Direct adaptive control using feedforward neural networks

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.

An adaptive integral plus states neural control of aerobic continuous stirred tank reactor

This paper presents a direct robust adaptive tracking control strategy for the Iongitudinal motion of electric vehicles (EVs) subject to parametric uncertainties, nonlinear dynamics, and external disturbances. The vehicle longitudinal dynamics are formulated as a second-order nonlinear system with unknown nonlinearities. Unlike conventional indirect adaptive approaches that first identify unknown system dynamics, a radial basis function neural network (RBFNN) is employed to directly approximate the ideal feedback control law derived from sliding mode theory and Lyapunov synthesis. A robust adaptive law incorporating -modification is designed for online neural network weight update, enhancing robustness against approximation errors and bounded disturbances without requiring prior knowledge of their bounds. Lyapunov-based stability analysis rigorously demonstrates that all closed-loop signals are uniformly ultimately bounded (UUB), with tracking error converging to a tunable residual set around zero. The controller achieves model-independent operation, requiring no exact knowledge of vehicle nonlinear dynamics. Comprehensive simulations under step commands, and multi-frequency trajectories, together with parametric variations and road grade disturbances, validate the effectiveness of the proposed scheme in achieving accurate velocity tracking and superior robustness compared to conventional PID and sliding mode control. The main source code of this paper, including all simulation scripts and neural network modules, can support information found in S1 Pdf file.

In direct adaptive inverse control (DAIC), parameters of the controller are estimated directly in the feed-forward loop. In this paper, we propose a closed loop direct adaptive inverse control (CDAIC) scheme which improves tracking, error convergence, and disturbance rejection properties of DAIC. CDAIC is applicable to stable or stabilized, minimum or nonminimum phase linear plants. CDAIC and DAIC are compared using computer simulations for disturbance free and disturbed discrete type nonminimum phase linear plants. CDAIC shows better results compared to DAIC in terms of mean square tracking error and disturbance rejection.

The problem of direct adaptive neural control for a class of nonlinear systems with an unknown gain sign and nonlinear uncertainty is discussed in this paper. Based on the principle of sliding mode control and the approximation capability of multilayer neural networks (MNNs), and using Nussbaum-type function, a novel design scheme of direct adaptive neural control is proposed. By adopting the adaptive compensation term of the upper bound function of the sum of residual and approximation error, the closed-loop control system is shown to be globally stable, with tracking error converging to zero. Simulation results show the effectiveness of the proposed approach.

This paper applies a parallel scheme for adaptive control that uses only one neural network to a CSTR (continuous stirred tank reactor). Convergence of the identification error is investigated by Lyapunov's second method. The training process of the neural network is carried out by using two different techniques: backpropagation and extended Kalman filter algorithm.

In this paper, we introduce a direct fractional order adaptive control design based on model reference adaptive control (MRAC) structure for a class of commensurate fractional order linear systems with an arbitrary relative degree, and whose parameters are unknown. By generalising the application of standard direct MRAC strategy to plants described by fractional order models, we develop a fractional adaptive control scheme (FOMRAC) based on the output feedback. We also define an adaptation control law ensuring the stability of the closed-loop system and the good tracking of the reference trajectory. The asymptotic stability of the fractional order control system is proven using an extension of the Lyapunov theorem. Simulation results show the effectiveness of the proposed control method even for plants with model parametric variations and additive noises.

In this paper, we present a neural adaptive control scheme for active vibration suppression of a composite aircraft fin tip. The mathematical model of a composite aircraft fin tip is derived using the finite element approach. The finite element model is updated experimentally to reflect the natural frequencies and mode shapes very accurately. Piezo-electric actuators and sensors are placed at optimal locations such that the vibration suppression is a maximum. Model-reference direct adaptive neural network control scheme is proposed to force the vibration level within the minimum acceptable limit. In this scheme, Gaussian neural network with linear filters is used to approximate the inverse dynamics of the system and the parameters of the neural controller are estimated using Lyapunov based update law. In order to reduce the computational burden, which is critical for real-time applications, the number of hidden neurons is also estimated in the proposed scheme. The global asymptotic stability of the overall system is ensured using the principles of Lyapunov approach. Simulation studies are carried-out using sinusoidal force functions of varying frequency. Experimental results show that the proposed neural adaptive control scheme is capable of providing significant vibration suppression in the multiple bending modes of interest. The performance of the proposed scheme is better than the H(infinity) control scheme.

