A primal-dual potential reduction method for problems involving matrix inequalities
Mathematical Programming: Series A and B
SIAM Review
Stochastic Linear Quadratic Regulators with Indefinite Control Weight Costs
SIAM Journal on Control and Optimization
Indefinite Stochastic Linear Quadratic Control and Generalized Differential Riccati Equation
SIAM Journal on Control and Optimization
On the Complexity of Semidefinite Programs
Journal of Global Optimization
Stabilization and destabilization of hybrid systems of stochastic differential equations
Automatica (Journal of IFAC)
Automatica (Journal of IFAC)
Technical communique: Infinite horizon H2/H∞ control for stochastic systems with Markovian jumps
Automatica (Journal of IFAC)
A generalized multi-period mean-variance portfolio optimization with Markov switching parameters
Automatica (Journal of IFAC)
Optimal control of the risk process in a regime-switching environment
Automatica (Journal of IFAC)
Automatica (Journal of IFAC)
Journal of Global Optimization
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This paper studies a stochastic linear quadratic (LQ) control problem in the infinite time horizon with Markovian jumps in parameter values. In contrast to the deterministic case, the cost weighting matrices of the state and control are allowed to be indinifite here. When the generator matrix of the jump process – which is assumed to be a Markov chain – is known and time-invariant, the well-posedness of the indefinite stochastic LQ problem is shown to be equivalent to the solvability of a system of coupled generalized algebraic Riccati equations (CGAREs) that involves equality and inequality constraints. To analyze the CGAREs, linear matrix inequalities (LMIs) are utilized, and the equivalence between the feasibility of the LMIs and the solvability of the CGAREs is established. Finally, an LMI-based algorithm is devised to slove the CGAREs via a semidefinite programming, and numerical results are presented to illustrate the proposed algorithm.