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, 14] 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 ...

This paper deals with the optimal control problem that arise when a hydraulic system with fixed-head hydroplants is considered. In the frame of a deregulated electricity market the resulting Hamiltonian for such systems is linear in the control variable and results in an optimal singular/bang-bang control policy. To avoid difficulties associated with the computation of optimal singular/bang-ban...

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...

String cosmology is revisited from cosmological viewpoint of holographic principle put forward by ‘t Hooft, and by Fischler and Susskind. It is shown that the holography requires existence of a ‘graceful exit’ mechanism, which renders the Universe nonsingular by connecting preand post-big bang phases smoothly. It is proven that flat Universe is consistent with the holography only if it starts w...

String cosmology is revisited from cosmological viewpoint of holographic principle put forward by ‘t Hooft, and by Fischler and Susskind. It is shown that the holography requires existence of a ‘graceful exit’ mechanism, which renders the Universe nonsingular by connecting preand post-big bang phases smoothly. It is proven that flat Universe is consistent with the holography only if it starts w...

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...