This work is concerned with the study of the linear quadratic (LQ) optimal control problem for linear systems with affine inequality constraints on the state and/or the input tra- jectories, and in particular for input/state-invariant linear systems. The study of such systems is motivated notably by the coexistence problem in a chemostat model where, for biologi- cal reasons, it is meaningful to aim at forcing the state and the input trajectories to remain in a cone. Necessary and sufficient optimality conditions are established for the input/state- invariant LQ problem by using the maximum principle with state and input constraints and by using the admissibility of the solution of the standard LQ problem. Similar and specific results are obtained for the particular LQ problem for positive systems, which are character- ized by the invariance of the nonnegative orthant of the state space. The methods developed in this thesis are applied to the chemostat model via the study of locally positively input/state- invariant nonlinear systems. The main results of this work are illustrated by some numerical examples.
The LQ-optimal control problem for invariant linear systems
Beauthier, C. (Author). 5 Apr 2011
Student thesis: Doc types › Doctor of Sciences