SUMMARYA linear-quadratic-Gaussian (LQG) delocalized control problem is formulated to require both specification of a control law and communication of measurements to controller and controls to plant. Efficient communication requires quantization of both measurement and control signals. The basic design problem is to allocate in an optimum fashion a fixed total communication rate to the measurement and control communication systems.A dynamic communication-rate allocation algorithm is developed on the basis of prediction error and entropy power. As intuitively expected, the rate allocation depends on both the measurement and plant noise powers as well as the overall quadratic performance measure. Solely on the basis of entropy power considerations, a larger rate should be allocated for communication of measurements than for communication of controls.

A linear-quadratic-Gaussian (LQG) delocalized cont r o l problem i s formulated t o require both specificat i o n of a control law and comunication of measurements t o c o n t r o l l e r and c o n t r o l s t o p l a n t . E f f i c i e n t communication requires quantization of both measurement and control signals.The basic design problem i s t o a l l o c a t e i n an optimum fashion a f i x e d t o t a l communication rate to the measurement and control communication sys terns.A dynamic communication rate allocation algorithm i s developed based on prediction error and entropy power. As intuitively expected, the rate allocation depends on b o t h the measurement and plant noise powers, as well as the overall quadratic performance measure. Based s o l e l y on entropy power considerations, a l a r g e r rate should be allocated for communication of measurements than for communication of controls. I . INTRODUCTIONI n extending the concepts of classical control theory to the analysis and design of large scale control systems, there is an (often imp1 i c i t ) need t o consider communications as well.Whether the control approach is decentralized or hierarchical with information sharing between various levels or c o n t r o l l e r s , or centralized with information gathered from various sensors, the implicit comnunication paths involved offer significant design constraints and analysis d i f f i c u l t i e s . With the usual continuum assumpti.on regarding state and measurement v a r i a b l e s , t h e f i n i t e r a t e l i m i t a t i o n s of most physically implementable channels imply the need to consider data compression or quantization of the measurement and control variables involved. Since communication system c o s t tends to increase with transmission rate there is cons i d e r a b l e p r a c t i c a l i n t e r e s t i n keeping the required rate as small as possible.I n addition, the stochast i c n a t u r e of information transmission suggests that both faulty measurements and controls are possibil it i e s t h a t must be considered in the design process. Perhaps most significant is the observation t h a t standard communication design c r i t e r i a ( e . g . meansquare error) are not necessarily fully compatible with the overall control objective [l]. Hence separate designs of the control law and communication system may lead to suboptimuin (or substandard) performance.The purpose of the present paper is to formulate and present solution concepts for the problem of optimum r a t e a l l o c a t i o n i n a closed loop control system. The model will necessarily be simple. A s i n g l e *This work was supported by the National Science sensor generates vector measurements to be communicated to a c o n t r o l l e r . Based on the received measurement infomation the controller generates vector controls t o be transmitted and applied t o the plant.The total transmission capacity (the sum of both measurement and control channel transmission rates) i s assumed t o be a constant. The basic problem ...