Baire category and the weak bang-bang property for continuous differential inclusions

A Baire Category Approach to the Bang-Bang Property

Aim of this paper is to develop a new technique, based on the Baire category theorem, in order to establish the closure of reachable sets and the existence of optimal trajectories for control systems, without the usual convexity assumptions. The bangbang property is proved for a new class of “concave” multifunctions, characterized by the existence of suitable linear selections. The proofs rely ...

The Bang-Bang theorem via Baire category. A Dual Approach

The paper develops a new approach to the classical bang-bang theorem in linear control theory, based on Baire category. Among all controls which steer the system from the origin to a given point x̄, we consider those which minimize an auxiliary linear functional φ. For all φ in a residual set, we show that the minimizing control is unique and takes values within a set of extreme points.

Generalized Baire Category and Differential Inclusions in Banach Spaces

where F is a Hausdorff continuous multifunction with closed, bounded values. In this paper we prove the local existence of a solution of (1.1 ), assuming that the convex closure of F(x,,) has finite codimension. More precisely, we assume the existence of a closed affine subspace E, G E with finite codimension, such that the interior of E. n E6 F(x,) relative to E,, is nonempty. Two special case...

Uncertain Bang-Bang Control for continuous Time Model

Attainable Subspaces and the Bang-Bang Property of Time Optimal Controls for Heat Equations

In this paper, we study two subjects on internally controlled heat equations with time varying potentials: the attainable subspaces and the bang-bang property for some time optimal control problems. We present some equivalent characterizations on the attainable subspaces, and provide a sufficient conditions to ensure the bang-bang property. Both the above-mentioned characterizations and the suf...