An adaptive tracking problem for a family of retarded time-delay plants

Most of the existing switching control techniques are developed specifically for finite-dimensional linear time-invariant (LTI) systems. In many practical applications, however, it is essential to take time delay into consideration in the modelling as the control system can be highly sensitive to delay. In this paper, a multi-model switching control algorithm is proposed for retarded time-delay systems. It is assumed that the plant is represented by a family of known multi-input multi-output, observable, LTI models with multiple delays in the states, and that corresponding to each model in the known family, there exists a high-performance finite-dimensional LTI controller. In addition, it is supposed that a bound on the magnitude of the external inputs and disturbances is available. It is then shown that the proposed switching controller can stabilize the uncertain system, and that under some mild conditions, output tracking can be achieved in the given problem setting. Copyright © 2007 John Wiley & Sons, Ltd.     

Robust adaptive tracking control of uncertain discrete time systems

In this paper, the problem of robust adaptive tracking for uncertain discrete‐time systems is considered from the slowly varying systems point of view. The class of uncertain discrete‐time systems considered is subjected to both 𝓁_∞ to 𝓁_∞ bounded unstructured uncertainty and external additive bounded disturbances. A priori knowledge of the dynamic model of the reference signal to be tracked is not completely known. For such problem, an indirect adaptive tracking controller is obtained by frozen‐time controllers that at each time optimally robustly stabilize the estimated models of the plant and minimize the worst‐case steady‐state absolute value of the tracking error of the estimated model over the model uncertainty. Based on 𝓁_∞ to 𝓁_∞ stability and performance of slowly varying system found in the literature, the proposed adaptive tracking scheme is shown to have good robust stability. Moreover, a computable upper bound on the size of the unstructured uncertainty permitted by the adaptive system and a computable tight upper bound on asymptotic robust steady‐state tracking performance are provided. Copyright © 2005 John Wiley & Sons, Ltd.     

An adaptive regulation method for a class of uncertain time‐delay systems

In this paper, a new adaptive robust stabilization scheme is proposed for uncertain neutral time‐delay systems. No upper bounds on the uncertainties are assumed to be available. An update law is first used to find estimates of these upper bounds. A state‐feedback controller is then designed, which is shown to stabilize the underlying system under some mild conditions. The asymptotic stability of the state trajectories is proved using the Lyapunov–Krasovskii approach. An example is provided, which demonstrates the efficacy of the proposed adaptive control scheme. Copyright © 2012 John Wiley & Sons, Ltd.     

A switching periodic adaptive control approach for time‐varying parameters with unknown periodicity

Periodic variations are encountered in many real systems, which can exist in the system parameters, as a disturbance or as the tracking objective. However, there exist a great number of situations where the periodicity is not known in advance. Hence, how to compensate for the effects of time‐varying parameters with unknown periodicity remains a challenge for the controller design. In this paper, we proposed a switching periodic adaptive control approach for continuous‐time nonlinear parametric systems with periodic uncertainties in which the period and bound are not known in advance. We utilized a fully saturated periodic adaptation law to identify the unknown periodic parameters in a pointwise manner. In addition, we provided a logic‐based switching scheme to estimate the unknown period and bound online simultaneously. By virtue of Lyapunov stability analysis, we show that the asymptotic convergence can be guaranteed irrespective of the initial conditions. Finally, we carried out numerical simulations to demonstrate the efficacy of the switching periodic adaptive control algorithm. The proposed approach can be applied to parametric nonlinear systems with time‐varying parameters of unknown periodicity irrespective of the types of periodic uncertainties. Copyright © 2015 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.     

Fault detection filter design for networked control systems with time‐varying sampling periods and packet dropouts

This paper investigates the problem of fault detection for networked control systems under simultaneous consideration of time‐varying sampling periods and packet dropouts. By taking time‐varying sampling periods into consideration, a new closed‐loop model for the considered networked control systems is established. The sampling period switching‐based approach and the parameter uncertainty‐based approach are adopted to deal with time‐varying sampling periods. Based on the established model, the observer‐based fault detection filter design criteria are proposed to asymptotically stabilize the residual system in the sense of mean‐square. The designed observer‐based fault detection filter can guarantee the sensitivity of the residual signal to faults. The simulation results illustrate the effectiveness of the obtain results. Copyright © 2015 John Wiley & Sons, Ltd.     

