Indirect fuzzy adaptive control: hyperstability approach

In this paper, we develop a discrete-time controller for continuous-time nonlinear plant. The exact dynamics of the plant are unknown, but some bounds of the dynamics are assumed. The controller consists of a supervisory controller and an adaptive fuzzy controller. The supervisory controller is designed to guarantee the boundedness of the state, and the adaptive fuzzy controller is designed to control the state to track a given trajectory. More specifically, the supervisory controller is constructed from the bounds of the plant dynamics in such a way that once the state moves outside the stable region, the supervisory controller will take action to draw it back. The adaptive fuzzy controller is constructed from the measured state and control data using the nearest neighborhood clustering algorithm. Both the supervisory controller and the adaptive fuzzy controller operate at discrete-time points, whereas the plant keeps running continuously. We give rigorous proofs of the properties of this sampled-data nonlinear adaptive control system.

Indirect adaptive fuzzy control of nonlinear descriptor systems

This paper addresses the problem of state estimation and the tracking control scheme combining fuzzy control technique for a class of MIMO nonlinear systems, in which some variables are not measurable, with plant uncertainties and external disturbances First, the nonlinearities are approximated using neural networks, and then are modeled based on linear difference inclusions(LDI), which makes the structure of the desired filter simpler and parameter turning easier. A unified framework is established to solve the addressed H ∞ filtering problem by exploiting linear matrix inequality (LMI) approach. The proposed control law is based on indirect adaptive fuzzy control and uses two on-line estimations. The adaptive fuzzy tracking control using Variable Structure (VS) control technique is derived based on Lyapunov criterion to resolve system uncertainties and external disturbances. This is done in such a way that all states of the system are bounded and the H ∞ tracking performance is achieved. Finally, A numerical example is investigated to demonstrate the feasibility and the effectiveness of the proposed methodology.

This paper develops a fuzzy model reference adaptive control of continuous-time nonlinear systems described by Takagi-Seguno (TS) fuzzy model. The tracking performance is assured using a direct TS fuzzy controller. Both full state information and observer-based control schemes are investigated. It is proved, using Lyapunov stability tools, that this adaptive scheme is asymptotically stable and the tracking and observation errors converge to zero. Simulation results illustrate the performance of the proposed approach.

Self-triggering adaptive optimal control for nonlinear systems based on encoding mechanism

An online adaptive optimal control is proposed for continuous-time nonlinear systems with completely unknown dynamics, which is achieved by developing a novel identifier-critic-based approximate dynamic programming algorithm with a dual neural network (NN) approximation structure. First, an adaptive NN identifier is designed to obviate the requirement of complete knowledge of system dynamics, and a critic NN is employed to approximate the optimal value function. Then, the optimal control law is computed based on the information from the identifier NN and the critic NN, so that the actor NN is not needed. In particular, a novel adaptive law design method with the parameter estimation error is proposed to online update the weights of both identifier NN and critic NN simultaneously, which converge to small neighbourhoods around their ideal values. The closed-loop system stability and the convergence to small vicinity around the optimal solution are all proved by means of the Lyapunov theory. The proposed adaptation algorithm is also improved to achieve finite-time convergence of the NN weights. Finally, simulation results are provided to exemplify the efficacy of the proposed methods.

This paper proposes a bioinspired reference model based fuzzy adaptive tracking control for active suspension systems. A general bioinspired nonlinear structure, which can present ideal nonlinear quasi-zero stiffness for vibration isolation, is adopted as tracking reference model. Fuzzy logic systems are used to approximate unknown nonlinear terms in nonlinear suspension systems. Particularly, a nonlinear damping is designed to improve damping characteristics of the bioinspired reference model. With beneficial nonlinear stiffness and improved nonlinear damping of the bioinspired reference model, the proposed fuzzy adaptive controller can effectively suppress vibration of suspension systems with less actuator force and much improved ride comfort, thus energy saving performance can be achieved. Finally, a quarter-vehicle active suspension system with considering payload uncertainties, general disturbance, and actuator saturation is provided for evaluating the validity and superiority of the bioinspired nonlinear dynamics based fuzzy adaptive control approach proposed in this paper.

