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Stabilizing optimal control of bilinear systems with a generalized cost

✍ Scribed by S. G. Tzafestas; K. E. Anagnostou; T. G. Pimenides

Publisher: John Wiley and Sons
Year: 1984
Tongue: English
Weight: 362 KB
Volume: 5
Category: Article
ISSN: 0143-2087
DOI: 10.1002/oca.4660050204

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✦ Synopsis

Stabilizing and optimizing feedback control policies are derived for the important class of bilinear systems with generalized quadratric cost functions. These policies as well as the resulting optimal costs are quadratic in the state. The optimal cost function is shown to be a Lyapunov function for the bilinear system at hand. The resulting optimal and stabilized closed-loop system is of third order with respect to the state. One illustrative example is included.

KEY WORDS Bilinear systems Stabilizing optimal control policy Linear state feedback Quadratic state feedback Generalized cost.

x = f ( x ) + x 5 , Bi(x)ui where ui, i = 1,2, ..., m, represent the control variables and the vector functions Bi(x); Bi: R" + R" are assumed to be continuous in x for i = 1,2, ..., m.

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