Abstract
This paper studies the indefinite stochastic linear quadratic (LQ) optimal control problem with an inequality constraint for the terminal state. Firstly, we prove a generalized Karush-Kuhn-Tucker (KKT) theorem under hybrid constraints. Secondly, a new type of generalized Riccati equations is obtained, based on which a necessary condition (it is also a sufficient condition under stronger assumptions) for the existence of an optimal linear state feedback control is given by means of KKT theorem. Finally, we design a dynamic programming algorithm to solve the constrained indefinite stochastic LQ issue.
Highlights
The study on linear quadratic (LQ) control problems can be traced back to the pioneering work of Kalman [1] and Wonham [2] several decades ago
This paper studies the indefinite stochastic linear quadratic (LQ) optimal control problem with an inequality constraint for the terminal state
We have studied the indefinite stochastic LQ optimal control problem with unequal terminal state constraint, which can be transformed into a hybrid constrained mathematical programming problem
Summary
The study on LQ control problems can be traced back to the pioneering work of Kalman [1] and Wonham [2] several decades ago. The LQ control theory is elegantly established and developed, and the main work can be seen in [3,4,5,6,7,8,9,10,11] It is found [6] that a stochastic LQ problem with indefinite control weighting matrices may still be well-posed. If we strengthen the condition, we can obtain a necessary and sufficient condition for the existence of the optimal linear feedback control to indefinite stochastic LQ optimal control problem with inequality constraint.
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