Adaptive neural dynamic surface control of MIMO nonlinear time delay systems with time‐varying actuator failures

In this paper, an adaptive dynamic surface control approach is developed for a class of multi‐input multi‐output nonlinear systems with unknown nonlinearities, bounded time‐varying state delays, and in the presence of time‐varying actuator failures. The type of the considered actuator failure is that some unknown inputs may be stuck at some time‐varying values where the values, times, and patterns of the failures are unknown. The considered actuator failure can cover most failures that may occur in actuators of the systems. With the help of neural networks to approximate the unknown nonlinear functions and combining the dynamic surface control approach with the backstepping design method, a novel control approach is constructed. 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 neighborhood of the origin. The proposed approach is employed for a double inverted pendulums benchmark as well as a chemical reactor system. The simulation results show the effectiveness of the proposed method. Copyright © 2016 John Wiley & Sons, Ltd.     

Adaptive backstepping control for a class of time delay systems with nonlinear perturbations

The sliding mode control method has been extensively employed to stabilize time delay systems with nonlinear perturbations. Although the resulting closed‐loop systems have good transient and steady‐state performances, the designed controllers are dependent on the time delays. But one knows that it is difficult to obtain the precise delay time in practical systems, especially when it is time varying. In this paper, we revisit the problem and use the backstepping method to construct the state feedback controller. First, a coordinate transformation is used to obtain a cascade time delay system. Then, a linear virtual control law is designed for the first subsystem. The memoryless controller is further constructed based on adaptive method for the second subsystem with the uncertainties bounded by linear function. By choosing new Lyapunov–Krasovskii functional, we show that the system state converges to zero asymptotically. Via the proposed approach, we also discuss the case that the uncertainties are bounded by nonlinear functions. Finally, simulations are done to verify the effectiveness of the main results obtained. Copyright © 2007 John Wiley & Sons, Ltd.     

Prescribed performance adaptive fuzzy dynamic surface control of nonaffine time‐varying delayed systems with unknown control directions and dead‐zone input

In this paper, an adaptive prescribed performance control method is presented for a class of uncertain strict feedback nonaffine nonlinear systems with the coupling effect of time‐varying delays, dead‐zone input, and unknown control directions. Owing to the universal approximation property, fuzzy logic systems are used to approximate the uncertain terms in the system. Since there is no systematic approach to determine the required upper bounds of errors in control systems, the prior selection of control parameters to have a satisfactory performance is somehow impossible. Therefore, the prescribed performance technique as a solution is applied in this study to bring satisfactory performance indices to the system such as overshoot and steady state performance within a predetermined bound. Dynamic surface control strategy is also introduced to the proposed control scheme to address the “explosion of complexity” behavior existing in conventional backstepping methods. To ease the control design, the mean‐value theorem is utilized to transform the nonaffine system into the affine one. Moreover, with the help of this theorem, the unknown dead‐zone nonlinearity is separated into the linear and nonlinear disturbance‐like bounded term. The proposed method relaxes a prior knowledge of control direction by employing Nussbaum‐type functions, and the effect of time‐varying delays are compensated by constructing the proper Lyapunov‐Krasovskii functions. The proposed controller guarantees that all the closed‐loop signals are semiglobally uniformly ultimately bounded and the error evolves within the decaying prescribed bounds. In the end, in order to demonstrate the superiority of this method, simulation examples are given.     

Adaptive neural dynamic surface control of MIMO stochastic nonlinear systems with unknown control directions

In this paper, an adaptive neural output‐feedback control approach is considered for a class of uncertain multi‐input and multi‐output (MIMO) stochastic nonlinear systems with unknown control directions. Neural networks (NNs) are applied to approximate unknown nonlinearities, and K‐filter observer is designed to estimate unavailable system's states. Due to utilization of Nussbaum gain function technique in the proposed approach, the singularity problem and requirement to prior knowledge about signs of high‐frequency gains are removed, simultaneously. Razumikhin functional method is employed to deal with unknown state time‐varying delays, so that the offered control approach is free of common assumptions on derivative of time‐varying delays. Also, an adaptive neural dynamic surface control is developed; hence, explosion of complexity in conventional backstepping method is eliminated, effectively. The boundedness of all the resulting closed‐loop signals is guaranteed in probability; meanwhile, convergence of the tracking errors to adjustable compact set in the sense of mean quartic value is also proved. Finally, simulation results are shown to verify and clarify efficiency of the offered approach. Copyright © 2016 John Wiley & Sons, Ltd.     

