Spectral theory of the linear-quadratic optimal control problem: A new algorithm for spectral computations

In a new formulation of the discrete-time linear-quadratic optimal control problem, the spectrum of a bounded self-adjoint Hilbert space operator, which can be decomposed as the sum of a Toeplitz operator and a compact perturbation, has been shown to elucidate the underlying structure of the problem. A new and efficient algorithm for computing this spectrum is presented.

[1]  B. Anderson.  Algebraic properties of minimal degree spectral factors , 1973 .

[2]  B.P. Molinari,et al.  The time-invariant linear-quadratic optimal control problem , 1977, Autom..

[3]  L. Silverman,et al.  Spectral theory of the linear-quadratic optimal control problem: Discrete-time single-input case , 1978 .

[4]  B. Molinari.  Conditions for nonpositive solutions of the linear matrix inequality , 1975 .

[5]  Leonard M. Silverman,et al.  Spectral Theory of the Linear-Quadratic Optimal Control Problem: Analytic Factorization of Rational Matrix-Valued Functions , 1981 .

[6]  L. Silverman,et al.  The general discrete-time linear-quadratic control problem , 1977, 1977 IEEE Conference on Decision and Control including the 16th Symposium on Adaptive Processes and A Special Symposium on Fuzzy Set Theory and Applications.

[7]  Erol Emre,et al.  New criteria and system theoretic interpretations for relatively prime polynomial matrices , 1976, 1976 IEEE Conference on Decision and Control including the 15th Symposium on Adaptive Processes.

[8]  J. Willems.  Least squares stationary optimal control and the algebraic Riccati equation , 1971 .

[9]  Jan C. Willems,et al.  On the existence of a nonpositive solution to the Riccati equation , 1974 .

[10]  J. Willems.  Mechanisms for the stability and instability in feedback systems , 1976, Proceedings of the IEEE.

[11]  M. Morf,et al.  A generalized resultant matrix for polynomial matrices , 1976, 1976 IEEE Conference on Decision and Control including the 15th Symposium on Adaptive Processes.

[12]  Brian D. O. Anderson.  Correspondence item: Corrections to: Algebraic properties of minimal degree spectral factors , 1975 .

[13]  P. Moylan.  On a frequency-domain condition in linear optimal control theory , 1975 .

[14]  Brian D. O. Anderson,et al.  Recursive algorithm for spectral factorization , 1974 .

[15]  Brian D. O. Anderson,et al.  Generalized Bezoutian and Sylvester matrices in multivariable linear control , 1976 .