Solvability and asymptotic behavior of generalized Riccati equations arising in indefinite stochastic LQ controls
- 1 March 2001
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Automatic Control
- Vol. 46 (3) , 428-440
- https://doi.org/10.1109/9.911419
Abstract
The optimal control problem in a finite time horizon with an indefinite quadratic cost function for a linear system subject to multiplicative noise on both the state and control can be solved via a constrained matrix differential Riccati equation. In this paper, we provide general necessary and sufficient conditions for the solvability of this generalized differential Riccati equation. Furthermore, its asymptotic behavior is investigated along with its connection to the generalized algebraic Riccati equation associated with the linear quadratic control problem in finite time horizon. Examples are presented to illustrate the results established.Keywords
This publication has 23 references indexed in Scilit:
- Stochastic Linear Quadratic Regulators with Indefinite Control Weight Costs. IISIAM Journal on Control and Optimization, 2000
- Relationship Between Backward Stochastic Differential Equations and Stochastic Controls: A Linear-Quadratic ApproachSIAM Journal on Control and Optimization, 2000
- Stochastic Linear Quadratic Regulators with Indefinite Control Weight CostsSIAM Journal on Control and Optimization, 1998
- Stochastic $H^\infty$SIAM Journal on Control and Optimization, 1998
- A New Approach to Linearly Perturbed Riccati Equations Arising in Stochastic ControlApplied Mathematics & Optimization, 1998
- Stability radii of linear systems with respect to stochastic perturbationsSystems & Control Letters, 1992
- Lectures on stochastic controlPublished by Springer Nature ,1982
- Criterion for the convergence of the solution of the Riccati differential equationIEEE Transactions on Automatic Control, 1981
- Conditions for Positive and Nonnegative Definiteness in Terms of PseudoinversesSIAM Journal on Applied Mathematics, 1969
- On a Matrix Riccati Equation of Stochastic ControlSIAM Journal on Control, 1968