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In this study, the decentralized model reference adaptive control (DMRAC) problem is tackled for a class of time‐varying delay interconnect systems that comprise unknown system matrices and unknown dead‐zone inputs. Two robust adaptive control methods are proposed for state tracking based on the moderate matching time‐varying delay nonlinear assumptions and the matching between the controlled system and reference model matrices, respectively. The control gain function is explicitly expressed, and it is applied to the adaptive law gains simultaneously. Moreover, a Lyapunov–Krasovskii functional with two integral functions is developed. Besides the properties of the type‐B Nussbaum function, the circumstance where the system parameters are fully unknown is considered. As indicated by the results, all signals in the closed‐loop system are bounded while fulfilling asymptotically tracked control objectives. The simulation example of this study verifies the effectiveness and feasibility of the proposed design method. [ABSTRACT FROM AUTHOR]

This paper addresses the adaptive output feedback control design problem for a class of nonlinear systems with unknown state time delays by combining the dynamic gain and neural network. A novel reduced-order dynamic gain observer is introduced to estimate the unmeasured system states. Radial basis function neural networks (RBF NNs) are used to approximate unknown functions. An adaptive NN output feedback controller is designed based on the backstepping technique. By arranging the proper Lyapunov–Krasovskii functional, we prove that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded. Finally, a physical example and a numerical example are given to prove the effectiveness of the proposed control scheme. [ABSTRACT FROM AUTHOR]

This article addresses the problem of adaptive tracking control for stochastic nonlinear systems with asymmetric full state constraints. Different from the traditional log‐type or tan‐type barrier Lyapunov functions (BLFs), a new asymmetric BLF is proposed in this article. Then, a state feedback controller is constructed with backstepping method so that all signals of the closed‐system are bounded and the asymmetric state constraint is well kept all the time. Without changing the structure of the controller, the design and the analysis for constrained and unconstrained systems are unified. Finally, the effectiveness of proposed control strategy has been demonstrated by simulations of numerical example and the single‐link robot arm model. [ABSTRACT FROM AUTHOR]

In this paper, by using bound estimation method, Nussbaum function, K‐filters and higher‐order Lyapunov function, an adaptive output feedback compensation control scheme is proposed for uncertain nonlinear systems with infinite number of actuator failures and unknown control direction. A parametric model with unknown system uncertainties and infinite actuator failures is established, which is different from the existing results. This scheme ensures that closed‐loop signals are globally uniformly bounded. By properly selecting the design parameters, the tracking errors converges to a small neighborhood of the origin. Finally, two simulation examples are given to demonstrate its efficiency of the proposed design scheme. [ABSTRACT FROM AUTHOR]

In this paper, asymptotic stabilization problem for a class of nonlinear systems with unknown time‐varying delays is addressed. With the introduced static gain functions and new Lyapunov–Krasovskii functionals, a novel output feedback control strategy is developed. A memoryless output feedback controller which does not need precise knowledge of time delays is designed. The asymptotic stabilization and the boundedness of the closed‐loop system are proved via Lyapunov analysis. Finally, numerical simulation validates the effectiveness of this method for the nonlinear time‐delay system. [ABSTRACT FROM AUTHOR]

Summary: This article develops a disturbance rejection control strategy using partial‐state feedback model reference adaptive control for discrete‐time uncertain systems with unknown input disturbances. Adaptive control schemes are proposed for constant disturbances, sinusoidal disturbances, and generic bounded disturbances. The partial‐state feedback control is designed based on measurable signals and the parameterization method to counteract the effect of disturbances. The plant‐model output matching condition is established. The developed control law is more flexible for applications and has a more concise structure than output feedback control. Additionally, closed‐loop stability and asymptotic output tracking are derived. The effectiveness and the feasibility of partial‐state feedback disturbance rejection control are verified by simulation results. [ABSTRACT FROM AUTHOR]

In this article, we extend the adaptive tracking control to more general nonlinear systems with multiple uncertainties, including output constraint, input delay, unknown parameter, and external disturbances for the first time. Without any growth assumptions, the adaptive backstepping technique is combined with the parameter separation technique to solve the parametric nonlinearities while the related results need to apply restrictive assumptions or use an approximation-based scheme to deal with them. To alleviate the serious uncertainties caused by output constraint and input delay, the barrier Lyapunov function (BLF) and the Pade approximation method are employed in a unified framework when the control coefficient is known. Under the case of the unknown control coefficient, the Nussbaum gain technique is further combined to compensate it. Then, under both cases, universal adaptive state-feedback control strategies merged with rigorous stability analysis are proposed, respectively, which guarantees all the signals are uniformly ultimately bounded. In addition, the reference signal tracks the system output into a compact set of the origin and the constraint of output is not violated. Finally, the proposed controllers are applied to an inverted pendulum system, which demonstrates the designed controller is effective. [ABSTRACT FROM AUTHOR]

