Sub-Optimal Control of a Stochastic Distributed Parameter System with Discrete Observation and Control Mechanism
Shiro Hata, Hiroshi Shibata, Shigeru Omatsu · Transactions of the Society of Instrument and Control Engineers · 1973
Practically and theoretically, it has become very important to discuss the optimization problems of a complex system with several parameters distributed in space. We have already proposed to apply the methods of functional analysis for solving these problems and studied the derivation of an optimal filter and the construction of an optimal control as independent problems.In this paper, we shall discuss the optimal control of a combined system which possesses both the observation mechanism and the control devices together. Furthermore, from the physically realizable point of view, we treat a system which is observed on discrete finite subdomains of the spatial domain and controlled on similar ones. And under these conditions, we shall derive the optimal filter and then construct the suboptimal control law by use of the optimal estimated values obtained from the filtering mechanism for the linear distributed parameter system with state-dependent noise. Moreover, we shall examine the separability between estimation and control which must be considered for this case.