Control of systems with interference of bounded magnitude (Q1904791)

Consider the controlled system \(\dot x = A(t)x + K(t,u)v + ug(t)\) where \(u\) is a scalar control and \(v\) a disturbance introduced by some error. Denoting, in general the ellipsoid \(E(a,Q) = \{x \in \mathbb{R}^n |(x - a)^* Q^{-1} (x - a) \leq 1\}\) assume that \(v \in E (0,B (t,u)) \). Then \(\dot x = A(t)x + w\), \(w \in E (ug(t)\), \(K(t,u) B(t,u) K^*(t,u))\). Assume that \(x(0) \in E(a (0), Q(0))\). The goal is to find ellipsoids of superattainability \(E(a(t), Q(t))\) such that for fixed \(T > 0\), \(Tr |CQ (T) |\to \min\) where \(C\) is a fixed positive definite matrix. The optimization problem is solved using Pontryagin maximum principle. Examples are given.