Robust adaptive dynamic surface control for linear time‐varying systems

In this paper, robust output‐feedback tracking control is considered for a class of linear time‐varying plants whose time‐varying parameters are unknown bounded with bounded derivatives and output is affected by unknown bounded additive disturbances. Using adaptive dynamic surface control technique, the proposed scheme possesses the following advantages: (1) the design procedure is simple and the control law is easy to be implemented, and (2) by introducing an initialization technique, together with adjusting some design parameters, the performance of system tracking error can be guaranteed regardless of the time variation. It is proved that with the proposed scheme, all the closed‐loop signals are semi‐globally uniformly ultimately bounded. Simulation results are presented to demonstrate the effectiveness of the proposed scheme. Copyright © 2013 John Wiley & Sons, Ltd.     

Decentralized adaptive control of nonlinear large‐scale pure‐feedback interconnected systems with time‐varying delays

In this paper, an adaptive decentralized neural control problem is addressed for a class of pure‐feedback interconnected system with unknown time‐varying delays in outputs interconnections. By taking advantage of implicit function theorem and the mean‐value theorem, the difficulty from the pure‐feedback form is overcome. Under a wild assumption that the nonlinear interconnections are assumed to be bounded by unknown nonlinear functions with outputs, the difficulties from unknown interconnections are dealt with, by introducing continuous packaged functions and hyperbolic tangent functions, and the time‐varying delays in interconnections are compensated by Lyapunov–Krasovskii functional. Radial basis function neural network is used to approximate the unknown nonlinearities. Dynamic surface control is successfully extended to eliminate ‘the explosion of complexity’ problem in backstepping procedure. To reduce the computational burden, minimal learning parameters technique is successfully incorporated into this novel control design. A delay‐independent decentralized control scheme is proposed. With the adaptive neural decentralized control, only one estimated parameter need to be updated online for each subsystem. Therefore, the controller is more simplified than the existing results. Also, semiglobal uniform ultimate boundedness of all of the signals in the closed‐loop system is guaranteed. Finally, simulation studies are given to demonstrate the effectiveness of the proposed design scheme. Copyright © 2013 John Wiley & Sons, Ltd.     

Adaptive fuzzy output feedback backstepping control of pure‐feedback nonlinear systems via dynamic surface control technique

In this paper, an adaptive fuzzy backstepping dynamic surface control approach is considered for a class of uncertain pure‐feedback nonlinear systems with immeasurable states. Fuzzy logic systems are first employed to approximate the unknown nonlinear functions, and then an adaptive fuzzy state observer is designed to estimate the immeasurable states. By the combination of the adaptive backstepping design with a dynamic surface control technique, an adaptive fuzzy output feedback backstepping control approach is developed. It is proven that all the signals of the resulting closed‐loop system are semi‐globally uniformly ultimately bounded, and the observer and tracking errors converge to a small neighborhood of the origin by choosing the design parameters appropriately. Simulation examples are provided to show the effectiveness of the proposed approach. Copyright © 2012 John Wiley & Sons, Ltd.     

Adaptive control for switched uncertain nonlinear systems with time‐varying output constraint and input saturation

This paper is concerned with adaptive tracking control for switched uncertain nonlinear systems, which contain the time‐varying output constraint (TVOC) and input asymmetric saturation characteristic. In response to the unknown functions, the fuzzy logic systems are adopted. The controller is constructed by the backstepping technique. Based on the Tangent Barrier Lyapunov Function (BLF‐Tan), an adaptive switched control scheme is designed. It is demonstrated that all signals in the resulted system are semiglobally uniformly ultimately bounded with TVOC under arbitrary switchings. Furthermore, the effectiveness of presented control method is validated via the simulation example.     

Adaptive robust H∞ state feedback control for linear uncertain systems with time‐varying delay

This paper considers the problem of adaptive robust H_∞ state feedback control for linear uncertain systems with time‐varying delay. The uncertainties are assumed to be time varying, unknown, but bounded. A new adaptive robust H_∞ controller is presented, whose gains are updating automatically according to the online estimates of uncertain parameters. By combining an indirect adaptive control method and a linear matrix inequality method, sufficient conditions with less conservativeness than those of the corresponding controller with fixed gains are given to guarantee robust asymptotic stability and H_∞ performance of the closed‐loop systems. A numerical example and its simulation results are given to demonstrate the effectiveness and the benefits of the proposed method. Copyright © 2008 John Wiley & Sons, Ltd.     

