NDLI: Optimization of quadratic performance indexes for nonlinear control systems

Content Provider	IEEE Xplore Digital Library
Author	Kazantzis, N. Kravaris, C. Wright, R.A.
Copyright Year	2001
Description	Author affiliation: Dept. of Chem. Eng., Worcester Polytech. Inst., MA, USA (Kazantzis, N.)
Abstract	The proposed approach aims at the development of a systematic method to optimally choose the controller tunable parameters in a nonlinear control system, where in addition to the traditional set of closed-loop performance specifications, optimality is also requested with respect to the physically meaningful quadratic performance index. In particular, the value of the performance index can be calculated exactly by solving the Zubov partial differential equation (PDE). It can be shown that the Zubov PDE admits a unique and locally analytic solution that is endowed with the properties of a Lyapunov function for the closed-loop system. Moreover, the analyticity property of the solution of Zubov PDE enables the development of a series solution method that can be easily implemented with the aid of a symbolic software package. It can be shown that the evaluation of the above Lyapunov function at the initial conditions leads to a direct calculation of the value of the performance index which now explicitly depends on the controller parameters. Therefore, the employment of static optimization techniques can provide the optimal values of the finite-set of controller parameters. Finally, it shown that an explicit estimate of the size of the closed-loop stability region can be provided by using results from the Zubov stability theory.
Sponsorship	IEEE Control Syst. Soc
Starting Page	2758
Ending Page	2762
File Size	504907
Page Count	5
File Format	PDF
ISBN	0780370619
DOI	10.1109/CDC.2001.980690
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2001-12-04
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Nonlinear control systems Optimal control Performance analysis Stability Control systems Linear feedback control systems Control nonlinearities Chemical engineering Electronic mail Employment
Content Type	Text
Resource Type	Article

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