In this article, adaptive state feedback stabilization is addressed for a class of delayed uncertain systems with external disturbance, where the time delays and the bound parameters of the delayed states and disturbance are assumed to be unknown. By introducing a new Lyapunov–Krasovskii functional, we present a memoryless control strategy to stabilize nonlinear time-delay systems through newly defined control gain function. The main contribution of this article lies in the construction of control gain function. Multiple gain functions can be revealed in a function set. The asymptotic stability of the closed delayed nonlinear system is ensured. Simulation examples are presented to show the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This article studies the adaptive backstepping control problem for a class of fractional-order (FO) nonlinear systems subject to input quantization and unknown control directions by combining with an indirect FO Lyapunov stability method, and a command filter-based FO dynamic surface control (FODSC) technique. First, a modified FODSC method is utilized to reduce the computational complexity existing in the conventional recursive procedure in which an FO command filter is designed to obtain the command signals and their FO derivatives. Furthermore, the Nussbaum function and neuro-fuzzy networks (NFNs) are adopted to deal with the problem of the unknown control directions and unknown nonlinear functions existing in the system. Moreover, by introducing the compensation and prediction mechanism to controller design, the adaptive controllers, and adaptive laws are constructed to ensure that all the signals of the controlled systems are bounded. Finally, two examples are given to show the validity of the developed control method. [ABSTRACT FROM AUTHOR]

For a class of nonlinear systems with mismatched time delays and disturbances, robust adaptive stabilization control is studied. The control law is split into two terms. One is used to cope with the delayed states, and the other is to handle the disturbance. The improved robust adaptive laws with control gain function and time-varying σ -modification are constructed to estimate the unknown integrated parameters. It is proved that the designed adaptive controller can ensure the asymptotic convergence of the closed-loop system states. Another adaptive algorithm is also proposed to ensure the asymptotic stability of the closed delayed nonlinear system without external disturbance. • We introduce control gain function ρ (⋅) and embed it into the Lyapunov–'Krasovskii functional. • Continuous memoryless control functions are designed. • The theoretical result is applied to chemical reactor. [ABSTRACT FROM AUTHOR]

The adaptive finite‐time event‐triggered quantized control for the nonlinear systems considering uncertain parameters and external disturbances is investigated in this article. First, for the parametric nonlinear systems with external disturbances, an adaptive finite‐time event‐triggered control scheme with input quantization is proposed. The designed controller can ensure the semiglobal finite‐time stability of the closed‐loop system. Then, to deal with the global finite‐time control problem for the parametric nonlinear systems, a novel adaptive quantized event‐triggered control scheme is constructed. Finally, two simulation examples are utilized to illustrate the effectiveness of the adaptive event‐triggered control schemes. [ABSTRACT FROM AUTHOR]

In this article, tracking control is considered for a class of uncertain multi-input–multi-output (MIMO) nonlinear systems, where the time-varying parameters, the time-varying control coefficient and the time-varying disturbance are assumed to be unknown but to be bounded. Three stable adaptive tracking schemes for a given reference signal are proposed by devising different control algorithms. In the first scheme, bounded-error tracking is achieved in the sense that the tracking error converges exponentially to an adjustable region around the origin, where the $\sigma $ -modification adaptive laws are used to ensure the boundedness of all closed-loop signals. In the second scheme, asymptotic tracking is obtained in the sense that the tracking error converges to zero asymptotically, where the strictly positive and integral functions are employed in the control law to ensure the signal boundedness and zero-error tracking. In the third scheme, exponential tracking is gotten in the sense that the tracking error exponentially converges to zero with a given convergence speed, where exponential functions are incorporated into control law and adaptive laws to ensure system stability and the faster convergence. Three adaptive tracking schemes are, respectively, applied to nonlinear chaotic Chua’s circuit with control inputs. The parametric model is developed for Chua’s circuit with uncertain parameters and external disturbances. The effectiveness of the proposed control algorithms is demonstrated by comparative simulation studies. [ABSTRACT FROM AUTHOR]

