INTRODUCTION Obstructive sleep apnoea (OSA) is a growing problem as more and more consequences of the condition become unveiled owing to continued research on the subject. It is essential to establish relevant, fast and accurate screening options, both in the primary sector and for preoperative screening in hospitals if we are to diagnose and treat this condition and thereby avoid the consequen...

Second order optimality conditions have been derived in the literature in two different forms. Osmolovskii (1988a, 1995, 2000, 2004) obtained second order necessary and sufficient conditions requiring that a certain quadratic form be positive (semi)-definite on a critical cone. Agrachev, Stefani, Zezza (2002) first reduced the bang-bang control problem to finite-dimensional optimization and the...

A unified, systematic controller design procedure is introduced for the class of linear time invariant systems with use both continuous and bang-bang control effectors. The sampled-data regulator weighting matrices and cost function are extended to this class of system, and modulates the bangbang effector to achieve desired performance levels. Controller synthesis is illustrated for a generic s...

This paper gives sufficient conditions for a class of bang-bang extremals with multiple switches to be locally optimal in the strong topology. The conditions are the natural generalizations of the ones considered in [5, 13] and [16]. We require both the strict bang-bang Legendre condition, and the second order conditions for the finite dimensional problem obtained by moving the switching times ...

The authors apply their recent work on the Lyapunov theorem in locally convex Hausdorff spaces to the bang-bang principle for control systems in infinite dimensions. They show that the bang-bang principle holds for every integrably bounded, measurable, weakly compact convex-valued multifunction if and only if the underlying measure space is saturated. They also demonstrate the equivalence of th...

We consider an expression for the second–order variation (SOV) of bang-bang controls derived by Agrachev and Gamkrelidze. The SOV plays an important role in both necessary and sufficient second–order optimality conditions for bang-bang controls. These conditions are stronger than the one provided by the first–order Pontryagin maximum principle (PMP). For a bang-bang control with k switching poi...

Time-optimal controls for 2-link robots are often of bang-bang type. Many algorithms to solve timeoptimal robot control problems a-priori assume the optimal control to be bang-bang. Industrial robot,s very often have 5 or 6 links and then the associated time-optimal controls are usually singular. This paper presents a new algorithm that enables computation of both bang-bang and singular time-op...