Theoretical approaches on multirate LQG control and their performance analyses

Abstract

In discrete-time system, sampling time is a critical parameter for control performance. Better performance demands a fast sampling rate, while the achievable sampling rate is often restricted by the availability of measuring system or actuating system. It is often useful to employ the different sampling rate in such cases. The system which has the different sampling mechanisms in each input and output are named multirate system. The research of multirate system have been treated from the transfer function perspective and the state space perspective. Recently, the state space approaches have been mainly issued for the availability of application to the multi-input multi-output (MIMO) system. State space realizations of multirate system are classified into the following research groups: 1) time-invariant realizations, 2) periodic realizations. Time-invariant realizations are constructed by the augmentation of the inputs and the outputs over one period. Such realizations enable us to apply the conventional control scheme directly, while the construction of the realization is not flexible to the sampling rate variations and it is impossible to describe the intersample behaviors directly. Furthermore the realizations need more computations than periodic realizations in order to construct the control loop. Periodic realizations require smaller computations to construct the control loop, while they demand periodic time-varying system theory and result in solving the periodic Riccati equation. In this thesis, we consider the linear quadratic Gaussian(LQG) control design of stochastic linear MIMO systems specified by a multirate sampling mechanism and present several approaches for the systems. First, a time-invariant realization is proposed for the system. The proposed realization enables us to employ the conventional LQG control scheme directly and to construct on-line control loop with smaller computations than other time-invariant realizations. The realization is ...