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This paper presents an adaptive neural control strategy for an ${n}$ -link rigid robotic manipulator with both state constraints and unknown time-varying delayed states. The design difficulties cause by the state constraints and unknown network-induced time-varying delays which appear in the ${n}$ -link rigid robot simultaneously. In order to overcome these difficulties, the novel Barrier Lyapunov functions and an iterative backstepping technique are employed to guarantee constraint satisfaction of the position of the robot, the opportune Lyapunov-Krasovskii functionals and separation techniques are utilized to eliminate the effect of unknown functions with time-varying delayed states in communication channels. As the universal approximator, the neural networks are used to estimate the unknown functions of systems. By using the Lyapunov analysis, we can achieve that all the closed-loop signals are semiglobal uniformly ultimately bound, the tracking errors converge to a small set about zero and the good tracking performances of the system output. The feasibility of the proposed control algorithm can be demonstrated by providing simulation results. [ABSTRACT FROM AUTHOR]

In this paper, an adaptive neural tracking control strategy is presented to stabilize a class of uncertain nonlinear strict-feedback systems with the full state constraints and time-delays. Because the full state constraints and time-delays appear simultaneously in the systems, they lead to the difficulties in the controller design. The opportune barrier Lyapunov functions (BLFs) are designed to ensure that the states constraints are not violated. The novel backstepping procedures with BLFs are utilized to eliminate the effect of the nonlinear system which caused by the time-delays. Finally, it is proved that all the signals in the closed-loop system are semiglobal uniformly ultimately bounded and the tracking errors converge to a small interval based on proposed Lyapunov and backstepping design method. The effectiveness of the proposed scheme is demonstrated by a simulation in this paper. [ABSTRACT FROM AUTHOR]

In this study, a controller design for nonlinear strict feedback systems with full state constrains is presented. A backstepping stable controller is designed by using the Integral Barrier Lyapunov Functionals (iBLF). Compared with the previous designs, the systems are required to contain the unknown parameters. Under the backstepping control-based iBLF, the output tracking is well achieved without violation of any constraint and the closed loop signals are bounded. The stability of the closed-loop system is analyzed by using the Lyapunov theorem. Finally, a simulation example is used to verify the effectiveness of the proposed design. [ABSTRACT FROM AUTHOR]

This paper presents an adaptive control strategy for a unified chaotic system with unknown functions and full state constraints. The unknown functions in the unified chaotic system are approximated by using the radial basis function neural networks. At present, a great many of the results for chaotic system neglect the situation of full state constraints. In the proposed scheme, we successfully utilize the barrier Lyapunov function approach to prevent the full state from violating constraint condition. In addition, when the full state constraints are considered, the computation online burden is very large in the previous works. In contrast with the existing results for unified chaotic system, the number of the adaptation laws has only two. The state feedback controllers and the adaptive laws for estimating the uncertainties were derived based on the Lyapunov stability theory. Finally, it is proved that all the signals in the unified chaotic system are bounded and the constraints are not violated. The performance of the proposed scheme was validated by using a simulation example. [ABSTRACT FROM AUTHOR]

An adaptive control scheme is studied for a class of continuous stirred tank reactors (CSTR). The considered reactors can be viewed as a class of MIMO systems with unknown functions and interconnections as well as the output constraints. These properties of the reactors will lead to a completed task for designing a stable control algorithm. To this end, several unknown functions are approximated based on the neural approximation, a novel recursive design method is used to remove the interconnection term, and Barrier Lyapunov function is introduced to avoid the violation of the output constraints. The stability of the proposed scheme is proved based on the Lyapunov analysis method. A simulation example for continuous stirred tank reactor is illustrated to verify the validity of the algorithm. [ABSTRACT FROM AUTHOR]

An adaptive control scheme is studied for unified chaotic systems with unknown function and dead-zone input. Because uncertain nonlinear property is included in the considered unified chaotic systems, the neural networks are used to approximate the uncertainties. An adaptive technique is employed to construct the neural controllers and compensate for the dead-zone parameters. By using the scheme, the chaotic phenomena for unified chaotic systems are overcome. It is proven that the proposed algorithm can guarantee that all the signals in the closed-loop system are bounded and the system states can converge to a neighborhood of zero based on the Lyapunov analysis method. The simulation example for a unified chaotic system is provided to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

For a class of continuous stirred tank reactor with output constraint and uncertainties, an adaptive control approach is proposed based on the approximation property of the neural networks. The considered systems can be viewed as a class of pure-feedback systems. At present, the control approach for the systems with output constraint is restricted to strict-feedback systems. No effective control approach is obtained for a general class of pure-feedback systems. In order to control this class of systems, the systems are decomposed by using the mean value theory, the unknown functions are approximated by using the neural networks, and Barrier Lyapunov function is introduced. Finally, it is proven that all the signals in the closed-loop system are bounded and the system output is not violated by using Lyapunov stability analysis method. A simulation example is given to verify the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

In this paper, an adaptive predictive control algorithm is applied to control a class of SISO continuous stirred tank reactor (CSTR) system in discrete time. The main contribution of the paper is that the considered systems belong to pure-feedback form where the unknown dead-zone is considered in the in-fan, and dead-zone is nonsymmetric, and it is first to control this class of systems. Radial basis function neural networks are used to approximate the unknown functions, and the mean value theorem is exploited in the design. Based on the Lyapunov analysis method, it is proven that all the signals of the resulting closed-loop system are guaranteed to be semi-global uniformly ultimately bounded, and the tracking error can be reduced to a small compact set. A simulation example for CSTR systems is studied to verify the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

