Signalling and Control in Nonlinear Partially Observable Stochastic Systems: An Information State Approach and LQG Applications
Charalambos D. Charalambous, Stelios Louka · 2025
We formulate and analyze the operational definition, called control-coding capacity, CFBin bits/second, of discrete-time nonlinear partially observable stochastic systems. CFBis the maximum rate of encoding signals or messages into randomized controller-encoder strategies, and reproducing the messages at the output of the system using a decoder, with arbitrary small asymptotic error probability.In the first part of the paper, we characterize CFBby an information theoretic optimization problem over randomized strategies, using posterior distributions of nonlinear filtering theory and information states.In the second part of the paper, we derive the formula of CFB, for linear-quadratic Gaussian partially observable stochastic systems (LQG-POSSs). We express CFBin terms of solutions of two Riccati equations of Kalman-filtering and a control Riccati equation. To derive CFBwe prove, (1) optimal randomized strategies consist of signalling, control, and estimation, and (2) a decentralized semi-separation principle holds between the control problem and the signalling and estimation problems.