Design of stochastic discrete time linear optimal regulators Part I. Relationship between control laws based on a time series approach and a state space approach

Abstract

Distinct approaches to sampled data control system design use either a state space model or a ‘ controlled autoregressive moving average ’ (CARMA) model, sometimes known as Åström's representation, One reason for the current interest in the CARMA model is that it is a useful basis for self-tuning controllers as its parameters can be readily estimated on-line. Moreover, simple transfer function controllers can be derived using κ-step-ahead prediction theory. On the other hand, these controllers can be interpreted as minimizing a single stage cost function in state space terms, and the corresponding performance can sometimes be poor. This paper explores the relationship between the κ-stop-ahead prediction approach and the state space approach, and is a generalization of the earlier work of Caines to include control weighting and time delay on the control. Two forms of state space model are used (‘ explicit ’ and ‘ implicit’ time delay models) and a new representation of the steady state Kalman filter is shown to be required in the generalization ; this filter is put into a computationally convenient form. The technical machinery created in this paper allows for a straightforward generalization to the control of systems described by CARMA models by minimizing an N-stage cost function ; this generalization will be discussed in paper II