Oriented Measures with Continuous Densities and the Bang-Bang Principle

The Bang-bang Principle for the Goursat-darboux Problem*

In the paper, the bang-bang principle for a control system connected with a system of linear nonautonomous partial differential equations of hyperbolic type (the socalled Goursat-Darboux problem or continuous Fornasini-Marchesini problem) is proved. Some density result is also obtained.

Uncertain Bang-Bang Control for continuous Time Model

An abstract ‘ bang - bang principle ’ and time - optimal boundary control of the heat equation 1

A principal technical result of this paper is that the onedimensional heat equation with boundary control is exactly null-controllable with control restricted to an arbitrary set E ⊂ [0, T ] of positive measure. A general abstract argument is presented to show that this implies the ‘bangbang’ property for time-optimal controls — i.e., such a control can take only extreme values of (the hull of)...

Second Order Optimality Conditions for Controls with Continuous and Bang-Bang Components

Second order necessary and sufficient optimality conditions for bang-bang control problems in a very general form have been obtained in Milyutin and Osmolovskii (1998). These conditions require the positive (semi)-definiteness of a certain quadratic form on the finite-dimensional critical cone. Using a suitable transformation via a linear matrix ODE, Maurer and Osmolovskii (2003, 2004) have dev...

A general “bang-bang” principle for predicting the maximum of a random walk

Let (Bt)0≤t≤T be either a Bernoulli random walk or a Brownian motion with drift, and let Mt := max{Bs : 0 ≤ s ≤ t}, 0 ≤ t ≤ T . This paper solves the general optimal prediction problem sup 0≤τ≤T E[f(MT −Bτ )], where the supremum is over all stopping times τ adapted to the natural filtration of (Bt), and f is a nonincreasing convex function. The optimal stopping time τ is shown to be of “bang-ba...