastic systems to enjoy the advantage of probability distribution characteristic of packet losses. Thirdly, by applying the Lyapunov‐Krasovskii functional approach and the stochastic stability theory, delay‐distribution–dependent robust exponential mean‐square stability criteria are derived, and the sufficient conditions for the design of the delay‐distribution–dependent controller are then proposed to guarantee the stability of the resulting system. Finally, a case study is given to show the effectiveness of the results derived. Moreover, the allowable upper bound of consecutive packet losses will be larger in the case that the probability distribution characteristic of packet losses is taken into consideration.     

Adaptive Neural Dynamic Surface Control For Nonlinear Pure‐Feedback Systems With Multiple Time‐Varying Delays: A Lyapunov‐Razumikhin Method

This paper focuses on the problem of adaptive neural control for a class of uncertain nonlinear pure‐feedback systems with multiple unknown time‐varying delays. The considered problem is challenging due to the non‐affine pure‐feedback form and the unknown system functions with multiple unknown time‐varying delays. Based on a novel combination of mean value theorem, Razumikhin functional method, dynamic surface control (DSC) technique and neural network (NN) parameterization, a new adaptive neural controller which contains only one parameter is developed for such systems. Moreover, The DSC technique can overcome the problem of ‘explosion of complexity’ in the traditional backstepping design procedure. All closed‐loop signals are shown to be semi‐globally uniformly ultimately bounded, and the tracking error converges to a small neighborhood of the origin. Two simulation examples are given to verify the effectiveness of the proposed design.     

Performance and Robustness of Flow Controllers Designed Using Non‐causal Uncertainty Blocks

According to some recent results, use of non‐causal uncertainty blocks may be advantageous in the robust controller design of systems with multiple uncertain time‐delays. In this work, performance and robustness improvements obtained by utilizing such an approach are presented. The flow controller design problem for networks with multiple uncertain time‐delays is considered as a case study. It is shown that higher performance levels and larger stability margins are, in general, obtained by using non‐causal uncertainty blocks. A number of simulations, which illustrate the time‐domain performance improvement, are also presented.     

Robust‐decentralized tracking control for a class of uncertain MIMO nonlinear systems with time‐varying delays

A new control design method based on signal compensation is proposed for a class of uncertain multi‐input multi‐output (MIMO) nonlinear systems in block‐triangular form with nonlinear uncertainties, unknown virtual control coefficients, strongly coupled interconnections, time‐varying delays, and external disturbances. By this method, the controller design is performed in a backstepping manner. At each step of backstepping procedure, a nominal virtual controller is first designed to get desired output tracking for the nominal disturbance‐free subsystem, and then a robust virtual compensator is designed to restrain the effect of the uncertainties, delays involved in the subsystem, and the couplings among the subsystems. The designed controller is linear and time‐invariant, so the explosion of complexity in the control law is avoid. It is proved that robust stability and robust practical tracking property of the closed‐loop system can be ensured, and the tracking errors can be made as small as desired. Copyright © 2013 John Wiley & Sons, Ltd.     

Stabilizing a first order system with an arbitrarily large time varying delay and an uncertain gain

Handling delays and uncertain parameters in control systems is difficult and of long-standing interest. In this paper, we consider the problem of stabilizing (in a bounded-input–bounded-output sense) a first order linear time invariant plant with an arbitrarily large time varying delay and an arbitrarily large uncertain gain; we propose the use of a mildly non-linear, periodic controller, which is simple to implement. We will derive a clear, simple formula relating the maximum delay duration, the location of the unstable plant pole and the bounds on the derivative of the delay for which our controller stabilizes the system.     

Almost Disturbance Decoupling for a Class of Nonlinear Systems Subject to Time‐Delays Via Sampled‐Data Output Feedback Control

This paper considers the problem of almost disturbance decoupling (ADD) via sampled‐data output feedback control for a class of uncertain nonlinear systems subject to time‐delays. Based on output feedback domination approach, a sampled‐data output feedback controller is designed to globally stabilize the system under a lower‐triangular linear growth condition. Gronwall‐Bellman‐like inequality and inductive method are introduced to estimate the state growth in the presence of time‐delays, uncertain nonlinearities and unknown disturbances. The proposed controller can attenuate the influence of disturbances on the output to an arbitrary degree in the L₂ gain sense. Finally, simulation results show the effectiveness of the control method.     

Dynamic output feedback control with output quantizer for nonlinear uncertain T‐S fuzzy systems with multiple time‐varying input delays and unmatched disturbances

The dynamic output feedback control problem with output quantizer is investigated for a class of nonlinear uncertain Takagi‐Sugeno (T‐S) fuzzy systems with multiple time‐varying input delays and unmatched disturbances. The T‐S fuzzy model is employed to approximate the nonlinear uncertain system, and the output space is partitioned into operating regions and interpolation regions based on the structural information in the fuzzy rules. The output quantizer is introduced for the controller design, and the dynamic output feedback controller with output quantizer is constructed based on the T‐S fuzzy model. Stability conditions in the form of linear matrix inequalities are derived by introducing the S‐procedure, such that the closed‐loop system is stable and the solutions converge to a ball. The control design conditions are relaxed and design flexibility is enhanced because of the developed controller. By introducing the output‐space partition method and S‐procedure, the unmatched regions between the system plant and the controller caused by the quantization errors can be solved in the control design. Finally, simulations are given to verify the effectiveness of the proposed method.     

