Backward Stochastic Riccati Equations and Infinite Horizon L-Q Optimal Control with Infinite Dimensional State Space and Random Coefficients

Journal Article · Tue Apr 15 04:00:00 EDT 2008 · Applied Mathematics and Optimization

DOI:https://doi.org/10.1007/S00245-007-9020-Y· OSTI ID:21064175

Guatteri, Giuseppina ^[1]; Tessitore, Gianmario ^[2]

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1. Politecnico di Milano, Dipartimento di Matematica (Italy)
2. Universita di Milano Bicocca, Dipartimento di Matematica e Applicazioni (Italy)

We study the Riccati equation arising in a class of quadratic optimal control problems with infinite dimensional stochastic differential state equation and infinite horizon cost functional. We allow the coefficients, both in the state equation and in the cost, to be random.In such a context backward stochastic Riccati equations are backward stochastic differential equations in the whole positive real axis that involve quadratic non-linearities and take values in a non-Hilbertian space. We prove existence of a minimal non-negative solution and, under additional assumptions, its uniqueness. We show that such a solution allows to perform the synthesis of the optimal control and investigate its attractivity properties. Finally the case where the coefficients are stationary is addressed and an example concerning a controlled wave equation in random media is proposed.

• OSTI ID: 21064175
• Journal Information: Applied Mathematics and Optimization, Journal Name: Applied Mathematics and Optimization Journal Issue: 2 Vol. 57; ISSN 0095-4616
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
MATHEMATICAL SOLUTIONS
MATHEMATICAL SPACE
OPTIMAL CONTROL
RANDOMNESS
RICCATI EQUATION
STOCHASTIC PROCESSES
WAVE EQUATIONS