Discrete-time interrupted stochastic control processes

✍ Scribed by J.H. Eaton

• Publisher: Elsevier Science
• Year: 1962
• Tongue: English
• Weight: 714 KB
• Volume: 5
• Category: Article
• ISSN: 0022-247X
• DOI: 10.1016/s0022-247x(62)80011-0

✦ Synopsis

This paper is concerned with the determination of optimal policies for applying inputs to discrete-time processes which are interrupted in the sense that at each time t, t = 1, 2, ..., there is a probability Pt (called the probability of interruption) that the state vector of the system cannot be observed. The policy is to be optimal with respect to a specified loss functional. It is shown that the optimal policy for controlling such processes can be expressed in terms of functional equations obtained by the usual procedures of dynamic programming_ An interrupted process involving a linear system and quadratic loss functional is examined in detail and the optimal policy as well as the expected cost of the process under the optimal policy is expressed in analytic form. The optimal policy is found to be independent of the probability of interruption. Asymptotic properties of the optimal policy and the expected cost of the process under the optimal policy are also obtained.