Discrete-Time Indefinite Stochastic LQ Control via SDP and LMI Methods

This paper studies a discrete-time stochastic LQ problem over an infinite time horizon with state-and control-dependent noises, whereas the weighting matrices in the cost function are allowed to be indefinite. We mainly use semidefinite programming (SDP) and its duality to treat corresponding problems. Several relations among stability, SDP complementary duality, the existence of the solution to stochastic algebraic Riccati equation (SARE), and the optimality of LQ problem are established. We can test mean square stabilizability and solve SARE via SDP by LMIs method

Indefinite LQ Optimal Control with Terminal State Constraint for Discrete-Time Uncertain Systems

Uncertainty theory is a branch of mathematics for modeling human uncertainty based on the normality, duality, subadditivity, and product axioms. This paper studies a discrete-time LQ optimal control with terminal state constraint, whereas the weighting matrices in the cost function are indefinite and the system states are disturbed by uncertain noises. We first transform the uncertain LQ problem into an equivalent deterministic LQ problem. Then, the main result given in this paper is the necessary condition for the constrained indefinite LQ optimal control problem by means of the Lagrangian multiplier method. Moreover, in order to guarantee the well-posedness of the indefinite LQ problem and the existence of an optimal control, a sufficient condition is presented in the paper. Finally, a numerical example is presented at the end of the paper

Discrete-Time Indefinite Stochastic Linear Quadratic Optimal Control with Second Moment Constraints

This paper studies the discrete-time stochastic linear quadratic (LQ) problem with a second moment constraint on the terminal state, where the weighting matrices in the cost functional are allowed to be indefinite. By means of the matrix Lagrange theorem, a new class of generalized difference Riccati equations (GDREs) is introduced. It is shown that the well-posedness, and the attainability of the LQ problem and the solvability of the GDREs are equivalent to each other