Abstract: An adaptive control scheme is studied for a class of continuous stirred tank reactors (CSTR) with unknown functions. Because the nonlinear property and the unknown functions are included in the considered reactor, it leads to a completed task for designing the controller. Based on the approximation property of the neural networks, several unknown functions are approximated. The main contribution of this paper is that a more general class of CSTR is controlled. A novel recursive design method is used to remove the interconnection term. It is proven that the proposed algorithm can guarantee that all the signals in the closed-loop system are bounded and the system output can converge to a neighborhood of zero based on the Lyapunov analysis method. A simulation example for continuous stirred tank reactor is illustrated to verify the validity of the algorithm. [Copyright &y& Elsevier]

This paper studies an adaptive output-feedback control for a class of nonlinear single-input and single-output (SISO) systems with the full-state constraints. A state observer is designed to estimate those unmeasured states. At present, all the results in the output-feedback area ignore the effects of the full-state constraints. The presence of these constraints results in a complicated procedure and the major difficulties in the design. The barrier Lyapunov function (BLF) and a novel design procedure are given to overcome these difficulties. The adaptation law and the controllers are obtained based on the backstepping design procedure. In addition, only one adjustable parameter needs to be updated, and thus, the online computation burden is alleviated. The stability of the closed-loop system is proven by using the Lyapunov theorem. A simulation example is given to verify the effectiveness of the approach. [ABSTRACT FROM PUBLISHER]

In this paper, an adaptive controller is investigated for a class of uncertain single-input-single-output nonlinear systems preceded by an unknown backlash-type hysteresis nonlinearity, which is modeled by a differential equation. Backstepping design procedure is employed to construct the control input and adaptation laws. A new algorithm is designed to reduce the computational burden compared with previous work for unknown backlash-type hysteresis. Based on Lyapunov stability theory, all the signals in the closed-loop system are bounded, and the system output can track the reference signal to a bounded compact set. An example for hard disk drives with hysteresis friction nonlinearity is given to verify the feasibility of the proposed approach. [ABSTRACT FROM AUTHOR]

The dynamic surface control technique can simplify the backstepping design for the control of nonlinear systems by overcoming the problem of 'explosion of complexity.' In this paper, we incorporate this design technique into a neural network-based adaptive control design framework for a class of nonlinear stochastic systems. The time delays exist in the gain of the stochastic disturbance in the systems, and the neural networks are employed to compensate for all unknown nonlinear terms depending on the delayed output. The proposed approach is able to eliminate the problem of 'explosion of complexity' inherent in the existing method. It can be proven that all the signals are semi-globally uniformly ultimately bounded in probability, and the system output tracks the reference signal to a bounded compact set. A simulation example is given to verify the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

In this article, a direct adaptive neural networks control algorithm is presented for a class of SISO discrete-time systems with non-symmetric dead-zone. The property of the dead-zone is discretized. Mean value theorem is used to transform the systems into a special form. The unknown functions in the input–output model are approximated using the radial basis function neural networks. Compared with the results for the discrete non-symmetric dead-zone, this article presents a new algorithm to reduce the computational burden. Lyapunov analysis method is utilized to prove that all the signals in the closed-loop systems are semi-global uniformly ultimately bounded. The tracking error is proved to converge to a small set around the zero. A simulation example provided to illustrate the effectiveness of the control schemes. [ABSTRACT FROM AUTHOR]

A robust adaptive NN output feedback control is proposed to control a class of uncertain discrete-time nonlinear multi-input-multi-output (MIMO) systems. The high-order neural networks are utilized to approximate the unknown nonlinear functions in the systems. Compared with the previous research for discrete-time MIMO systems, robustness of the proposed adaptive algorithm is obvious improved. Using Lyapunov stability theorem, the results show all the signals in the closed-loop system are semi-globally uniformly ultimately bounded, and the tracking errors converge to a small neighborhood of zero by choosing the design parameters appropriately. [ABSTRACT FROM AUTHOR]

An adaptive control scheme is developed in the paper for nonlinear stochastic systems with unknown parameters. All the states in the systems are required to be constrained in a bounded compact set, i.e., the full state constraints are considered in the systems. It is for the first time to control nonlinear stochastic systems with the full state constraints. In contrast to deterministic systems, the stochastic systems with the full state constraints are more difficult to be stabilized and the design procedures are more complicated. By constructing Barrier Lyapunov Functions (BLF) in symmetric and asymmetric forms, it can be ensured that all the states of the stochastic systems are not to transgress their constraint bounds. Thus, the proposed scheme not only solves the stability problem of stochastic systems, but also overcomes the effect of the full state constraints on the control performance. Finally, it is proved that all the signals in the closed-loop system are semi-global uniformly ultimately bounded (SGUUB) in probability, the system output is driven to follow the reference signals, and all the states are ensured to remain in the predefined compact sets. The validity of the proposed scheme is verified by a simulation example. [ABSTRACT FROM AUTHOR]