Design And Analysis Of Quantized Estimation Systems Under Communication Constraints

With the development of communication and computer technology, complex control systems, remote control systems and networked control systems (NCSs) are applied widely in areas of industrial control, avigation and robot. The performance of these systems is affected by communication constraints of the channel, e.g. bandwidth constraint, access constraint, etc. Hence, new characters are introduced into control systems.State estimation and on-line parameter identification of communication constrained control systems are discussed from the information theoretic point of view in this thesis. Our work consists of the design of states preprocessing and quantization, analysis of states estimability, parameter identifiability and stochastic observability. The main contributions are specifically stated as follows:(1) States preprocessing and quantization are designed for states estimation in different systems. One is the system with communication power constraint and limited number of data to be transmitted simultaneously. The other is similar to the former, besides, the effect of quantization is considered because of the low transmission rate. For the first system, states dimension reduction is designed based on minimum error entropy estimation criterion and Kalman filter; For the second, states dimension reduction and quantizer are designed jointly based on minimum mean square error estimation criterion and MLQ-KF. Analytical analysis and simulation results show that, the estimation performance of these methods are both satisfactory.(2) The states estimability of systems under communication constraints is analyzed. Based on the existing definitions and results, we propose new information theoretic definition of estimability for general systems by considering the intrinsic property of the system. Our analysis for communication power limited systems shows that certain power condition should be satisfied in order to preserve the estimability of the original system. Criterions of estimability, i.e. estimability Gramians, for systems with quantized outputs and quantized innovations are both proposed based on the measure of mutual information. The obtained conditions of estimability consist with our intuition very well and provide us with valuable hints on the quantizer design. The conclusions also show that a well designed quantizer can preserve the estimability of the original system even if the quantizer is as coarse as one bit. Further analysis shows that the Gramians of quantized systems converge to that of unquantized systems.(3) The stochastic observability of systems with quantized outputs or quantized innovations is analyzed based on the quantity of mutual information between the states and the quantized measurements. Our discussion begins with the analysis of observability of systems with discrete-valued random initial state and no process and measurement noise, and certain information theoretic conclusion about observability is obtained. Following the similar line of argument as the analysis of estimability for quantized systems, criterions of stochastic observability for quantized systems are proposed. The formations of quantized estimability Gramians and quantized stochastic observability Gramians are similar, so similar conclusions can be inferred from them, and also the convergence property.(4) The relation between estimability and stochastic observability of stochastically autonomous systems is established based on the above discussion, and corresponding conclusions are obtained. For unquantized systems, if the system tansition matrix is nonsingular, the estimability and stochastic observability of time-invariant autonomous systems are equivalent, whereas for time-variant system, its estimability implies its stochastic observability, but not the vice versa; we have similar conclusions for the quantized systems, where the difference is that another condition, i.e. the weights of the Gramians are nonzero at any time instant, should be additionally included for the equivalence between the two properties of time-invariant autonomous systems.(5) Motivated by the research of adaptive control, the parameter identifiability of quantized systems with Gauss-Markov parameters is analyzed from the viewpoint of information theory, following the analysis of states estimability. The problem of parameter identifiability can be treated as states estimability by the transformation from input-output model to state space model. The presented definition of parameter identifiability is reviewed and extended to quantized systems by considering the intrinsic property of the system. The criterion of parameter identifiability of linear systems with quantized outputs is proposed. Furthermore, the convergence property of the quantized parameter identifiability Gramian is proved. The mathematical analysis is verified by illustrative simulation.Our work indicates that, the estimation performance of the design methods of states dimension reduction and quantizer is satisfactory. Provided that the system (e.g. the quantizer) is well designed, the estimability, identifiability or stochastic observability of the original system, which may be changed by communication constraints, can be preserved. Hence, our work provides some hints on the design of NCSs.