Dissipativity and passivity analysis for discrete‐time complex‐valued neural networks with leakage delay and probabilistic time‐varying delays

In this paper, the problem of dissipativity and passivity analysis is investigated for discrete‐time complex‐valued neural networks with time‐varying delays. Both leakage and discrete time‐varying delays have been considered. By constructing a suitable Lyapunov–Krasovskii functional and by using discretized Jensen's inequality approach, sufficient conditions have been established to guarantee the (Q ,S ,R ) ? γ dissipativity and passivity of the addressed discrete‐time complex‐valued neural networks. These conditions are derived in terms of complex‐valued linear matrix inequalities (LMIs), which can be checked numerically using Yet Another LMI Parser toolbox in Matrix Laboratory. Finally, three numerical examples are established to illustrate the effectiveness of the obtained theoretical results. Copyright © 2016 John Wiley & Sons, Ltd.     

Synchronization in nonlinear complex networks with multiple time‐varying delays via adaptive aperiodically intermittent control

This article is concerned with the problem of synchronization in nonlinear complex networks with multiple time‐varying delays via adaptive aperiodically intermittent control. The couplings inside nodes are assumed to be nonlinear and subject to multiple time‐varying delays. Meanwhile, the connection topology among the nodes can be directed and weighted. Then, the adaptive aperiodically intermittent control method is employed to realize synchronization and automatic modification to compensate the changes in dynamic errors. In addition, several synchronization criteria are rigorously induced based on the Lyapunov stability theory. Finally, the proposed control method is evaluated by utilizing numerical simulation. The results can be also applied to linear complex networks with delays.     

Adaptive observer for a class of nonlinear systems with time‐varying delays

The adaptive observer design problems have been extensively studied in literature for both linear and nonlinear systems. Some researches have also been carried out on adaptive observer design for linear time‐delay systems, but there is no significant work on adaptive observer design for nonlinear time‐delay systems. In this work, the adaptive observer design problem for a class of nonlinear time‐delay systems is considered. The observer is designed for the nonlinear systems whose nonlinear functions satisfy Lipschitz condition. Like conventional adaptive observers for the systems without time delays, this observer also estimates both states and unknown parameters simultaneously. For this property, it will be very much useful for many real‐time systems where time delays cannot be avoided. The sufficient conditions for existence of the observer are derived using the linear matrix inequality approach. With the help of a numerical example, effectiveness of the proposed observer is demonstrated. Copyright © 2012 John Wiley & Sons, Ltd.     

A combined backstepping and dynamic surface control to adaptive fuzzy state‐feedback control

This paper studies an adaptive fuzzy dynamic surface control for a class of nonlinear systems with fuzzy dead zone, unmodeled dynamics, dynamical disturbances, and unknown control gain functions. The unknown system functions are approximated by the Takagi‐Sugeno–type fuzzy logic systems. There are 3 main features for the presented systematic design scheme. First, by adopting an integrated method, a novel adaptive fuzzy controller is constructed for the nonlinear system with fuzzy dead zone. Second, only 3 online learning parameters need to be tuned, which significantly reduces the computation burden. Third, the possible controller singularity problem in some of the existing adaptive control methods with feedback linearization techniques can be avoided. On the basis of the backstepping technique and dynamic surface control, all the signals of the closed‐loop system are guaranteed to be semiglobally uniformly ultimately bounded. Finally, 2 simulation examples are provided to illustrate the effectiveness of the proposed scheme.     

Delay‐dependent robust stability analysis for interval neural networks with time‐varying delay

This article deals with the problem of robust stability for interval neural networks with time‐varying delay. By constructing an appropriate Lyapunov–Krasovskii functional, using the S‐procedure and taking the relationship among the time‐varying delay, its upper bound and their difference into account, some linear matrix inequality(LMI) ‐based delay‐dependent stability criteria are obtained without ignoring any terms in the derivative of the Lyapunov–Krasovskii functional. Finally, two numerical examples are given to demonstrate the effectiveness and benefits of the proposed method. © 2011 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.     

Adaptive reconfigurable control of systems with time‐varying delay against unknown actuator faults

This work is concerned with the problem of delay‐dependent adaptive fault‐tolerant controller design against unknown actuator faults for linear continuous systems with time‐varying delay. Based on the online estimation of possible faults by discontinuous adaptation law, identification parameters of the adaptive state feedback controller are updated autonomously to compensate the fault effects on the delayed system. For the first time, a convex combination idea and a projection‐type adaptive approach are combined organically to derive the main results. A set of new delay‐dependent reconfigurable stabilization criteria, which guarantee the stability of closed‐loop systems in both fault‐free and faulty cases, is established in terms of linear matrix inequalities. Two numerical instances for linear delayed systems and the linearized model for the lateral motion of Boeing 747 are respectively simulated to illustrate the superiority and the effectiveness of the presented adaptive delay‐dependent results. Copyright © 2013 John Wiley & Sons, Ltd.     

