The problem of minimum-time damping of a pendulum is a classical problem of control theory. In the linear case, described by the equation ẍ+ x = u, |u| ≤ 1, its solution is stated in [1]. The optimal control is of bang-bang type, i.e. it takes values u = ±1, and the switching curve which separates the domain of the phase plane, where u = −1 from the domain u = +1 consists of unit semicircles ce...

The big bang-big crunch (BB-BC) algorithm is a popular metaheuristic optimization technique proposed based on one of the theories for the evolution of the universe. The algorithm utilizes a two-phase search mechanism: big-bang phase and big-crunch phase. In the big-bang phase the concept of energy dissipation is considered to produce disorder and randomness in the candidate population while in ...

The problem of minimum-time damping of a pendulum is a classical problem of control theory. In the linear case, described by the equation ẍ + x = u, |u| ≤ 1, its solution is stated in [1]. The optimal control is of bang-bang type, i.e. it takes values u = ±1, and the switching curve which separates the domain of the phase plane, where u = −1 from the domain u = +1 consists of unit semicircles c...

Nonadiabatic unitary evolution with tailored time-dependent Hamiltonians can prepare systems of coldatomic gases with various desired properties such as low excess energies. For a system of two one-dimensional quasicondensates coupled with a time-varying tunneling amplitude, we show that the optimal protocol, for maximizing any figure of merit in a given time, is bang-bang, i.e., the coupling a...

In the present work we use the variational approach in order to discretize elliptic optimal control problems with bang-bang controls. We prove error estimates for the resulting scheme and present a numerical example which supports our analytical findings. Mathematics Subject Classification (2000): 49J20, 49K20, 35B37

The paper investigates the stability of the solutions of linearquadratic optimal control problems with bang-bang controls in terms of metric sub-regularity and bi-metric regularity. New sufficient conditions for these properties are obtained, which strengthen the known conditions for sub-regularity and extend the known conditions for bi-metric regularity to Bolza-type problems.

A numerical method is proposed for constructing an approximation of the Pareto front of nonconvex multi-objective optimal control problems. First, a suitable scalarization technique is employed for the multi-objective optimal control problem. Then by using a grid of scalarization parameter values, i.e., a grid of weights, a sequence of single-objective optimal control problems are solved to obt...

Delta kick cooling (DKC) is used to compress the momentum distribution of ultracold quantum matter. It combines expansion dynamics with use pulses, designed via classical methods, that bring system rest. We introduce an exact approach DKC for arbitrary scale-invariant gases, lifting original restrictions free evolution and noninteracting systems, account control atomic clouds in a time-dependen...

We investigate the bang-bang property for fairly general classes of L∞−L1 constrained bilinear optimal control problems in case parabolic equations set one-dimensional torus. Such a study is motivated by several applications applied mathematics, most importantly reaction-diffusion models. The main equation writes ∂tum−∂xx2um=mum+f(t,x,um), where m=m(x) control, which must satisfy some L∞ bounds...

A SEIR control model describing the Ebola epidemic in a population of a constant size is considered over a given time interval. It contains two intervention control functions reflecting efforts to protect susceptible individuals from infected and exposed individuals. For this model, the problem of minimizing the weighted sum of total fractions of infected and exposed individuals and total costs...