Sliding mode control of singularly perturbed Markovian jump delayed systems with nonlinearity

This paper is concerned with sliding mode control (SMC) of a class of time‐delay nonlinear singularly perturbed Markovian jump systems. Firstly, a switching surface function is designed, and a delay‐dependent condition is derived in terms of ?‐independent linear matrix inequality, which guarantees that the resulting sliding mode dynamics is mean‐square exponentially stable. Then an algorithm is given to estimate the stability bound. Moreover, an adaptive SMC law is synthesized to drive the system trajectories onto the designed switching surface in a finite time. Finally, a numerical example is presented to show the effectiveness of proposed method. Copyright © 2012 John Wiley & Sons, Ltd.     

Model‐free fault‐tolerant control approach for uncertain state‐constrained linear systems with actuator faults

This paper investigates the robust adaptive fault‐tolerant control problem for state‐constrained continuous‐time linear systems with parameter uncertainties, external disturbances, and actuator faults including stuck, outage, and loss of effectiveness. It is assumed that the knowledge of the system matrices, as well as the upper bounds of the disturbances and faults, is unknown. By incorporating a barrier‐function like term into the Lyapunov function design, a novel model‐free fault‐tolerant control scheme is proposed in a parameter‐dependent form, and the state constraint requirements are guaranteed. The time‐varying parameters are adjusted online based on an adaptive method to prevent the states from violating the constraints and compensate automatically the uncertainties, disturbances, and actuator faults. The time‐invariant parameters solved by using data‐based policy iteration algorithm are introduced for helping to stabilize the system. Furthermore, it is shown that the states converge asymptotically to zero without transgression of the constraints and all signals in the resulting closed‐loop system are uniformly bounded. Finally, two simulation examples are provided to show the effectiveness of the proposed approach. Copyright © 2016 John Wiley & Sons, Ltd.     

A design of multivariable,self‐tuning PID controllers with an internal model structure

Self‐tuning control schemes (STC) are useful for systems with unknown or slowly time‐varying parameters. Some single‐input/single‐output PID control schemes based on STCs have been proposed for such systems. However, there are a lot of multivariable systems in real process industries. And these systems often have relatively large time delays. In this paper, a design scheme of self‐tuning PID control system is proposed for multivariable systems with unknown parameters and time delays. The controlled object is equipped with an internal model in order to compensate the time delay and also unstable zeros. Subsequently, a multivariable PID controller is designed for the augmented or compensated system. The PID parameters are calculated recursively based on the relationship between the minimum variance control law and the PID control law. A simulation example is presented to demonstrate the effectiveness of the proposed scheme. © 2004 Wiley Periodicals, Inc. Electr Eng Jpn, 146(4): 58–64, 2004; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.10241     

Robust output tracking of uncertain nonlinear time‐delay systems with unknown dead‐zone inputs via control schemes with a simple structure

The adaptive robust output tracking control problem is considered for a class of uncertain nonlinear time‐delay systems with completely unknown dead‐zone inputs. A new design method is proposed so that some adaptive robust output tracking control schemes with a rather simple structure can be constructed. It is not necessary to know the nonlinear upper bound functions of uncertain nonlinearities. In fact, the constructed output tracking control schemes are structurally linear in the state and have a self‐tuning control gain function that is updated by an adaptation law. In this paper, the dead‐zone input is nonsymmetric, and its information is assumed to be completely unknown. In addition, a numerical example is given to describe the design procedure of the presented method, and the simulations of this numerical example are implemented to demonstrate the validity of the theoretical results.     

Delay‐dependent model reduction for continuous‐time switched state‐delayed systems

This paper studies the problem of exponential H_∞ model reduction for continuous‐time switched delay system under average dwell time (ADT) switching signals. Time delay under consideration is interval time varying. Our attention is focused on the construction of the desired reduced order models, which guarantee that the resulting error systems under ADT switching signals are exponentially stable with an H_∞ norm bound. By introducing a block matrix and making use of the ADT approach, delay‐dependent sufficient conditions for the existence of reduced order models are derived and formulated in terms of strict linear matrix inequalities (LMIs). Owing to the absence of non‐convex constraints, it is tractable to construct an admissible reduced order model. The effectiveness of the proposed methods is illustrated via two numerical examples. Copyright © 2011 John Wiley & Sons, Ltd.     

Adaptive sliding mode control for fuzzy singular systems with time delay and input nonlinearity

This paper addresses the sliding mode control problem for a class of uncertain Takagi‐Sugeno fuzzy singular systems with state delay and subject to input nonlinearity. Our purpose is focused on designing an adaptive sliding mode controller for such a complex system. First, a new fuzzy integral‐type sliding function is designed. Then, an adaptive sliding mode control scheme is established such that the resulting closed‐loop system is insensitive to all admissible uncertainties and satisfies the reaching condition. Moreover, delay‐dependent sufficient conditions are derived such that the admissibility and the L₂‐L_∞ performance requirement of the sliding mode dynamics can be guaranteed in the presence of time delays, external disturbances, and sector nonlinearity input. Finally, the validity and applicability of the proposed theory are illustrated by a numerical example.     

