TY - BOOK

T1 - The algebraic Riccati equation and singular optimal control

AU - Geerts, A.H.W.

PY - 1989

Y1 - 1989

N2 - The paper links the class of nonnegative definite linear-quadratic optimal control problems to a subset of the set of real symmetric matrices that satisfy the dissipation inequality. This important subset is characterized by means of a certain algebraic Riccati equation and a linear condition. Moreover, we attach every positive semi-definite element of the subset in a one-to-one way to a certain subspace of a properly defined factor space. If the input weighting matrix in the cost functional is positive semi-definite, then the known results on bijective relations between positive semi-definite solutions of the algebraic Riccati equation and certain subspaces of the state space are recovered.
Keywords: Linear-quadratic control problems, dissipation inequality, algebraic Riccati equation, strongly reachable subspace, induced map.

AB - The paper links the class of nonnegative definite linear-quadratic optimal control problems to a subset of the set of real symmetric matrices that satisfy the dissipation inequality. This important subset is characterized by means of a certain algebraic Riccati equation and a linear condition. Moreover, we attach every positive semi-definite element of the subset in a one-to-one way to a certain subspace of a properly defined factor space. If the input weighting matrix in the cost functional is positive semi-definite, then the known results on bijective relations between positive semi-definite solutions of the algebraic Riccati equation and certain subspaces of the state space are recovered.
Keywords: Linear-quadratic control problems, dissipation inequality, algebraic Riccati equation, strongly reachable subspace, induced map.

M3 - Report

T3 - Memorandum COSOR

BT - The algebraic Riccati equation and singular optimal control

PB - Technische Universiteit Eindhoven

CY - Eindhoven

ER -