Nonlinear bang-bang principle in Rn

Abstract

A computer model of "a sense of humour" is formulated. The humorous effect is treated as a specific malfunction in the processing of information, conditioned by the necessity of a quick deletion from consciousness of a false version. The biological function of a sense of humour consists in quickenning the transmission of processed information into conscioussness and in a more effective use of brain resources. 2 According to Darwin [2] antropoid monkeys possess a clearly distinct sense of humour.

Hybrid Systems: A Control Theoretic Perspective

“…By the Filippov-Wažewski relaxation theorem the solution set of of the differential inclusion defined by (4) is dense in the set of relaxed solutions, i.e., the solutions of the differential inclusion whose right hand side is the convex hull of the original set valued map, see [3], [25], [7]. This implies that the corresponding attainable sets coincide.…”

On the Bang-Bang Principle for Differential Variational Inequalities in Banach Spaces

“…In recent years, bang-bang priciple and relaxation type properties for evolution differential inclusions in Banach spaces have been studied from different points of view by several authors. For example, the "bang-bang" principle [3,17,25,28,30] focuses on the existence of solutions for inclusions with right-hand side extco F (t, x) (here F (t, x) is a multifunction, the same as below) and whether the solution set of such an inclusion is dense in the solution set of the inclusion with the convexified right-hand side. The relaxation property [16,36,37] is aimed to show that the solution set of an inclusion with non-convex right-hand side is dense in the solution set of the inclusion with the convexified right-hand side coF (t, x).…”

“…Furthermore, the great majority of bang-bang priciple problems have aimed to certify that if a certain state can be reached by using a control u(t) with values in a compact convex set Ω (for example Ω = [0, 1]) then the same outcome can be achieved by a control using only extreme values of Ω (the values 0 and 1 in the example) [3,28,30]. The key tools for solving these investigations are topological method and nonsmooth analysis.…”