A general linear quadratic stochastic control and information value

Abstract

This paper introduces a generalized linear quadratic problem (for short, GLQ) in which two cooperative controllers are posed with two types of constraints both: admissibility (input) constraint and information (randomness) constraint. Our GLQ includes most existing stochastic LQ forms as its special cases, and also widens new frontier beyond. We first derive a generalized stochastic maximum principle for GLQ which involves projection and conditional expectation operators both. Then, focusing on information constraint, we further study its open-loop solvability in dynamically recursive context. Moreover, we derive and compare the optimal values for various information structures of GLQ via closed-loop representation, that reveals a novel insight on underlying information capacity. In particular, information redundancy, efficiency and monotonicity in stochastic LQ setting are first addressed.