Minimax control of a discrete object with mixed perturbations (Q1180942)

The authors consider the problem of synthesizing an optimal linear regulator for a discrete linear system \(a(\nabla)y_ t=b(\nabla)u_ t+f_ t\), \(t=0,\pm 1,\pm 2,\dots,\) where \(y_ t\) is the scalar output, \(u_ t\) is the control, \(a\) and \(b\) are polynomials, \(\nabla x_ t=x_{t-1}\), and \(f_ t\) is a perturbation. The sequence of perturbations, \(\{f_ t\}\), is assumed to belong to a certain set \(\mathcal F\) called a uniform renewal process. This set generalizes a uniformly bounded sequence and is characterized by a reduction in the dependence of future perturbations and those already observed as the time interval between them increases. The authors also consider more complex models with additional perturbations of limited power. The problem of synthesizing an optimal regulator \(\alpha(\nabla)u_ t=\beta(\nabla)y_ t\) which minimizes the quality criterion \(J=\sup_{\{f_ t\}\in{\mathcal F}}| y_ T|\) (\(T\) some fixed time) is reduced to numerical minimization of a convex function of a finite number of parameters. Analytic solutions are obtained for special cases.