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| Natura: | Preprint |
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2024
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| Accesso online: | https://arxiv.org/abs/2407.18588 |
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| author | Charalambous, Charalambos D. Louka, Stelios |
| author_facet | Charalambous, Charalambos D. Louka, Stelios |
| contents | We consider optimal signalling and control of discrete-time nonlinear partially observable stochastic systems in state space form. In the first part of the paper, we characterize the operational {\it control-coding capacity}, $C_{FB}$ in bits/second, by an information theoretic optimization problem of encoding signals or messages into randomized controller-encoder strategies, and reproducing the messages at the output of the system using a decoder or estimator with arbitrary small asymptotic error probability. Our analysis of $C_{FB}$ is based on realizations of randomized strategies (controller-encoders), in terms of information states of nonlinear filtering theory, and either uniform or arbitrary distributed random variables (RVs). In the second part of the paper, we analyze the linear-quadratic Gaussian partially observable stochastic system (LQG-POSS). We show that simultaneous signalling and control leads to randomized strategies described by finite-dimensional sufficient statistics, that involve two Kalman-filters, and consist of control, estimation and signalling strategies. We apply decentralized optimization techniques to prove a separation principle, and to derive the optimal control part of randomized strategies explicitly in terms of a control matrix difference Riccati equation (DRE). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_18588 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Signalling and Control in Nonlinear Stochastic Systems: An Information State Approach with Applications Charalambous, Charalambos D. Louka, Stelios Information Theory 93E20 We consider optimal signalling and control of discrete-time nonlinear partially observable stochastic systems in state space form. In the first part of the paper, we characterize the operational {\it control-coding capacity}, $C_{FB}$ in bits/second, by an information theoretic optimization problem of encoding signals or messages into randomized controller-encoder strategies, and reproducing the messages at the output of the system using a decoder or estimator with arbitrary small asymptotic error probability. Our analysis of $C_{FB}$ is based on realizations of randomized strategies (controller-encoders), in terms of information states of nonlinear filtering theory, and either uniform or arbitrary distributed random variables (RVs). In the second part of the paper, we analyze the linear-quadratic Gaussian partially observable stochastic system (LQG-POSS). We show that simultaneous signalling and control leads to randomized strategies described by finite-dimensional sufficient statistics, that involve two Kalman-filters, and consist of control, estimation and signalling strategies. We apply decentralized optimization techniques to prove a separation principle, and to derive the optimal control part of randomized strategies explicitly in terms of a control matrix difference Riccati equation (DRE). |
| title | Signalling and Control in Nonlinear Stochastic Systems: An Information State Approach with Applications |
| topic | Information Theory 93E20 |
| url | https://arxiv.org/abs/2407.18588 |