Study on Stochastic Linear Quadratic Optimal Control with Quadratic and Mixed Terminal State Constraints

This paper studies the indefinite stochastic LQ control problem with quadratic and mixed terminal state equality constraints, which can be transformed into a mathematical programming problem. By means of the Lagrangian multiplier theorem and Riesz representation theorem, the main result given in this paper is the necessary condition for indefinite stochastic LQ control with quadratic and mixed terminal equality constraints. The result shows that the different terminal state constraints will cause the endpoint condition of the differential Riccati equation to be changed. It coincides with the indefinite stochastic LQ problem with linear terminal state constraint, so the result given in this paper can be viewed as the extension of the indefinite stochastic LQ problem with the linear terminal state equality constraint. In order to guarantee the existence and the uniqueness of the linear feedback control, a sufficient condition is also presented in the paper. A numerical example is presented at the end of the paper

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

A Quasi-Monte-Carlo-Based Feasible Sequential System of Linear Equations Method for Stochastic Programs with Recourse

A two-stage stochastic quadratic programming problem with inequality constraints is considered. By quasi-Monte-Carlo-based approximations of the objective function and its first derivative, a feasible sequential system of linear equations method is proposed. A new technique to update the active constraint set is suggested. We show that the sequence generated by the proposed algorithm converges globally to a Karush-Kuhn-Tucker (KKT) point of the problem. In particular, the convergence rate is locally superlinear under some additional conditions

Study on Stochastic Linear Quadratic Optimal Control with Quadratic and Mixed Terminal State Constraints

This paper studies the indefinite stochastic LQ control problem with quadratic and mixed terminal state equality constraints, which can be transformed into a mathematical programming problem. By means of the Lagrangian multiplier theorem and Riesz representation theorem, the main result given in this paper is the necessary condition for indefinite stochastic LQ control with quadratic and mixed terminal equality constraints. The result shows that the different terminal state constraints will cause the endpoint condition of the differential Riccati equation to be changed. It coincides with the indefinite stochastic LQ problem with linear terminal state constraint, so the result given in this paper can be viewed as the extension of the indefinite stochastic LQ problem with the linear terminal state equality constraint. In order to guarantee the existence and the uniqueness of the linear feedback control, a sufficient condition is also presented in the paper. A numerical example is presented at the end of the paper