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Asymptotic Tracking

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W. E. Dixon – 1st expert on this subject based on the ideXlab platform

  • Robust Asymptotic Tracking of a class of nonlinear systems using an adaptive critic based controller
    Proceedings of the 2010 American Control Conference, 2010
    Co-Authors: Shubhendu Bhasin, P. M. Patre, Nitin Sharma, W. E. Dixon

    Abstract:

    Traditional Reinforcement Learning (RL) controllers are based on a discrete formulation of the Dynamic Programming (DP) problem, which impedes the development of rigorous stability analysis of continuous-time closed loop controllers for uncertain nonlinear systems. Non-DP based RL controllers typically yield a uniformly ultimately bounded (UUB) stability result due to the presence of disturbances and unknown approximation errors. In this paper a non-DP based reinforcement learning scheme is developed for Asymptotic Tracking of a class of uncertain nonlinear systems with bounded disturbances. A recently developed RISE (Robust Integral of the Sign of the Error) feedback technique is used in conjunction with a feedforward neural network (NN) based Actor-Critic architecture to yield a semi-global Asymptotic result. A composite weight tuning law for the Action NN, consisting of both unsupervised and reinforcement learning terms, is developed based on Lyapunov stability analysis.

  • Asymptotic Tracking for Systems With Structured and Unstructured Uncertainties
    IEEE Transactions on Control Systems Technology, 2008
    Co-Authors: P. M. Patre, C. Makkar, W. Mackunis, W. E. Dixon

    Abstract:

    The control of systems with uncertain nonlinear dynamics has been a decades-long mainstream area of focus. The general trend for previous control strategies developed for uncertain nonlinear systems is that the more unstructured the system uncertainty, the more control effort (i.e., high gain or high-frequency feedback) is required to cope with the uncertainty, and the resulting stability and performance of the system is diminished (e.g., uniformly ultimately bounded stability). This brief illustrates how the amalgamation of an adaptive model-based feedforward term (for linearly parameterized uncertainty) with a robust integral of the sign of the error (RISE) feedback term (for additive bounded disturbances) can be used to yield an Asymptotic Tracking result for Euler-Lagrange systems that have mixed unstructured and structured uncertainty. Experimental results are provided that illustrate a reduced root-mean-squared Tracking error with reduced control effort.

  • Asymptotic Tracking for Uncertain Dynamic Systems via a Multilayer NN Feedforward and RISE Feedback Control Structure
    2007 American Control Conference, 2007
    Co-Authors: P. M. Patre, W. Mackunis, K. Kaiser, W. E. Dixon

    Abstract:

    The use of a neural network (NN) as a feedforward control element to compensate for nonlinear system uncertainties has been investigated for over a decade. Typical NN-based controllers yield uniformly ultimately bounded (UUB) stability results due to residual functional reconstruction inaccuracies and an inability to compensate for some system disturbances. Several researchers have proposed discontinuous feedback controllers (e.g., variable structure or sliding mode controllers) to reject the residual errors and yield Asymptotic results. The research in this paper describes how a recently developed continuous robust integral of the sign of the error (RISE) feedback term can be incorporated with a NN-based feedforward term to achieve semi-global Asymptotic Tracking. To achieve this result, the typical stability analysis for the RISE method is modified to enable the incorporation of the NN-based feedforward terms, and a projection algorithm is developed to guarantee bounded NN weight estimates.

P. M. Patre – 2nd expert on this subject based on the ideXlab platform

  • Asymptotic Tracking forSystems withStructured andUnstructured Uncertainties
    , 2020
    Co-Authors: P. M. Patre, William Mackunis, C. Makkar, E. Dixon

    Abstract:

    Thecontrol ofsystems withuncertain nonlinear dynamics hasbeena decades longmainstream areaoffocus. Thegeneral trendforprevious control strategies developed for uncertain nonlinear systems isthatthemoreunstructured the systemuncertainty, themorecontrol effort (i.e., highgainor highfrequency feedback) isrequired toreject theuncertainty, andtheresulting stability andperformance ofthesystemis diminished (e.g., uniformly ultimately boundedstability). This paperisthefirst result thatillustrates howtheamalgamation ofanadaptive model-based feedforward termwithahighgain integral feedback termcanbeusedtoyield an Asymptotic Tracking result forsystems thathavemixedunstructured and structured uncertainties.