This paper is concerned with application of a game-theoretic formulation for direct adaptive optimal control of nonlinear systems affected by bounded noise/disturbances. Almost all of the reinforcement learning (RL) approaches employ a Markov decision process (MDP) setting, which is inadequate for handling noise/disturbances as it disallows an explicit representation of noise/disturbances. The work in this paper addresses this problem by showing how a game theoretic RL formulation can effectively cope with disturbances with no preliminary offline learning. The work demonstrates the application of neural networks (NN) in a Markov game setup. We provide empirical results of applying the approach on an inverted pendulum swing-up task and compare its performance against Q learning. The results bring out the superiority of the Markov game formulation for direct adaptive optimal control over the MDP setting. Further, the results demonstrate that NN could be used as an effective tool for speeding up learning in large Markov games and for extending the game theoretic direct adaptive optimal control to a continuous state space.

A parameterization for a linear system is presented to design a direct model reference adaptive pole placement controller. This parameterized model is one of the structured nonminimal models. The exponentially weighted least-squares algorithm is employed to estimate the control parameters. The direct adaptive controller has the exponential weighting properties by the proposed method of selecting the characteristic polynomials of the sensitivity function filters in connection with the reference model.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

This paper investigates the application of direct adaptive control to suppress the aeroelastic response of a flexible wing model for a range of flight conditions, including pre- and post-flutter airspeeds, while also subject to unmodeled nonlinearities such as nonlinear structural stiffness and actuator free-play. A three-dimensional aeroelastic wing is developed in which the structural dynamics are modeled using a three-dimensional extension of a typical aeroelastic section by mode shape weighting. The aerodynamic forcing is incorporated via an unsteady vortex lattice method. Nonlinear structural stiffness and actuator free-play models are developed and incorporated into the aeroelastic model as well as exogenous disturbances, such as continuous turbulence and discrete gust models. A direct adaptive control strategy is employed that takes the form of an adaptive regulator in which the feedback gain represents the adaptive augmentation of a baseline linear quadratic regulator (LQR) that is designed using the linear aeroelastic model at a pre-flutter flight condition. Simulation studies are presented to evaluate the performance of the adaptive controller in comparison to the baseline LQR controller for a range of flight conditions and with the inclusion of a torsional structural nonlinearity and actuator free-play. The results show that the adaptive controller provides improved attenuation of the linear aeroelastic model as the airspeed increases past the flutter point. In addition, for the case where torsional nonlinearity is included, the adaptive controller is able to stabilize the aeroelastic response at the flutter speed whereas the closed-loop response using the baseline LQR controller is unstable.

A direct adaptive neural control scheme with single and double integral-plus-state (IPS) actions is proposed. The control scheme contains two recurrent trainable neural network (RTNN) models, which are a plant parameter identifier and state estimator, an IPS feedback/feedforward controller, and one or two I-terms. The good performance of the adaptive IPS control scheme is confirmed by closed-loop systems analysis and by simulation results obtained with a MIMO plant, corrupted by noise. © 2005 Wiley Periodicals, Inc. Int J Int Syst 20: 213–224, 2005.

A controller to rotate a rigid body between two successive orientations is designed. Particular features are the fact that it is based on the quaternion approach, known to provide singularity-free attitude description, and it is adaptive in the sense that it does not need specific knowledge of the inertia matrix. Global stability of the overall controller is proved analytically and tested in computer simulations. © 1994 American Institute of Aeronautics and Astronautics, Inc., All rights reserved.

Direct adaptive control covers schemes where the parameters of the controller are directly updated from a signal error (adaption error) reflecting the performance error. The chapter presents strategies for direct adaptive control in a deterministic and in a stochastic environment and the corresponding analysis. This includes adaptive tracking and regulation with independent objectives, adaptive minimum variance control and their extensions. Robustification of direct adaptive control schemes is also discussed.KeywordsController ParameterUnmodeled DynamicAdaptive Control SchemeModel Reference Adaptive ControlAdaptive TrackingThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

A new design scheme of direct adaptive neural network controller for a class of nonlinear systems with unknown function control gain is proposed in this paper. The design is based on the principle of sliding mode control and the approximation capability of multilayer neural networks (MNNs). By adopting the adaptive compensation term of the upper bound function of the sum of residual and approximation error, the closed-loop control system is shown to be globally stable, with tracking error converging to zero. Simulation results demonstrate the effectiveness of the approach.