Application of adaptive fuzzy control to ac machines

Intelligent switching adaptive control for uncertain nonlinear dynamical systems

This paper presents a robust indirect adaptive stabilization controller for systems with linear time-invariant (LTI) nominal parts, uncertain dynamic errors, and bounded disturbances. The a priori knowledge required for designing the adaptive controller is that the nominal part of the system is of known order and is stabilizable.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

In this note we address the problem of indirect adaptive (regulation or tracking) control of nonlinear, input affine dissipative systems. It is assumed that the supply rate, the storage and the internal dissipation functions may be expressed as nonlinearly parameterized regression equations where the mappings (depending on the unknown parameters) satisfy a monotonicity condition—this encompasses a large class of physical systems, including passive systems. We propose to estimate the system parameters using the “power‐balance” equation, which is the differential version of the classical dissipation inequality, with a new estimator that ensures global, exponential, parameter convergence under the very weak assumption of interval excitation of the power‐balance equation regressor. To design the indirect adaptive controller we make the standard assumption of existence of an asymptotically stabilizing controller that depends—possibly nonlinearly—on the unknown plant parameters, and apply a certainty‐equivalent control law. The benefits of the proposed approach, with respect to other existing solutions, are illustrated with examples.

Adaptive Control of MIMO T-S Fuzzy Systems with General Delay Matrices

A parameter dependent Riccati equation approach is taken to analyze the stability properties of an output feedback adaptive control law design. The adaptive controller is intended to augment a nominal, fixed gain, observer based output feedback control law. Although the formulation is in the setting of model following adaptive control, the realization of the adaptive controll er does not require implementing the reference model. In this regard, the cost of implementing the adaptive controller above that of a fixed gain control law is far less than that of other methods. The error signals are shown to be uniformly ultimately bounded and an expression for the ultimate bound is provided. The control design process and theoretical results are illustrated using a model for wing-rock dynamics. Research in adaptive output feedback control of uncertain nonlinear systems is motivated by the many emerging applications that employ novel actuation devices for active control of flexible structures and fluid flows. These applications include actuators such as piezo-electric films and s ynthetic jets, which are typically nonlinearly coupled to t he plant dynamics they are intended to control. Models for these applications vary from accurate low frequency models to models that crudely approximate the true dynamics even at low frequencies. Examples of applications include active damping of flexible structures, control of aeroservoelasti c aircraft, and active control of flows. Adaptive control can be used to satisfy performance requirements in the presence of large scale parameter uncertainty, and improved safety in the event of actuator failure.

Based on input-output stability theory, a multi-input multi-output indirect adaptive fuzzy tracking control method for satellite attitude systems with parametric uncertainty and external disturbance is presented. First, a nonlinear controller is designed based on the satellite precision model, and stability of the closed-loop system is analyzed; then, because of contained the parametric uncertainty and external disturbance in the model, an adaptive fuzzy controller is constructed through using fuzzy logic system to approximate the uncertain section. Last, it is proved that the proposed controller can make the satellite track to the located place, and force the tracking error to converge to a small neighborhood of the origin. Simulation results show the satisfied control accuracy and robustness to the model uncertainty.

The force tracking error is dependent on both the position tracking error and the estimated parameter error so that, in constrained adaptive robot control, the convergence of the estimated parameter error becomes more important than in unconstrained adaptive robot control. However, in the direct adaptive controller, the parameter adaptation is driven only by the tracking error in the joint motion, while in the indirect adaptive controller, the parameter estimation is driven only by the prediction error in the joint torque. Based on this observation a new combined direct and indirect adaptive controller driven by both the tracking error and the prediction error is developed for constrained robots with inertia parameter uncertainty. Stability of the combined adaptive controllers is established in the Lyapunov sense. The combined control improves both position and force tracking performance compared with direct adaptive control. The computer simulations are presented to demonstrate the proposed schemes.