Robust adaptive control for nonlinear uncertain systems

Synthesis of smoother robust control for nonlinear uncertain dynamical systems is considered. The existing saturation-type robust controller guarantees asymptotic stability or stability of uniform ultimate boundedness. It is shown that, mainly due to the part of uncertainties that is bounded by a constant, the controller may potentially have a very large rate of change in order to achieve a small ultimate bound for the state. This study, on its gain or the property of its partial derivative, reveals the need for designing smoother nonlinear robust controller along two directions. First, in a recursive design of robust control, fictitious robust control must be designed to be as smooth as possible so that the actual robust control will not have too large of a magnitude for implementation purposes. Second, if the uncertainties are known to have bounded rate of change, it is both practically and theoretically important to design a robust controller which rate of change is limited by that of the uncertainties. The objective of this paper is to design smoother robust controls by providing results on those two topics. >

The problem of adaptive robust control for uncertain nonlinear systems with time-varying delay is considered in this paper. The upper bound of the uncertainty is assumed to be nonlinear functions with unknown coefficients. By using adaptive control method, a class of adaptive robust state feedback controller is proposed. Based on Lyapunov-Krasovskii method and Lyapunov stability theory, it is shown that the controller designed can render the uniform asymptotic stability of the system. Finally, a numerical example is given to show the controller is valid.

This paper deals with an adaptive robust tracking control using a multilayer neural network (NN) for a class of nonlinear dynamic systems with unknown time varying state delays. Typical adaptive NN backstepping controllers for uncertain nonlinear systems with time-delay give rise to computation complexity caused by the the repeated derivatives of virtual controllers and nonlinear functions. Moreover, the combined techniques usually result in only uniformly ultimately bounded (UUB) stability caused by the inherent NN approximation error. This paper presents a control scheme that uses an integral sliding mode control as a feedback term and an adaptive neural controller as a feedforward term based on the desired compensation adaptive law (DCAL) technique. First, we develop a new DCAL formulation which avoids the explosion of complexity caused by the general NN backstepping scheme to compensate for nonlinear system uncertainties, bounded system disturbances, and unknown state time delays. Then, using a Lyapunov-Krasovskii (LK) functional, it is shown that the proposed controller renders the class of uncertain nonlinear time-delay systems asymptotically stable.

In this paper, a robust adaptive fuzzy control for a class of nonlinear uncertain systems preceded by an unknown dead-zone and with unknown upper bound of uncertainties is developed. The dead-zones are quite commonly encountered in many systems (e.g., DC servosystem, robot, and machine tools), are usually poorly known, and may severely limit the performance of control. In addition, the system uncertainties (e.g., parameter variations, or external load, unmodeled dynamics) often exist. Therefore, the controllers are required to deal with the robust stability and performance of the systems with unknown dead-zone and in the presence of uncertainties, whose upper bound is generally unknown. In the beginning, an adaptive dead-zone compensation is employed to improve system performance. Then the unknown system functions and the unknown upper bound of system uncertainties are respectively approximated by fuzzy logic systems with unknown weights. The unknown bounds caused by the learning error of the slope of dead-zone and the system functions are also tackled by an extra learning law. The above weights are all on-line learned to provide for the controller design. Moreover, the projection terms in these learning laws are designed such that the boundedness of the learning weight can be assured.

A fully actuated system approach: Desired compensation adaptive robust control for uncertain nonlinear systems

This article proposes a robust adaptive controller design method for strict feedback nonlinear systems with unmodeled dynamics and input saturation. By using command filters, the explosion of complexity is obviated. The influence of filter errors bought in by command filters is eliminated by introducing compensating signals. Moreover, by skillfully constructing annth‐order auxiliary dynamic system, the effect of input saturation is avoided, where the disadvantages of conventional methods based on the hyperbolic tangent function are overcome. To tackle the effect of unmodeled dynamics which can destroy the performance and even destabilize the system, based on input‐to‐state stability theory, a dynamic signal is designed. Finally, the Lyapunov theory‐based stability analysis proves that all the closed‐loop signals are uniformly ultimately bounded. The effectiveness of the proposed controller design scheme is verified in simulation experiments.

