State Estimation and Control for LTI Systems Over Communication Channels

In this thesis, state estimation and control problems in linear time invariant (LTI) systems where the controller and the plant are connected through digital noiseless channels and communication networks are investigated. For deterministic (noiseless) systems, uniform quantization noise is shown to be the effective one, and distortion-constrained quantization is introduced as a time-invariant stable quantization method. Forward-looking schemes where the intention is the stabilization of the state estimation error, and recursive schemes where the objective is to achieve a monotonic variance in state estimation error are considered. In deterministic systems both approaches are shown to lead to the same performance in terms of the communication rate values. In stochastic (noisy) systems however, forward-looking schemes require less stringent conditions. For systems with communication networks, the rate required for the stability of the differential entropy of the state estimation error is determined as a function of the system and network parameters. The trade-off between the sampling period, packet loss probability and the rate requirements is illustrated, a Markov chain model is introduced to capture the state of reliability of the network, and conditions for stability in the mean in a control theoretic setting are studied. Conditions for the mean-square stability in the state estimation error, stability in the mean, and stability in the mean-square of an LTI system with communication networks are introduced, and in case of a packet loss, the usage of the latest control and the zero control usage are compared. The communication rate requirements for higher dimensional centralized and decentralized control systems where the controller and the plant are connected via a noiseless bandlimited channel are also studied. Recursive time-invariant quantizers that achieve stability in the sense of worst-case state estimation error are introduced. Rate requirements for centralized schemes are shown to be lower than those for decentralized schemes. A quantification of the information sharing between the controllers, such as full, instant, and one-step delayed information sharing, is shown to be an important factor contributing to communication requirements and complexity. Slepian-Wolf coding argument is used to show that information sharing by the controllers, and not by the plants, is sufficient for optimality, and schemes confirming this efficiency are constructed. Finally, the linear quadratic regulator (LQR) problem for systems with digital channels (and hence subject to bandwidth constraints) is solved and the structure of the optimal quantizer for this class of problems is determined.National Science FoundationOpe