Estimate And Control Of Linear Stochastic Systems Under Several Communication Constraints

Networked control system (NCS) has attracted much attentions in the past few years. Its potential applications cover a broad range of areas such as mobile sensor networks, unmanned aerial vehicles, etc. Due to the use of a shared network to transmit information between different parts, communication constraints are introduced in NCS such as limited bandwidth, delays, packet dropout, etc. Consequently, we need take into account communication constraints when discussing the analysis and design of these systems.Based on stochastic control theory and information theory, LQG control, stochastic observability and estimability, and stochastic adaptive control of linear stochastic systems are respectively discussed for systems with fading channels, access constraints and quantization. The major contributions of this thesis include the following three aspects.(1) LQG control of linear stochastic systems with fading channels is discussed, where the system outputs are assumed to be amplified and transmitted to the controller over a Rayleigh flat fading channel. Aiming at the tradeoff between controller design and signal amplification, an item concerning communication power is added into the LQG cost function and then the controller and amplification factor are derived in a finite horizon, based on the off-line design of amplification factor. Simulation result shows that the designed amplification factor will turn to a constant as time approaches infinity. This inspires us to extend the method to infinite horizon. It is shown that the asymptotic stability of LQG control system will be preserved by using the proposed method under fading constraints. Simulations illustrate the effectiveness of the proposed method.(2) The definition of stochastic observability for linear stochastic systems is proposed in the view of information theory and then we focus on the stochastic observability under access constraints. The existence of an admissible access scheduling under access constraints in the case of non-zero-order-holding (ZOH) to preserve the stochastic observability of original time-varying systems is proved. It is also proved that the use of ZOH does not change the stochastic observability. For time-invariant systems, we further discuss two special access scheduling including the short-period access scheduling (SPAS) and the universal access scheduling (UAS). Taking into account the similarity between stochastic observability and estimability, the relationship between them is then discussed based on the backwards Markov model and conclusions are further extended to estimability under access constraints.(3) Stochastic adaptive control of linear stochastic single-input-single-output systems with quantization is discussed, where parameters are modeled by a Gauss-Markov process. Aiming at the tracking control, dual properties in the output quantization case can be achieved respectively by controller and quantizer based on separation principle, where the controller focuses on the current control performance while the quantizer focuses on the future parameter estimates and makes a compromise between the estimator performance and the excitation. Inspired by it, for the input quantization case, the design of the quantizer is further proposed considering the excitation effect of quantizer. Simulations demonstrate the analysis and method.Our work indicates that in NCSs, though communication constraints can change the estimation and control performance, the system that is well designed will preserve the properties of original systems.