Invariant Theory, the Riccati Group, and Linear Control Problems

Casti, J.L. (1976). Invariant Theory, the Riccati Group, and Linear Control Problems. IIASA Research Memorandum. IIASA, Laxenburg, Austria: RM-76-059

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Abstract

The classical algebraic theory of invariants is applied to the linear-quadratic-gaussian (LQG) control problem to derive a canonical form under a certain matrix transformation group. The particular group of transformations, termed here the "Riccati group," is induced from the matrix Riccati equation characterizing the LQG problem solution.

Examples of the invariant-theoretic approach are given along with a discussion of topics meriting further study, including geometric interpretation of the group orbits, extension of the Riccati group, and connections with the generalized X-Y functions.

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