# Accession Number:

## AD0750784

# Title:

## An Application of Maximal Dissipative Sets in Control Theory,

# Descriptive Note:

# Corporate Author:

## BROWN UNIV PROVIDENCE R I DIV OF APPLIED MATHEMATICS

# Personal Author(s):

# Report Date:

## 1972-01-01

# Pagination or Media Count:

## 21.0

# Abstract:

Consider the linear control system in Hilbert space given by dxdt Ax Bu. Here A is the infinitesimal generator of a C sub o semigroup of bounded linear operators Tt, t or O, on a real Hilbert space E. The author assumes that Tt is such that normTtsub LE,E or Me sup- omega t for some constants M or 1 and omega O. B is a bounded linear operator from a real Hilbert space H to E and NB is properly contained in H. The author attempts to synthesize a feedback control ut fxt whose active part is bounded, preserves the property of exponential asymptotic stability possessed by the uncontrolled system u O, and is suboptimal in some sense. The synthesis is formally obtained but leads to a nonlinear singular evolution equation for the state variable Xt. The theory of maximal dissipative sets is then applied to show that the state evolution equation possesses a unique solution when the synthesis is modified in an appropriate multivalued way at the singularities. Author

# Descriptors:

# Subject Categories:

- Theoretical Mathematics