NDLI: Inverse optimal adaptive control—The interplay between update laws, control laws, and Lyapunov functions

Content Provider	IEEE Xplore Digital Library
Author	Krstic, M.
Copyright Year	2009
Description	Author affiliation: Department of Mechanical and Aerospace Engineering, University of California, San Diego, La Jolla, 92093-0411, USA (Krstic, M.)
Abstract	Approaching the problem of optimal adaptive control as “optimal control made adaptive,” namely, as a certainty equivalence combination of linear quadratic optimal control and standard parameter estimation, fails on two counts: numerical (as it requires a solution to a Riccati equation at each time step) and conceptual (as the combination actually does not possess any optimality property). In this note we present a particular form of optimality achievable in Lyapunov-based adaptive control. State and control are subject to positive definite penalties, whereas the parameter estimation error is penalized through an exponential of its square, which means that no attempt is made to enforce the parameter convergence, but the estimation transients are penalized simultaneously with the state and control transients. The form of optimality we reveal here is different from our work in [Z. H. Li and M. Krstic, “Optimal design of adaptive tracking controllers for nonlinear systems,” Automatica, vol. 33, pp. 1459–1473, 1997] where only the terminal value of the parameter error was penalized. We present our optimality concept on a PDE example—boundary control of a particular parabolic PDE with an unknown reaction coefficient. Two technical ideas are central to the developments in the note: a non-quadratic Lyapunov function and a normalization in the Lyapunov-based update law. The optimal adaptive control problem is fundamentally nonlinear and we explore this aspect through several examples that highlight the interplay between the non-quadratic cost and value functions.
Starting Page	1250
Ending Page	1255
File Size	967687
Page Count	6
File Format	PDF
ISBN	9781424445233
ISSN	07431619
DOI	10.1109/ACC.2009.5159800
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2009-06-10
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	American Automatic Control Council(AACC)
Subject Keyword	Optimal control Programmable control Adaptive control Lyapunov method Automatic control Parameter estimation Riccati equations Error correction Convergence State estimation
Content Type	Text
Resource Type	Article
Subject	Electrical and Electronic Engineering

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