The robust neural adaptive control scheme is developed for a class of nonlinear MIMO uncertain systems. Two types of uncertainties are considered: parametric uncertainty and unknown nonlinearities. In the control procedure, neural networks are implemented to estimate the uncertain system owing to parametric uncertainty and robust compensating controllers are designed in H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> sense for attenuating the unmatched nonlinearities, in which no property of uncertainties is assumed and needed for design, only its possible bound which may not unique, is used for analytical purposes. And also relaxes some of restrictive assumptions that are usually made in neural adaptive control schemes, one such assumption is the requirement of a known bound on the network reconstruction error. It is shown that the proposed control is continuous, guarantees global stability and the H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> performance index. Extensive simulations on the tracking control of a two-link rigid robotic manipulator verify the effectiveness of the design methodology and controller.

This paper deals with the problem of robust control for Uncertain Nonlinear System via fuzzy control approach. First, a fuzzy controller with robust control capability is proposed. For avoiding complex controller parameters adjustment, Multi-objective particle swarm Optimization (PSO) algorithm is adopted during the controller design. Secondly, the multi-model is employed to represent the nonlinear system with norm-bounded parameter uncertainties. Finally, a simulation example illustrates the effectiveness and the feasibility of the proposed approach.

Robust tracking control of uncertain nonlinear systems with adaptive dynamic programming

In this paper, an integrated adaptive-robust control approach using sliding-mode method is developed for control of nonlinear uncertain systems. The new approach possesses the advantages of both adaptive control and robust control, and eliminates disadvantages of each. It has the ability to learn, like an adaptive controller, and the ability to handle various uncertainties and reject disturbances like a robust controller. When compared with pure adaptive control the approach used here improves the transient performance, and when compared with pure robust control the conservatism of the design is reduced. Furthermore, global asymptotic stability of the closed loop system is guaranteed. This paper presents the methodology and illustrates the approach using a one-DOF robot arm in the vertical plane under gravity.

A direct adaptive control framework for nonlinear uncertain systems with input quantizers is developed. The proposed framework is Lyapunov-based and guarantees ultimate boundedness (practical stability) of the closed-loop system. Specifically, the input quantizers are logarithmic and characterized by sector-bound conditions with the conic sector adjusted at each time instant by the adaptive controller in conjunction with the system response. Furthermore, for practical reasons we assume that the input logarithmic quantizers have deadzone around zero control input. Finally, a numerical example is provided to demonstrate the efficacy of the proposed approach

This paper describes a hybrid approach to the problem of controlling a class of nonlinear systems in the face of both unknown nonlinearities and unmodeled dynamics. In the proposed methodology, neural networks and direct adaptive control compensate for unknown nonlinear mappings while dynamic nonlinear damping provides robustness to unmodeled dynamics. To illustrate the theoretical development, the authors design a longitudinal autopilot for a simplified nonlinear missile aerodynamic model with input unmodeled dynamics. Simulation results demonstrate robustness in the face of this type of uncertainty.

This paper proposes a wavelet based adaptive tracking controller for uncertain nonlinear systems. The controller is designed to provide the desired performance in the presence of actuator constraints. Proposed controller comprises of wavelet based tracking controller and a robust controller. Wavelet tracking controller is the principal controller while robust controller is designed to achieve the desired performance by attenuating the effect of approximation error caused by wavelet identifier. Wavelet networks, which are having superior learning capability in comparison to conventional neural network, are used for the approximation of unknown system dynamics. Also the adaptation laws are derived in the sense of Lyapunov function assuring the stability of the system. To deal with the actuator constraints, the system is augmented with additional wavelet network to work as a saturation compensator so as to recover the unconstrained response rapidly while preserving the system stability

International audience

Simplified adaptive backstepping control for uncertain nonlinear systems with unknown input saturation and its application