Stable direct adaptive periodic control of nonminimum-phase systems

Stable direct adaptive neural controller of nonlinear systems based on single auto-tuning neuron

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.

Globally stable direct adaptive backstepping NN control for uncertain nonlinear strict-feedback systems

Robust Adaptive Control

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.

A globally stable direct adaptive control algorithm for robotic manipulators is proposed. The algorithm is based on a desired compensation adaptation law and control law such that the measurement noise is no longer correlated with the regression vector. Therefore the parameter estimates are not susceptible to parameter drift. Lyapunov theory is used to design both the control law and the adaptation law. Based on stability theory we establish sufficient conditions for the choice of the controller gains. These sufficient conditions are formulated directly from the bounds on the inertial parameters. The performance of the proposed algorithm is demonstrated by computer simulation. The proposed method is also compared to the methods proposed by Slotine and Li (1987), and Sadegh and Horowitz (1990).

In this paper, output feedback direct adaptive robust NN control is investigated for a class of nonlinear discrete-time systems in strict-feedback form. To construct output feedback control, the original strict-feedback system is transformed into a cascade form, which the output feedback of the nonlinear discrete-time system can be carried out. Then with employment of the inputs and outputs, the output feedback direct adaptive robust NN control is developed. The HONNs is exploited to approximate unknown function, and a stable adaptive NN controller is synthesized. The proposed algorithm improves the rubostness of the discrete-time nonlinear systems. It is proven that all the signals in closed-loop system are uniformly ultimately bounded (UUB). A simulation example is presented to illustrate the effectiveness of the proposed algorithm.Keywordsoutput feedbackrubostnessdirect adaptive NN controldiscrete-time nonlinear system

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

This paper analyzes a direct adaptive pole placement control for linear stable minimum-phase systems with input magnitude and rate constraints. The key feature is the derivation of a governing equation relating the prediction error to the "input discrepancy" between the adaptive control and corresponding non-adaptive one, independent of how parameter estimates were obtained. With the governing equation, one is able to establish the input matching property of the adaptive constrained control, i.e., asymptotic convergence to zero of the "input discrepancy".

In this paper, we develop a Direct Model Reference Adaptive Tracking Controller for linear systems with unknown delays, sometimes known as retarded equations. This controller can also reject bounded disturbances of known wave form but unknown amplitude, e.g. steps or sinusoids. We prove that the controller produces global asymptotic tracking with bounded controller gains when the delay-free open-loop plant is almost strictly positive real (equivalently, is minimum phase and has CB positive definite) and the internal delay terms satisfy a linear matrix inequality. The adaptive controller has no knowledge of the delay. An illustrative example is provided.

In this paper we considered the existing stable adaptive fault-tolerant control system design from references [3, 4] for achieving acceptable flight performance in the presence of control effector failures. This controller is developed for the overactuated case, i.e. the case when the number of control effectors exceeds the number of controlled outputs. We have shown that, in some cases, single or multiple effector failures introduce disturbances that are too large to be effectively handled by a single adaptive controller. To address this problem, in this paper we developed an adaptive fault-tolerant flight control system based on the concept of multiple models, switching and tuning from reference [11]. We have shown that such a controller yields a stable overall system, is sufficiently robust in the presence of severe control effector failures, and achieves excellent overall performance as illustrated through simulations of F/A-18A carrier landing maneuver.

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.

In this paper, we propose a direct adaptive iterative learning control for a class of nonaffine nonlinear discrete-time systems with unknown control direction. The fuzzy neural network is firstly used as approximator to compensate for the unknown certainty equivalent controller. Then, in order to solve the uncertainties from approximation errors and random input disturbances, a dead zone like auxiliary error with a time-varying boundary layer is introduced. The auxiliary error is designed for the construction of adaptive laws and the time-varying boundary layer is applied as a bounding parameter. Based on a Lyapunov like analysis, it is shown that the internal signals are bounded and the norm of output tracking error will asymptotically converge to a residual set which is bounded by the width of the boundary layer. Finally, a simulation example is given to verify effectiveness of the proposed direct adaptive iterative learning control.

Design methods of asymptotically stable adaptive consensus control of multi-agent systems composed of the first-order and the second-order regression models are presented based on inverse optimal control criterion. The proposed control schemes are derived as solutions of certain H∞ control problems, where estimation errors of tuning parameters are regarded as external disturbances to the process. The resulting control systems are robust to uncertain system parameters and the desirable consensus tracking is achieved asymptotically via adaptation schemes and L2-gain design parameters together with an introduction of a generating model of a leader.

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.