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In this paper, adaptive optimal control is proposed for a class of strict-feedback nonlinear systems with unmodeled dynamics and output constraints. The controller design procedure contains two parts. In the first part, to satisfy output constraints, nonlinear mapping is used to transform constrained system into a novel one without output constraints. A dynamical signal is utilized to deal with unmodeled dynamics. A feedforward controller is designed using the dynamics surface control technique. In the second part, an auxiliary dynamical system is introduced to optimize cost function, and neural-network based adaptive dynamic programming(ADP) is employed to approximate the optimal cost function and the optimal control law. It is proved that the closed-loop system is semi-globally uniformly ultimately bounded (SGUUB) and the output constraints are not triggered by theoretical analysis. Two simulation examples are provided to illustrate the effectiveness of the proposed scheme.

In this work, the problem of adaptive neural dynamic surface control (DSC) with the minimum adjustable parameters is discussed for a class of multi-input multi-output (MIMO) pure-feedback nonlinear systems with unmodeled dynamics and output constraints. An auxiliary signal designed by the characteristics of unmodeled dynamics is used to handle the dynamical uncertainties. The unknown continuous black-box functions produced in the controller design process are approximated by using radial basis function neural networks (RBFNNs). Based on an one-to-one nonlinear mapping(NM), the MIMO nonaffine nonlinear system with output constraints is transformed into a novel block-structure MIMO nonaffine nonlinear system without output constraints. Based on the transformed system and modified DSC, robust adaptive neural tracking control scheme is developed. Through theoretical analysis, all the signals in the closed-loop system are shown to be semi-globally uniformly ultimately bounded (SGUUB). A numerical example is provided to demonstrate the effectiveness of the proposed design strategy.

This paper is concerned with adaptive output feedback tracking control for a class of uncertain nonlinear systems with quantized input and unmodeled dynamics as well as output constraints. Quantized reduced-order K-filters are designed to observe parts of unmeasured states. The considered system is of two types of uncertainties. To deal with these uncertainties, we adopts global exponential stability technique of the state unmodeled dynamics with a Lyapunov description and the fuzzy approximation approach to those uncertain functions. To avoid the chattering of the quantized control signal, a hysteretic quantizer is introduced, and by designing a novel control law based on dynamic surface control (DSC) method, many assumptions of the quantized system in early literatures are removed. Combining quantized DSC with an one to one mapping from output error to the first dynamic surface, the robust quantized adaptive controller is constructed to guarantee that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded (SGUUB), and the tracking error is restricted within the prescribed output constraints. A numerical simulation example shows the effectiveness of the proposed approach.

In this paper, adaptive neural dynamic surface control(DSC) is developed for a class of constrained strict-feedback nonlinear systems with input unmodeled dynamics. By introducing a one to one nonlinear mapping, the output constrained strict-feedback system in the presence of unmodeled dynamics is transformed into a novel unconstrained strict-feedback system. Neural networks (NNs) are employed to approximate unknown nonlinear continuous functions. A normalization signal and an updating parameter are used to handle the uncertain term which input unmodeled dynamics brings about in the design final step. By adding the normalization signal to the whole Lyapunov function and using the defined compact set in stability analysis, all the signals in the closed-loop system are proved to be semi-globally uniformly ultimately bounded (SGUUB), and output constraint is not violated. Two numerical examples are used to illustrate the effectiveness of the proposed adaptive DSC method in handling input unmodeled dynamics.

In this paper, adaptive prescribed performance output feedback control is investigated for a class of nonlinear systems with unmodeled dynamics. Neural networks are used to approximate the unknown nonlinear functions. MT-filters are employed to estimate the unmeasured states. The unmodeled dynamics is dealt with by introducing an available dynamic signal. Adaptive output feedback dynamic surface control and parameter adaptive laws are proposed based on introducing the prescribed performance function and output error transformation. It is proved that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded. Simulation results are provided to demonstrate the effectiveness of the proposed approach.

This paper addresses a novel anti-disturbance dynamical tracking problem for a class of MIMO systems subject to unknown disturbances and nonlinear dynamics. Different from some traditional anti-disturbance results, T-S fuzzy models are firstly employed to describe the nonlinear disturbances, in which a disturbance observer based on T-S exogenous models is designed under different conditions to estimate the unknown nonlinear disturbances for the plants with known and unknown nonlinearities, respectively. By integrating the estimates of disturbance with PI-type control input, a composite controller based on convex optimization theory is proposed to ensure the system stability and convergence of the tracking error to zero. Meanwhile, the favorable disturbance estimation and attenuation performance can also be achieved by the designed convex optimization algorithm. Finally, the effectiveness of the proposed control schemes is verified by simulations for flight control systems with three different types of nonlinear disturbances.

In this paper, two adaptive output feedback control schemes are proposed for a class of nonlinear systems with unmodeled dynamics and unmeasured states as well as unknown high-frequency gain. Radial basis function (RBF) neural networks (NNs) are used to approximate the unknown nonlinear functions. K-filters are designed to estimate the unmeasured states. An available dynamic signal is introduced to dominate the unmodeled dynamics. By introducing the dynamic surface control (DSC) method, the bounded condition of the approximation error is removed, and the tracking control is achieved. Moreover, the number of adjustable parameters and the complexity of the design are both reduced. By theoretical analysis, the closed-loop system is shown to be semi-globally uniformly ultimately bounded (SGUUB). Simulation results are provided to illustrate the effectiveness of the proposed approach.

In this paper, robust adaptive control is proposed for a class of pure-feedback nonlinear systems with unmodeled dynamics and unknown gain signs using radial basis function neural networks (RBFNNs). Dynamic uncertainties are dealt with using a dynamic signal. The unknown virtual gain signs are solved using the Nussbaum functions. Using mean value theorem and Young's inequality, only one learning parameter needs to be tuned online at each step of recursion. It is proved that the proposed design scheme can guarantee semi-global uniform ultimate boundedness (SGUUB) of all signals in the closed-loop system. Simulation results demonstrate the effectiveness of the proposed approach.

The state feedback control scheme combined with backstepping, neural network and adaptive control is proposed for the tracking control problem of a class of nonlinear systems with uncertain input delay and disturbances. A filter and a virtual observer are constructed to produce the auxiliary signal. Neural networks are employed to estimate the unknown continuous functions. The tracking error is proved to ultimately converge to an adequately small compact set. The theoretical result is illustrated through a simulation example.

An output feedback control scheme combined with backstepping, radial basis function (RBF) neural networks, and adaptive control is proposed for the stabilization of nonlinear system with input delay and disturbances. A filter and a virtual observer are constructed to substitute the immeasurable system state. By using state transformation, the original system is converted to the system without input delay. Neural networks are employed to estimate the unknown continuous functions. The control scheme ensures that the closed-loop system is semi-globally uniformly ultimately bounded (SGUUB).

A control scheme combined with backstepping, radius basis function (RBF) neural networks and adaptive control is proposed for the stabilization of nonlinear system with input and state delay. By using state transformation, the original system is converted to the system without input delay. The RBF neural network is employed to estimate the unknown continuous function. The controller is designed for the converted system so that the closed-loop system is bounded. According to the relation between the original system and the converted one, the state of the original system is proved to be bounded. The control scheme ensures that the closed-loop system is semi-globally uniformly ultimately bounded.