Use of models with aftereffect in the problem of the design of optimal digital control systems (Q1320787)

Let \(\varepsilon> 0\) be a small period of time. The author considers a quadratic optimal control problem governed by systems of linear ordinary differential equations, where the admissible controls are constant on the intervals \([k\varepsilon,(k+1)\varepsilon]\), \(k=0,1,2,\dots\) . The control system can be described in the form of differential equations with after-effect. So, one obtains a decomposition of the boundary value problem of the maximum principle into a Cauchy problem for a system of two first-order partial differential equations and a boundary value problem for a system of ordinary differential equations. This allows to express an asymptotic feedback law (as \(\varepsilon\to 0\)) by solving an ordinary Riccati differential equation.