# The totally singular linear quadratic problem with indefinite cost

H.L. Trentelman

### Abstract

In this paper we study the most general version of the stationary, infinite horizon linear quadratic optimal control problem. In the literature that has appeared on this problem up to now, mostly one (or both) of the following two assumptions are made: (i) the integrand of the cost criterion is given by a positive semi-definite quadratic form, (ii) the latter quadratic form is positive definite in the control variable alone. In the present paper we propose a problem formulation for the case that neither (i) nor (ii) are imposed. Subsequently, we treat the case that the problem is completely singular.
Original language English Eindhoven Technische Universiteit Eindhoven 24 Published - 1989

### Publication series

Name Memorandum COSOR 8905 0926-4493

### Fingerprint

Singular Problems
Costs
Positive semidefinite
Infinite Horizon
Integrand
Positive definite
Optimal Control Problem
Formulation

### Cite this

Trentelman, H. L. (1989). The totally singular linear quadratic problem with indefinite cost. (Memorandum COSOR; Vol. 8905). Eindhoven: Technische Universiteit Eindhoven.
Trentelman, H.L. / The totally singular linear quadratic problem with indefinite cost. Eindhoven : Technische Universiteit Eindhoven, 1989. 24 p. (Memorandum COSOR).
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Trentelman, HL 1989, The totally singular linear quadratic problem with indefinite cost. Memorandum COSOR, vol. 8905, Technische Universiteit Eindhoven, Eindhoven.

The totally singular linear quadratic problem with indefinite cost. / Trentelman, H.L.

Eindhoven : Technische Universiteit Eindhoven, 1989. 24 p. (Memorandum COSOR; Vol. 8905).

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AB - In this paper we study the most general version of the stationary, infinite horizon linear quadratic optimal control problem. In the literature that has appeared on this problem up to now, mostly one (or both) of the following two assumptions are made: (i) the integrand of the cost criterion is given by a positive semi-definite quadratic form, (ii) the latter quadratic form is positive definite in the control variable alone. In the present paper we propose a problem formulation for the case that neither (i) nor (ii) are imposed. Subsequently, we treat the case that the problem is completely singular.

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Trentelman HL. The totally singular linear quadratic problem with indefinite cost. Eindhoven: Technische Universiteit Eindhoven, 1989. 24 p. (Memorandum COSOR).