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A polynomial solution to regulation and tracking. I: Deterministic problem. (English) Zbl 0542.93013

Summary: Recent results on polynomial techniques in solving the discrete-time linear-quadratic regulation and/or tracking problems are presented. Both deterministic and stochastic problems are considered in order to let appear their formal similarity and to contrast the inherent differences. The analysis is based on external polynomial models and the construction of the optimal controller or control sequence is reduced to the solution of linear polynomial equations, combined with spectral factorization. The existence of admissible controls that yield a finite performance index is studied and all such controls are specified in a parametric form. The optimal control then corresponds to the zero parameter and is shown to be recurrent, i.e. realizable by a linear finite dimensional system.

MSC:

93B25 Algebraic methods
93C05 Linear systems in control theory
93C55 Discrete-time control/observation systems
93B15 Realizations from input-output data
12E12 Equations in general fields
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