Robust Control of Positive Fractional‐Order Interconnected Systems with Heterogeneous Delays

The problem of robust decentralized control of positive fractional‐order interconnected systems with heterogeneous time‐varying delays is studied in this paper. Necessary and sufficient conditions are first derived for internal positiveness of the system. By exploiting the monotonicity induced from positivity of the system, robust stability conditions subject to uncertain system parameters are derived. The derived stability conditions are then utilized to address the controller synthesis problem. The design conditions for obtaining controller gains of stabilizing decentralized controllers are formulated using linear programming, which can be effectively solved by various convex optimization algorithms. Finally, the effectiveness of the obtained results is validated by two numerical examples.     

Robust approximation‐based adaptive control of multiple state delayed nonlinear systems with unmodeled dynamics

This paper addresses the problem of tracking control for a class of uncertain nonstrict‐feedback nonlinear systems subject to multiple state time‐varying delays and unmodeled dynamics. To overcome the design difficulty in system dynamical uncertainties, radial basis function neural networks are employed to approximate the black‐box functions. Novel continuous functions that deal with whole states uncertainties are introduced in each step of the adaptive backstepping to make the controller design feasible. The robust problem caused by unmodeled dynamics when constructing a stable controller is solved by employing an auxiliary signal to regulate its boundedness. A novel Lyapunov‐Krasovskii functional is developed to compensate for the delayed nonlinearity without requiring the priori knowledge of its upper bound functions. On the basis of the proposed robust adaptive neural controller, all the closed‐loop signals are semiglobal uniformly ultimately bounded with good tracking performance.     

Robust containment control in a leader–follower network of uncertain Euler–Lagrange systems

A distributed controller is developed that yields cooperative containment control of a network of autonomous dynamical systems. The networked agents are modeled with uncertain nonlinear Euler–Lagrange dynamics affected by an unknown time‐varying exogenous disturbance. The developed continuous controller is robust to input disturbances and uncertain dynamics such that asymptotic convergence of the follower agents' states to the dynamic convex hull formed by the leaders' time‐varying states is achieved. Simulation results are provided to demonstrate the effectiveness of the developed controller. Copyright © 2016 John Wiley & Sons, Ltd.     

IQC‐synthesis with general dynamic multipliers

Analogously to the existing μ‐synthesis tools, we propose an alternative algorithm for the systematic design of robust controllers based on an iteration of standard nominal controller synthesis and integral quadratic constraint (IQC) analysis with general dynamic multipliers. The suggested algorithm enables us to perform robust controller synthesis for a significantly larger class of uncertainties if compared with the existing methods. Indeed, while the classical approaches are restricted to the use of real/complex time invariant or arbitrarily fast time‐varying parametric uncertainties, the IQC framework also offers, for example, the possibility to efficiently handle sector‐bounded and slope restricted nonlinearities or time‐varying parametric uncertainties and uncertain time‐varying time‐delays, both with bounds on the rate‐of‐variation. Secondly, in contrast to the classical approaches, the proposed techniques completely avoid gridding and curve‐fitting. We present new insights that allow us to reformulate the robust IQC analysis LMIs into a standard quadratic performance problem. This enables us to generate suitable initial conditions for each subsequent iteration step. Depending on the size of the problem, this can significantly speed up the synthesis process. The results are illustrated by means of two numerical examples. Copyright © 2013 John Wiley & Sons, Ltd.     

Delay‐dependent robust stability and stabilization of uncertain neutral systems

This paper discusses the problems of the delay‐dependent robust stability and stabilization of uncertain neutral systems with time‐varying delays. Delay‐dependent stability criteria are derived by taking the relationships between the terms in the Leibniz‐Newton formula into account. Free‐weighting matrices are employed to express these relationships, and they are easy to obtain because the new criteria are based on linear matrix inequalities. Moreover, the stability criteria are extended to the design of a stabilizing state feedback controller. Numerical examples demonstrate that these criteria are effective and are an improvement on previous ones. Copyright © 2008 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Robust stabilization and H∞ control of uncertain stochastic time‐delay systems with nonlinear perturbation

This paper investigates the problem of delay‐dependent robust stochastic stabilization and H_∞ control for uncertain stochastic nonlinear systems with time‐varying delay. System uncertainties are assumed to be norm bounded. Firstly, by using novel method to deal with the integral terms, robustly stochastic stabilization results are obtained for stochastic uncertain systems with nonlinear perturbation, and an appropriate memoryless state feedback controller can be chosen. Compared with previous results, the new technique can sufficiently utilize more negative items information. Then, robust H_∞ control for uncertain stochastic system with time‐varying delay and nonlinear perturbation is considered, and the controller is designed, which will guarantee that closed‐loop system is robustly stochastically stable with disturbance attenuation level. Finally, two numerical examples are listed to illustrate that our results are effective and less conservative than other reports in previous literature. Copyright © 2016 John Wiley & Sons, Ltd.     

Output Feedback Stabilization for a Class of Stochastic High‐Order Feedforward Nonlinear Systems with Time‐Varying Delay

This paper considers the output feedback control problem for a class of stochastic high‐order feedforward nonlinear systems with time‐varying delay. Compared with existing works, the features of our system include different bounded time‐varying delays, more general high‐order power and homogeneous feedforward growth conditions. Firstly, we use the adding one power integrator technique to construct an output feedback controller without nonlinearities. Then, by introducing a scaling gain into the controller and choosing an appropriate Lyapunov–Krasovskii functional, the closed‐loop system can be rendered globally asymptotically stable in probability. A simulation example is provided to illustrate the effectiveness of the designed controller.