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- W2017285802 abstract "We consider the problem of infimizing the steady state quadratic cost-functional, whose integrand is given by $phi 'D'Dphi + u'Ru$, with R positive semidefinite, subject to the constraint $dot phi = Aphi + Bu$, with fixed initial state. It is shown that there may be two separate cost infima, one under the assumption of bounded control energy and one under the additional assumption of partially bounded inputs. Each of them is a positive semidefinite quadratic function of the initial state whose coefficient matrix is one of the positive semidefinite solutions of a pair of algebraic Riccati relations, provided there are no system modes which are uncontrollable, observable and unstable. The cost infimum can be found by solving a sequence of algebraic Riccati equations in a reduced state space. Let $B_0$ denote the restriction of B to kernel R. If the unobservable subspace of the pair $(D,A)$ is the same as the supremal $(A,B_0 )$ invariant subspace contained in kernel D then the coefficient matrix of the cost infimum is a maximal solution of the pairs of algebraic Riccati relations. In case the cost infimum is a true minimum, then the optimal control is a feedback control when the order of singularity is finite." @default.
- W2017285802 created "2016-06-24" @default.
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- W2017285802 date "1982-03-01" @default.
- W2017285802 modified "2023-09-27" @default.
- W2017285802 title "The Singular Steady State Linear Regulator" @default.
- W2017285802 doi "https://doi.org/10.1137/0320019" @default.
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