Nonlinear Regulators for a Class of Decomposable Systems

[+] Author and Article Information
S. Kimbrough

KYOTE Scientific Co., Los Angeles, CA 90025

J. Dyn. Sys., Meas., Control 109(2), 128-132 (Jun 01, 1987) (5 pages) doi:10.1115/1.3143829 History: Received March 10, 1986; Online July 21, 2009


This paper presents nonlinear regulators for a large class of systems that includes many linear systems, bilinear systems, and variable structure systems. Membership in this class requires that the dynamic equations of a system decompose into a set of stable equations and into a set of equations which are nulled by some feasible control value. When the stable set of equations represents a linear system and the remaining set of equations is linear in the control variables (with other variables fixed), the resulting regulators become attractive alternatives to linear regulators. They have time invariant forms suitable for real-time control, have the capability to handle complicated constraints, and have control properties beyond the range of linear regulators. The procedure followed is to obtain a Lyapunov function for the stable set of equations, which is then used to assure closed loop stability. Sufficient conditions for maintaining Lyapunov stability are treated as constraints in optimizations that yield the control policies. These constraints can always be satisfied because it is assumed that some feasible control nulls the remaining set of equations. The benefits of this procedure are that stability can be obtained by working with a smaller more manageable set of equations than the full system equations and control policies can be obtained from readily solvable optimizations. Although the resulting nonlinear regulators are suboptimal their performance can often be bounded by the performance of an optimal linear regulator.

Copyright © 1987 by ASME
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