In the paper, we consider ODE driven optimal control problems with bang-bang type extremals. The specific nature of bang-bang controls causes some difficulties in optimality and stability analysis. Usual convexity arguments like (strong) Legendre-Clebsch condition fail to hold, and the control discontinuity has to be taken into account. In recent years, substantial results on secondorder optima...

A systematic controller design procedure is developed for the class of linear time-invariant systems which use both continuous and bang-bang control effectors. The sampled-data regulator and its associated weighting matrices and cost function are extended to this class of system, and are used to modulate the bang-bang effector to achieve desired performance levels. Stability, sensitivity, and r...

In this paper, an intelligent-gradient based algorithm is proposed to solve time optimal bang-bang control problem. The proposed algorithm is a combination of an intelligent algorithm called improved particle swarm optimization algorithm (IPSO) in the first stage of optimization process together with a gradient-based algorithm called successive quadratic programming method (SQP) in the second s...

The solution for an inflationary universe without singularities is derived from the Einstein-Lemaı̂tre equations. The present state of the universe evolved from a steady state solution for a tiny, but classical micro-universe with large cosmological constant or large equivalent vacuum energy density and with an equal energy density of radiation and/or some kind of relativistic primordial matter ...

*Correspondence: [email protected] 1College of Fundamental Studies, Shanghai University of Engineering Science, Shanghai, 201620, P.R. China Full list of author information is available at the end of the article Abstract This paper investigates the lag projective synchronization and anti-synchronization problems for a general master-slave chaotic system with bounded nonlinearity. An adaptive cont...

We consider a general mathematical model for cancer chemotherapy as optimal control problem for a bilinear system and give necessary and sufficient conditions for strong local optimality of bang-bang controls. These results apply to a 3-compartment model which besides a killing agent also includes a recruiting agent, i.e. a drug which acts on the residuum of dormant cells in the cell cycle. For...

T.H. Jensen Feedback stabilization of the resistive wall mode is usually accomplished by using linear amplifiers. In this paper a study is made of a possibility of controlling resistive wall modes using switches instead of linear amplifiers, i.e., using bang-bang control. The motivation is that bangbang control systems may be cheaper than conventional feedback systems. A distinct disadvantage o...

The evolution of the rotational inhomogeneities is investigated in the specific framework of four-dimensional pre-big bang models. While minimal (dilaton-driven) scenarios do not lead to rotational fluctuations, in the case of non-minimal (string-driven) models, fluid sources are present in the pre-big bang phase. The rotational modes of the geometry, coupled to the divergenceless part of the v...

We analyze a general mechanism for producing a nearly scale-invariant spectrum of cosmological curvature perturbations during a contracting phase preceding a big bang, that can be entirely described using 4d effective field theory. The mechanism, based on first producing entropic perturbations and then converting them to curvature perturbations, can be naturally incorporated in cyclic and ekpyr...