Team decision theory and information structures in optimal control problems--Part I

General dynamic team decision problems with linear information structures and quadratic payoff functions are studied. The primitive random variables are jointly Gaussian. No constraints on the information structures are imposed except causality. Equivalence relations in information and in control functions among different systems are developed. These equivalence relations aid in the solving of many general problems by relating their solutions to those of the systems with perfect memory. The latter can be obtained by the method derived in Part I. A condition is found which enables each decision maker to infer the information available to his precedents, while at the same time the controls which will affect the information assessed can be proven optimal. When this condition fails, upper and lower bounds of the payoff function can still be obtained systematically, and suboptimal controls can be obtained.