This article deals with the adaptive prescribed performance tracking for nonlinear time-varying systems. To handle multiple unknown control directions, a novel lemma is established by using a general class of Nussbaum functions. To handle unknown time-varying parameters, the congelation of variables method is employed. Different novel functions are introduced to achieve prescribed performance tracking and finite-time prescribed performance tracking, respectively. Meanwhile, the problem of explosion of complexity is avoided by utilizing the command filter and the compensation mechanism. For reasons of saving network resources and reducing communication burden, a new event-triggered mechanism is proposed, which can circumvent the Zeno behavior. Then, an event-triggered adaptive prescribed performance tracking control scheme is constructed and is extended to event-triggered finite-time adaptive prescribed performance tracking, both of which guarantee that all closed-loop signals are bounded and the trajectory of the tracking error can be limited to the prescribed region. Finally, the availability of the control scheme is demonstrated by two examples. • A new Nussbaum lemma is tailored for nonlinear time-varying systems with multiple unknown control directions. • New performance transformation functions are designed to achieve asymmetric global prescribed performance tracking. • The command filter and a novel error compensation scheme are constructed to handle the explosion of complexity. • The congelation of variables method is adopted to cope with unknown time-varying parameters. • An STETS adaptive prescribed performance tracking controller is constructed, which can avert the Zeno behavior successfully. [ABSTRACT FROM AUTHOR]

Summary: In this article, the adaptive tracking control problem is considered for a class of uncertain nonlinear systems with input delay and saturation. To compensate for the effect of the input delay and saturation, a compensation system is designed. Radial basis function neural networks are directly utilized to approximate the unknown nonlinear functions. With the aid of the backstepping method, novel adaptive neural network tracking controllers are developed, which can guarantee all the signals in the closed‐loop system are semiglobally uniformly ultimately bounded, and the system output can track the desired signal with a small tracking error. In the end, a simulation example is given to illustrate the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

In this paper, the problem of adaptive practical tracking is investigated by output feedback for a class of uncertain nonlinear systems subject to nonsymmetric dead-zone input nonlinearity with parameters of dead-zone being unknown. Instead of constructing the inverse of dead-zone nonlinearity, an adaptive robust control scheme is developed by designing an output compensator including two dynamic gains based respectively on identification and non-identification mechanism. With the aid of dynamic high-gain scaling approach and Backstepping method, stability analysis of the closed-loop system is proceeded using non-separation principle, which shows that the proposed controller guarantees that all closed-loop signal is bounded while the output of system tracks a broad class of bounded reference trajectories by arbitrarily small error prescribed previously. Finally, two examples are given to illustrate our controller effective. • An adaptive robust control scheme is developed by designing an output compensator including two dynamic gains based respectively on identification and non-identification mechanism instead of constructing the inverse of dead-zone nonlinearity. • Stability analysis of the closed-loop system is proceeded using non-separation principle, which shows that the proposed controller guarantees that all closed-loop signal is bounded while the output of system tracks a broad class of bounded reference trajectories by arbitrarily small error prescribed previously. [ABSTRACT FROM AUTHOR]

Summary: This paper gives a first try to the finite‐time control for nonlinear systems with unknown parametric uncertainty and external disturbances. The serious uncertainties generated by unknown parameters are compensated by skillfully using an adaptive control technique. Exact knowledge of the upper bounds of the disturbances is removed by employing a disturbance observer–based control method. Then, based on the disturbance observer–based control, backstepping technique, finite‐time adaptive control, and Lyapunov stability theory, a composite adaptive state‐feedback controller is strictly designed and analyzed, which guarantees the closed‐loop system to be practically finite‐time stable. Finally, both the practical and numerical examples are presented and compared to demonstrate the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

In this paper, we propose a partial-state feedback model reference adaptive control strategy for uncertain linear time-invariant systems with unmatched disturbances. The new control design is based on parametrization and observer technique. The control structure and output matching of nominal partial-state feedback disturbance rejection are presented. The adaptive partial-state feedback disturbance rejection scheme guarantees closed-loop system stability and asymptotic output tracking. A simulation example indicates the effectiveness of the presented adaptive partial-state feedback control design. [ABSTRACT FROM AUTHOR]

