DocumentCode :
1501185
Title :
Linear dynamically varying LQ control of nonlinear systems over compact sets
Author :
Bohacek, Stephan ; Jonckheere, Edmond A.
Author_Institution :
Dept. of Math., Univ. of Southern California, Los Angeles, CA, USA
Volume :
46
Issue :
6
fYear :
2001
fDate :
6/1/2001 12:00:00 AM
Firstpage :
840
Lastpage :
852
Abstract :
Linear-quadratic controllers for tracking natural and composite trajectories of nonlinear dynamical systems evoluting over compact sets are developed. Typically, such systems exhibit “complicated dynamics”, i.e., have nontrivial recurrence. The controllers, which use small perturbations of the nominal dynamics as input actuators, are based on modeling the tracking error as a linear dynamically varying (LDV) system. Necessary and sufficient conditions for the existence of such a controller are linked to the existence of a bounded solution to a functional algebraic Riccati equation (FARE). It is shown that, despite the lack of continuity of the asymptotic trajectory relative to initial conditions, the cost to stabilize about the trajectory, as given by the solution to the FARE, is continuous. An ergodic theory method for solving the FARE is presented. Furthermore, it is shown that wrapping the LDV controller around the nonlinear system secures a stable tracking dynamics. Finally, an example of controlling the Henon map to follow an aperiodic orbit is presented
Keywords :
Riccati equations; asymptotic stability; linear quadratic control; nonlinear dynamical systems; time-varying systems; tracking; uncertain systems; Henon map; asymptotic stability; ergodic theory; functional algebraic Riccati equation; linear-quadratic control; nonlinear dynamical systems; time varying systems; tracking; uncertain system; Control systems; Costs; Error correction; Hydraulic actuators; Nonlinear control systems; Nonlinear dynamical systems; Nonlinear systems; Riccati equations; Sufficient conditions; Trajectory;
fLanguage :
English
Journal_Title :
Automatic Control, IEEE Transactions on
Publisher :
ieee
ISSN :
0018-9286
Type :
jour
DOI :
10.1109/9.928585
Filename :
928585
Link To Document :
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