  • Asymptotic Tracking for Aircraft via Robust and Adaptive Dynamic Inversion Methods
    IEEE Transactions on Control Systems Technology, 2010
    Co-Authors: W. Mackunis, P. M. Patre, M K Kaiser, W E Dixon

    Abstract:

    Two Asymptotic Tracking controllers are designed in this paper, which combine model reference adaptive control and dynamic inversion methodologies in conjunction with the robust integral of the signum of the error (RISE) technique for output Tracking of an aircraft system in the presence of parametric uncertainty and unknown, nonlinear disturbances, which are not linearly parameterizable (non-LP). The control designs are complicated by the fact that the control input is multiplied by an uncertain, non-square matrix. A robust control design is presented first, in which partial knowledge of the aircraft model along with constant feedforward estimates of the unknown input parameters are used with a robust control term to stabilize the system. Motivated by the desire to reduce the need for high-gain feedback, an adaptive extension is then presented, in which feedforward adaptive estimates of the input uncertainty are used. These results show how Asymptotic Tracking control can be achieved for a nonlinear system in the presence of a non-square input matrix containing parametric uncertainty and nonlinear, non-LP disturbances. Asymptotic output Tracking is proven via Lyapunov stability analysis, and high-fidelity simulation results are provided to verify the efficacy of the proposed controllers.

  • Robust Asymptotic Tracking of a class of nonlinear systems using an adaptive critic based controller
    Proceedings of the 2010 American Control Conference, 2010
    Co-Authors: Shubhendu Bhasin, P. M. Patre, Nitin Sharma, W. E. Dixon

    Abstract:

    Traditional Reinforcement Learning (RL) controllers are based on a discrete formulation of the Dynamic Programming (DP) problem, which impedes the development of rigorous stability analysis of continuous-time closed loop controllers for uncertain nonlinear systems. Non-DP based RL controllers typically yield a uniformly ultimately bounded (UUB) stability result due to the presence of disturbances and unknown approximation errors. In this paper a non-DP based reinforcement learning scheme is developed for Asymptotic Tracking of a class of uncertain nonlinear systems with bounded disturbances. A recently developed RISE (Robust Integral of the Sign of the Error) feedback technique is used in conjunction with a feedforward neural network (NN) based Actor-Critic architecture to yield a semi-global Asymptotic result. A composite weight tuning law for the Action NN, consisting of both unsupervised and reinforcement learning terms, is developed based on Lyapunov stability analysis.

M. Tomizuka – 3rd expert on this subject based on the ideXlab platform

  • Asymptotic Tracking for linear systems with actuator saturation by output feedback control
    Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148), 2001
    Co-Authors: M. Kanamori, M. Tomizuka

    Abstract:

    This paper is concerned with Asymptotic Tracking for linear systems with actuator saturation by output feedback control. Both reference inputs and disturbances are represented as zero-input responses of linear systems. The controller includes the internal model with an anti-windup term for the reference and disturbance signals and a state observer for the system to allow output feedback control. The overall system is shown to be Asymptotically stable for any initial condition of the system as long as the magnitudes of the reference and disturbance signals are sized such that the Asymptotic Tracking of the reference signal can be achieved without saturating the actuator. A simulation example is presented to verify the effectiveness of the proposed approach.

  • an anti windup design for linear system with Asymptotic Tracking subjected to actuator saturation
    Journal of Dynamic Systems Measurement and Control-transactions of The Asme, 2000
    Co-Authors: M. Tomizuka

    Abstract:

    This paper deals with Asymptotic Tracking for linear systems with actuator saturation in the presence of disturbances. Both reference inputs and disturbances are assumed to belong to a class which may be regarded as the zero-input responses qf linear systems. The controller includes an anti-windup term which reduces the degradation in the system performance due to saturation. The stability of the overall system is established based on the Lyapunov stability theory, Both state and output feedback solutions are given. The proposed scheme is evaluated for a two axis motion control system by simulation.

  • An anti-windup design for the Asymptotic Tracking of linear system subjected to actuator saturation
    Proceedings of the 1998 American Control Conference. ACC (IEEE Cat. No.98CH36207), 1998
    Co-Authors: M. Tomizuka

    Abstract:

    Deals with Asymptotic Tracking of linear systems with actuator saturation in the presence of disturbances. Both reference inputs and disturbances are assumed to belong to a class which may be regarded as the zero-input response of a linear system. The controller includes an anti-windup term which reduces the degradation in the system performance due to saturation. The stability of the overall system is established based on the Lyapunov stability theory. The proposed scheme is evaluated for a two axis motion control system by simulation.