In this paper, an optimal control for Hamiltonian control systems with external variables will be formulated and analysed. Necessary and sufficient conditions which lead to Pantryagin’s principle are stated and elaborated. Finally it is shown how the Pontryagin’s principle fits very well to the theory of Hamiltonian systems. The case of Potryagin’s maximum principle will be considered in detail...

Discontinuous, time-invariant controllers have been recently proposed in the literature as an alternative method to stabilize nonholonomic systems. These control laws are not Lipschitz continuous at the origin and hence they may use signiicant amount of control eeort, especially if the initial conditions are close to an equilibrium manifold. We seek to remedy this situation by constructing boun...

The power stage of the PWM DC-DC converter is modeled and analyzed using the sampleddata approach. This work complements the companion paper [1] which develops sampled-data models and analysis for the closed-loop converter. Separate models for the power stage are essential for controller design. The work addresses continuous and discontinuous conduction mode under voltage mode control, and cont...

The power stage of the PWM DC-DC converter is modeled and analyzed using the sampleddata approach. This work complements the companion paper [1] which develops sampled-data models and analysis for the closed-loop converter. Separate models for the power stage are essential for controller design. The work addresses continuous and discontinuous conduction mode under voltage mode control, and cont...

This paper generalises the approach taken by Dasgupta & Maskin (1986) and Simon (1989) and provides necessary and su¢ cient conditions for the existence of pure and mixed strategy Nash equilibrium in games with continuous strategy spaces and discontinuous payo¤ functions. The conditions can be applied widely, and examples for existence of pure strategy and monotonic equilibria in First-Price au...

We have compared two methods for separating the isoenzymes of creatine kinase in serum and measuring their activity: chromatography on diethylaminoethyl-Sephadex A-50, with both continuous and discontinuous gradient elution, and electrophoresis on cellulose acetate. Results by continuous and discontinuous gradient elution correlated well both for tissue extracts and sera. Electrophoresis on cel...

We propose a new class of Discontinuous Galerkin (DG) methods based on variational multiscale ideas. Our approach begins with an additive decomposition of the discontinuous finite element space into continuous (coarse) and discontinuous (fine) components. Variational multiscale analysis is used to define an interscale transfer operator that associates coarse and fine scale functions. Compositio...

We study the general problem of stabilization of globally asymptotically controllable systems. We construct discontinuous feedback laws, and particularly we make it possible to choose these continuous outside a small set (closed with measure zero) of discontinuity in the case of control systems which are affine in the control; moreover this set of singularities is shown to be repulsive for the ...

the aim of this paper is to design a fractional order sliding mode controllers (fosmc)for a class of dc-dc converters such as boost and buck converters. firstly, the control lawis designed with respect to the properties of fractional calculus, the design yields an equiv-alent control term with an addition of discontinuous (attractive) control law. secondly, themathematical proof of the stabilit...