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Robust adaptive control of linear time-varying systems

Posted on:1990-01-20Degree:Ph.DType:Dissertation
University:University of PittsburghCandidate:Koh, KwangillFull Text:PDF
GTID:1478390017952971Subject:Engineering
Abstract/Summary:
The purpose of this dissertation is to derive an adaptive control scheme for a class of unknown linear time-varying discrete-time systems. The control scheme is required to be robust against unmodeled dynamics and bounded disturbances so that the scheme can be applied to actual systems arising in applications.; We take the approach of indirect adaptive control, wherein the controller consists of a parameter estimator and a linear dynamic controller whose coefficients are functions of the estimated system parameters. Parameter estimation is achieved by using the recursive least squares scheme with a modification insuring that a key property (called the GOPE property) of the output prediction error can be obtained even in the presence of unmodeled dynamics and bounded disturbances. Since the GOPE property does not require convergence of the estimated parameters into a neighborhood of true parameters, the persistency of excitation condition is not necessary for the parameter estimation scheme to perform as desired. An adaptive observer is then constructed based on the estimated system parameters. The control is finally obtained by providing feedback of the observer state through a state feedback gain matrix which exponentially stabilizes the estimated system model.; With this structure of the adaptive controller, stability of the nonlinear and time-varying closed-loop system is analyzed. It is shown that there exist upperbounds for the rate of parameter variation and the relative magnitude of unmodeled dynamics such that global stability of the closed-loop system is insured for operation within these bounds.; In addition to the stability analysis, tracking a set-point reference signal is investigated. It is shown that by using a discrete-time integrator, the tracking error of the adaptive control system is proportional to the magnitude of the rate of time variation of the system parameters, the relative magnitude of unmodeled dynamics, and the magnitude of the bounded disturbance.
Keywords/Search Tags:Adaptive control, System, Time-varying, Linear, Unmodeled dynamics, Scheme, Magnitude
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