Name
Abstract | ||
|---|---|---|
We consider the infinite horizon quadratic cost minimization problem for a linear system with finitely many inputs and outputs. A common approach to treat a problem of this type is to construct a semigroup in an abstract state space, and to use infinite-dimensional control theory. However, this approach is less appealing in the case where there are discrete time delays in the impulse response, because such time delays force both the control operator and the observation operator to be unbounded at the same time. In order to be able to include this case we take an alternative approach. We work in an input-output framework, and reduce the problem to a symmetric Wiener-Hopf problem, that can be solved by means of a canonical factorization of the symbol. In a standard shift semigroup realization this amounts to factorizations of the Riccati operator and the feedback operator into convolution operators and projections. Our approach leads to a new significant discovery: in the case where the impulse response of the system contains discrete time delays, the standard Riccati equation is incorrect; to get the correct Riccati equation the feed-through matrix of the system must be partially replaced by the feed-through matrix of the spectral factor. This means that, before it is even possible to write down the correct Riccati equation, a spectral factorization problem must first be solved to find one of the weighting matrices in this equation. |
Year | DOI | Venue |
|---|---|---|
1995 | 10.1007/BF01210206 | MCSS |
Keywords | Field | DocType |
shift semigroup realization,canonical factorization,discrete delays,continuous delays.,wiener-hopf factorization,abstract linear system,riccati equation,control theory,impulse response,spectral factorization,state space,discrete time,linear system,convolution operator,input output,quadratic optimization | Mathematical optimization,Optimal control,Algebra,Linear system,Control theory,Riccati equation,Operator (computer programming),Algebraic Riccati equation,Factorization,Linear-quadratic regulator,Mathematics,Spectral theorem | Journal |
Volume | Issue | ISSN |
8 | 2 | 1435-568X |
Citations | PageRank | References |
10 | 2.92 | 3 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Olof J. Staffans | 1 | 66 | 15.08 |
| Olof J. Staffans | 2 | 66 | 15.08 |