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This paper addresses the problem of adaptive tracking control for a class of strict-feedback nonlinear state constrained systems with input delay. To alleviate the major challenges caused by the appearances of full state constraints and input delay, an appropriate barrier Lyapunov function and an opportune backstepping design are used to avoid the constraint violation, and the Pade approximation and an intermediate variable are employed to eliminate the effect of the input delay. Neural networks are employed to estimate unknown functions in the design procedure. It is proven that the closed-loop signals are semiglobal uniformly ultimately bounded, and the tracking error converges to a compact set of the origin, as well as the states remain within a bounded interval. The simulation studies are given to illustrate the effectiveness of the proposed control strategy in this paper. [ABSTRACT FROM AUTHOR]

In the paper, the adaptive observer and controller designs based fuzzy approximation are studied for a class of uncertain nonlinear systems in strict feedback. The main properties of the considered systems are that all the state variables are not available for measurement and at the same time, they are required to limit in each constraint set. Due to the properties of systems, it will be a difficult task for designing the controller and the stability analysis. Based on the structure of the considered systems, a fuzzy state observer is framed to estimate the unmeasured states. To ensure that all the states do not violate their constraint bounds, the Barrier type of functions will be employed in the controller and the adaptation laws. In the stability analysis, the effect caused by the constraints for all the states can be overcome by using the Barrier Lyapunov functions. Based on the proposed control approach, it is proved that the system output is driven to track the reference signal to a bounded compact set, all the signals in the closed-loop system are guaranteed to be bounded, and all the states do not transgress their constrained sets. The effectiveness of the proposed control approach can be verified by setting a simulation example. [ABSTRACT FROM AUTHOR]

In this paper, an adaptive output feedback control is framed for uncertain nonlinear discrete-time systems. The considered systems are a class of multi-input multioutput nonaffine nonlinear systems, and they are in the nested lower triangular form. Furthermore, the unknown dead-zone inputs are nonlinearly embedded into the systems. These properties of the systems will make it very difficult and challenging to construct a stable controller. By introducing a new diffeomorphism coordinate transformation, the controlled system is first transformed into a state-output model. By introducing a group of new variables, an input-output model is finally obtained. Based on the transformed model, the implicit function theorem is used to determine the existence of the ideal controllers and the approximators are employed to approximate the ideal controllers. By using the mean value theorem, the nonaffine functions of systems can become an affine structure but nonaffine terms still exist. The adaptation auxiliary terms are skillfully designed to cancel the effect of the dead-zone input. Based on the Lyapunov difference theorem, the boundedness of all the signals in the closed-loop system can be ensured and the tracking errors are kept in a bounded compact set. The effectiveness of the proposed technique is checked by a simulation study. [ABSTRACT FROM AUTHOR]

An adaptive control approach based on the fuzzy systems for a class of uncertain nonlinear multi-input multi-output (MIMO) systems is presented in this paper. This class of systems is in the nested multiple coupling structure and their states are constrained in the corresponding compact sets. The properties of the system structure are inevitable to bring about a complicated design and a difficult task. The fuzzy logic systems are employed to approximate the unknown functions of systems, and the decoupling backstepping way is proposed to design the stability controller and adaptation laws. Barrier Lyapunov functions (BLFs) are constructed in the backstepping design to guarantee that the constraint bounds are not violated. Based on Lyapunov analysis in barrier form, we can prove the stability of the closed-loop system. Two simulation examples are viewed to verify the feasibility of the approach. [ABSTRACT FROM AUTHOR]

A neural network (NN) adaptive control design problem is addressed for a class of uncertain multi-input-multi-output (MIMO) nonlinear systems in block-triangular form. The considered systems contain uncertainty dynamics and their states are enforced to subject to bounded constraints as well as the couplings among various inputs and outputs are inserted in each subsystem. To stabilize this class of systems, a novel adaptive control strategy is constructively framed by using the backstepping design technique and NNs. The novel integral barrier Lyapunov functionals (BLFs) are employed to overcome the violation of the full state constraints. The proposed strategy can not only guarantee the boundedness of the closed-loop system and the outputs are driven to follow the reference signals, but also can ensure all the states to remain in the predefined compact sets. Moreover, the transformed constraints on the errors are used in the previous BLF, and accordingly it is required to determine clearly the bounds of the virtual controllers. Thus, it can relax the conservative limitations in the traditional BLF-based controls for the full state constraints. This conservatism can be solved in this paper and it is for the first time to control this class of MIMO systems with the full state constraints. The performance of the proposed control strategy can be verified through a simulation example. [ABSTRACT FROM PUBLISHER]

This paper deals with the tracking control problem for a class of nonlinear multiple input multiple output unknown time-varying delay systems with full state constraints. To overcome the challenges which cause by the appearances of the unknown time-varying delays and full-state constraints simultaneously in the systems, an adaptive control method is presented for such systems for the first time. The appropriate Lyapunov–Krasovskii functions and a separation technique are employed to eliminate the effect of unknown time-varying delays. The barrier Lyapunov functions are employed to prevent the violation of the full state constraints. The singular problems are dealt with by introducing the signal function. Finally, it is proven that the proposed method can both guarantee the good tracking performance of the systems output, all states are remained in the constrained interval and all the closed-loop signals are bounded in the design process based on choosing appropriate design parameters. The practicability of the proposed control technique is demonstrated by a simulation study in this paper. [ABSTRACT FROM PUBLISHER]

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 paper, an adaptive fuzzy controller is constructed for a class of nonlinear discrete-time systems with unknown functions and bounded disturbances. The main characteristics of the systems are that they take into account the effect of discrete-time dead zone and the system states are not required to be measurable. The stability problem of this class of systems is for the first time to be addressed in this paper. Due to the unavailability of the states and the presence of the discrete-time dead zone, the controller design becomes more difficult. To stabilize the uncertain nonlinear discrete-time systems, the fuzzy logic systems are used to approximate the unknown functions, a fuzzy state observer is designed to estimate the immeasurable states, and the effect caused by discrete-time dead zone can be solved via establishing an adaptation auxiliary signal. Based on the Lyapunov approach, it is proved that all the signals of the closed-loop system are the semiglobal uniformly ultimately bounded, and the tracking error is made within a small neighborhood around zero. The feasibility of the developed control scheme is verified via two simulation examples. [ABSTRACT FROM PUBLISHER]

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 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]

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]

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]