On Prediction and Control of Discrete‐Time First‐Order Linear Stochastic Systems with Prospective Strong Intervention

Abstract

This paper is devoted to studying the issue of modeling, forecasting, and optimal feedback control of discrete-time first-order linear stochastic systems with prospective strong intervention (PSI). First, one type of PSI is formulated. Then, one class of induced mechanisms of PSI is characterized, and, with respect to the induced mechanisms, two multi-step forecasting methods for estimating the occurrence time and terminal time of PSI are discussed. Based on these fundamental results, the problem of optimal control with respect to an improved minimum variance performance index is discussed. Finally, the effectiveness and advantages of the proposed control strategy and approach are verified and demonstrated through numerical simulations.

On Constrained MMVC of Discrete‐Time First‐Order Linear Stochastic Systems with PSI I: The Critically Stable Case

“…where a, b and c are parameters, {d k } is defined as [11] ) respectively, and k l = 0 for all k, l ∈ 0 . Assume the initial state x 0 be independent of { k } and { k } in the sense that x 0 k = 0 and x 0 k = 0 for all k ∈ 0 .…”

“…As in [7,11], by introducing new variables, the state variables x k , output variables y k and control input u k can be discomposed into the following forms:…”

“…With the above preparation, the following theorem given in [11] as the basis for this paper, is expressed as follows:…”

“…The study of modeling, forecasting and control for systems with prospective strong intervention (PSI) was initiated in [11], and it was pointed out that the concept of PSI came from practical backgrounds in economics [2,20], finance [9], industry [16,19], and agriculture [14,15]. The issue is distinctly different from the current research concerning disturbance or intervention to systems in both idea and content [3][4][5][6]8,10,12,13,17,18,20].…”

“…In fact, the modeling of inducement mechanisms and intervention patterns of PSI, forecast of occurrence time, termination time and intensity of PSI, and control of stochastic systems with PSI, constitute three main tasks in the study of systems with PSI. Based on this motivation, a study on the three topics of the inducement mechanism of PSI, prediction methods of occurrence time and termination time of PSI and modified minimal variance control (MMVC) with constraints on control input was systematically carried out in .…”