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.     

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.     

Multi‐objective optimization power control for code division multiple access systems

In code division multiple access (CDMA) communication systems, the communication channel is usually corrupted with time‐varying interferences, which include channel fading, multiple access interference, round‐trip delay, and noise. Power control is an important issue for CDMA systems to achieve higher communication link quality and better system capacity under time‐varying interferences. In the previous studies, most of power control algorithms only considered the user's target signal‐to‐interference‐and‐noise‐ratio (SINR) to maintain quality of service. In this study, a multi‐objective optimization method is proposed for power control design in CDMA systems. With a shadow system and an h _∞ filter to compensate for the round‐trip delay, the proposed power control scheme can simply adjust transmission power to achieve the best compromise between several objectives, such as minimization of SINR deviation, minimization of power consumption, and minimization of the system outage. Several simulation results are given to confirm the performance of the proposed power control scheme. Copyright © 2013 John Wiley & Sons, Ltd.     

Adaptive TS‐FNN control for a class of uncertain multi‐time‐delay systems: The exponentially stable sliding mode‐based approach

This paper presents an adaptive Takagi–Sugeno fuzzy neural network (TS‐FNN) control for a class of multiple time‐delay uncertain nonlinear systems. First, we develop a sliding surface guaranteed to achieve exponential stability while considering mismatched uncertainty and unknown delays. This exponential stability result based on a novel Lyapunov–Krasovskii method is an improvement when compared with traditional schemes where only asymptotic stability is achieved. The stability analysis is transformed into a linear matrix inequalities problem independent of time delays. Then, a sliding mode control‐based TS‐FNN control scheme is proposed to achieve asymptotic stability for the controlled system. Since the TS‐FNN combines TS fuzzy rules and a neural network structure, fewer numbers of fuzzy rules and tuning parameters are used compared with the traditional pure TS fuzzy approach. Moreover, all the fuzzy membership functions are tuned on‐line even in the presence of input uncertainty. Finally, simulation results show the control performance of the proposed scheme. Copyright © 2008 John Wiley & Sons, Ltd.     

Optimal control of uncertain quantized linear discrete‐time systems

In this paper, the adaptive optimal regulator design for unknown quantized linear discrete‐time control systems over fixed finite time is introduced. First, to mitigate the quantization error from input and state quantization, dynamic quantizer with time‐varying step‐size is utilized wherein it is shown that the quantization error will decrease overtime thus overcoming the drawback of the traditional uniform quantizer. Next, to relax the knowledge of system dynamics and achieve optimality, the adaptive dynamic programming methodology is adopted under Bellman's principle by using quantized state and input vector. Because of the time‐dependency nature of finite horizon, an adaptive online estimator, which learns a newly defined time‐varying action‐dependent value function, is updated at each time step so that policy and/or value iterations are not needed. Further, an additional error term corresponding to the terminal constraint is defined and minimized along the system trajectory. The proposed design scheme yields a forward‐in‐time and online scheme, which enjoys great practical merits. Lyapunov analysis is used to show the boundedness of the closed‐loop system; whereas when the time horizon is stretched to infinity as in the case of infinite horizon, asymptotic stability of the closed‐loop system is demonstrated. Simulation results on a benchmarking batch reactor system are included to verify the theoretical claims. The net result is the design of the optimal adaptive controller for uncertain quantized linear discrete‐time systems in a forward‐in‐time manner. Copyright © 2014 John Wiley & Sons, Ltd.     

Decentralized output feedback controller design for nonlinear interconnected systems with unknown control direction and time‐varying delays

The decentralized output feedback control problem is considered for a class of large‐scale systems with unknown time‐varying delays. The uncertain interconnections are bounded by general nonlinear functions with unknown coefficients. The control direction parameters are unknown for each subsystem, which brings a challenging issue for decentralized controller design. To deal with this problem, we propose a new decentralized control scheme with the help of Nussbaum function. The decentralized filter is designed at first. By constructing Lyapunov–Krasovskii functional, we design the dynamic output feedback controller. It is rigorously proved that the closed‐loop system is asymptotically stable. Finally, the simulation is performed, and the results verify the effectiveness of the proposed method. Copyright © 2013 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.     

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.