In this paper, we aim to develop adaptive asymptotic stability for heterodirectional 2 × 2 hyperbolic PDEs with parametric-strict-feedback nonlinear actuator dynamics. First, we transform the heterodirectional 2 × 2 hyperbolic PDEs with spatially varying coefficients into a stable target subsystem by utilizing the infinite-dimensional backstepping transformation. Second, an adaptive state feedback controller is constructed by combining finite-dimensional state transformation and adaptive compensation technology to assure the boundedness of all the signals in the closed-loop system. Meanwhile, we show that the PDE states converge to zero pointwise in space, the nonlinear ODE states and the control input also converge to zero. Finally, a simulation example is provided to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper is concerned with the control design problem for a class of nonlinear systems with the state time-varying time delays and nonsymmetric dead zone. The problem addressed is to design adaptive controllers that guarantee the exact tracking of a given reference signal. Two continuous robust adaptive control schemes are proposed. A positive nonlinear control gain function, which is not required to satisfy an inequality but is expressed explicitly, is carefully constructed and is used in the control law and adaptive law. An illustrative example is provided to demonstrate the validity of the proposed design method. [ABSTRACT FROM AUTHOR]

Two adaptive control schemes for a class of uncertain nonlinear systems preceded by actuator nonlinearity are presented. We consider two possible input nonlinearities, that is, backlash-like hysteresis and symmetric dead-zone, which can be simultaneously dealt with by using the proposed compensation controllers. The knowledge on the signs of the unknown plant parameters and the parameters in the input nonlinearity models is not required. Only the boundedness of the reference signal is assumed. The Nussbaum gain approach is employed to remove the assumption on the control gain sign. The first scheme is based on the backstepping technique. The final step of the recursive design is crucial for the closed-loop stability. In the second scheme, a direct adaptive control law is designed. The controller has a simple structure and only one adaptation parameter is updated. In both controllers, it is shown that asymptotic tracking is ensured. Two numerical examples are provided to show the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, an adaptive control scheme is proposed for the synchronization of two single-degree-of-freedom oscillators with unknown parameters. We only assume that the master system has the bounded solutions, which is generally satisfied for chaotic systems. Unlike the existing literature, the boundedness of the states of the slave system with control input is not necessarily known in advance. The boundedness of the controlled states is rigorously proved. The unknown parameters not only in the slave system but also in the master system are estimated by designing adaptive laws. By choosing appropriate Lyapunov function and employing Barbalat’s lemma, it is theoretically shown that the synchronization errors can converge to zero asymptotically. Finally, two illustrative examples are provided to demonstrate the effectiveness of the proposed adaptive control design. [Copyright &y& Elsevier]

A new adaptive learning control approach is proposed for a class of first-order nonlinear systems with two unknown time-varying parameters and an unknown time-varying delay. By reconstructing the system equation, all unknown time-varying terms, including the time-varying delay, are combined into an unknown periodic time-varying vector, which is estimated by a periodic adaptive mechanism. By constructing a Lyapunov-Krasovskii-like composite energy function (CEF), we prove the boundedness of all signals and the convergence of the tracking error. The results are extended to two classes of high-order nonlinear systems with mixed parameters. Three simulation examples are provided to illustrate the effectiveness of the control algorithms proposed in this paper. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society [ABSTRACT FROM AUTHOR]

In this paper, to resist stochastic cyber attacks and suppress the influence of the exogenous disturbance in synchronization of multiplex neural networks, an adaptive quantization control strategy is proposed. To overcome uncertainties and represent constraints in communication, an adaptive quantitative controller is designed, which is used to arrive outer synchronized behavior with an H ∞ performance between the multiplex neural networks under stochastic cyber attacks and exogenous disturbance. The node of the multiplex networks is neural networks which is named neural sub-networks. It is assumed that the neural sub-networks in the multiplex networks with delay topology are coupled by nonlinear functions. Based on Lyapunov stability method, the conditions for the multiplex networks to achieve synchronization with an H ∞ performance are presented. Finally, numerical example illustrates the effective of the theoretical framework. [ABSTRACT FROM AUTHOR]

Abstract This paper presents a unified study on adaptive control of multi-input multi-output (MIMO) uncertain approximation systems in non-canonical forms. For adaptive control of such systems, this paper develops a new state feedback parametrization-based adaptive control scheme, by specifying relative degrees and establishing a normal form, deriving new system reparametrizations needed for adaptive control designs, and constructing adaptive state feedback parametrized controllers for the controlled plant with different vector relative degrees, where the uncertain control gain matrices are handled using a matrix decomposition technique. The main features of such a new control framework are demonstrated by new results for non-canonical MIMO recurrent high-order neural network systems with closed-loop stability and output tracking performance analyzed. An illustrative example with simulation results is presented to show the control design procedure and desired system performance. [ABSTRACT FROM AUTHOR]