Linear quadratic control. State space vs. polynomial equations. (English) Zbl 0549.93030

Kučera, Vladimír

Kybernetika 19, 185-195 (1983).

Summary: A class of linear quadratic control problems, the state space solution of which is well known, is solved here using the method of polynomial equations. The discussion includes linear regulator, state estimator, observer for a linear functional of state and finally the case of linear quadratic control with incomplete and/or noisy measurements. The emphasis is placed on relating the two design techniques and on demonstrating the basic features of the polynomial equation approach. This provides further insight as well as simple and efficient algorithms for control system design.

MSC:

93C05	Linear systems in control theory
12E12	Equations in general fields
93E10	Estimation and detection in stochastic control theory
93B50	Synthesis problems
93E20	Optimal stochastic control

Keywords:

linear quadratic control problems; polynomial equations

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