Adaptive stabilization of neutral systems with nonlinear perturbations and mixed time‐varying delays

This paper addresses the stabilization problem of neutral systems. The neutral systems assumed to be subjected to nonlinear perturbations and mixed time‐varying delays. Specifically, the adaptive control method is used to stabilize the unknown neutral systems. If the system states and the delayed states with its derivatives are available for measurement, a new and less conservative adaptive control algorithm is proposed, and sufficient conditions for the existence of the adaptive control are derived based on Lyapunov's stability theory. The main idea is to make all the stability conditions of the system depend on desired arbitrary matrices, not on the given system matrices. This is accomplished by the adaptation process. Illustrative examples with numerical simulations are studied. The simulation results show the effectiveness of the proposed design methods. Copyright © 2015 John Wiley & Sons, Ltd.     

Composite learning fuzzy synchronization for incommensurate fractional‐order chaotic systems with time‐varying delays

This paper presents a composite learning fuzzy control to synchronize two different uncertain incommensurate fractional‐order time‐varying delayed chaotic systems with unknown external disturbances and mismatched parametric uncertainties via the Takagi‐Sugeno fuzzy method. An adaptive controller together with fractional‐order composite learning laws is designed based on both a parallel distributed compensation technology and a fractional Lyapunov criterion. The boundedness of all variables in the closed‐loop system and the Mittag‐Leffler stability of tracking error can be guaranteed. T‐S fuzzy systems are provided to tackle unknown nonlinear functions. The distinctive features of the proposed approach consist in the following: (1) a supervisory control law is designed to compensate the lumped disturbances; (2) both the prediction error and the tracking error are used to estimate the unknown fuzzy system parameters; (3) parameter convergence can be ensured by an interval excitation condition. Finally, the feasibility of the proposed control strategy is demonstrated throughout an illustrative example.     

Adaptive neural control for nonstrict‐feedback stochastic nonlinear time‐delay systems with input and output constraints

This paper investigates an adaptive neural tracking control for a class of nonstrict‐feedback stochastic nonlinear time‐delay systems with input saturation and output constraint. First, the Gaussian error function is used to represent a continuous differentiable asymmetric saturation model. Second, the appropriate Lyapunov‐Krasovskii functional and the property of hyperbolic tangent functions are used to compensate the time‐delay effects, the neural network is used to approximate the unknown nonlinearities, and a barrier Lyapunov function is designed to ensure that the output parameters are restricted. At last, based on Lyapunov stability theory, a robust adaptive neural control method is proposed, and the designed controller decreases the number of learning parameters and thus reduces the computational burden. It is shown that the designed neural controller can ensure that all the signals in the closed‐loop system are 4‐Moment (or 2 Moment) semi‐globally uniformly ultimately bounded and the tracking error converges to a small neighborhood of the origin. Two examples are given to further verify the effectiveness of the proposed approach.     

Robust adaptive output‐feedback control for a class of nonlinear systems with time‐varying actuator faults

A robust adaptive output‐feedback control scheme is proposed for a class of nonlinear systems with unknown time‐varying actuator faults. Additional unmodelled terms in the actuator fault model are considered. A new linearly parameterized model is proposed. The boundedness of all the closed‐loop signals is established. The desired control performance of the closed‐loop system is guaranteed by appropriately choosing the design parameters. The properties of the proposed control algorithm are demonstrated by two simulation examples. Copyright © 2010 John Wiley & Sons, Ltd.     

Adaptive backstepping repetitive learning control design for nonlinear discrete‐time systems with periodic uncertainties

This paper addresses a tracking problem for uncertain nonlinear discrete‐time systems in which the uncertainties, including parametric uncertainty and external disturbance, are periodic with known periodicity. Repetitive learning control (RLC) is an effective tool to deal with periodic unknown components. By using the backstepping procedures, an adaptive RLC law with periodic parameter estimation is designed. The overparameterization problem is overcome by postponing the parameter estimation to the last backstepping step, which could not be easily solved in robust adaptive control. It is shown that the proposed adaptive RLC law without overparameterization can guarantee the perfect tracking and boundedness of the states of the whole closed‐loop systems in presence of periodic uncertainties. In addition, the effectiveness of the developed controller is demonstrated by an implementation example on a single‐link flexible‐joint robot. Copyright © 2014 John Wiley & Sons, Ltd.