Related papers: Analytical solution of the optimal laser control p…
We formulate and study the infinite dimensional linear programming (LP) problem associated with the deterministic discrete time long-run average criterion optimal control problem. Along with its dual, this LP problem allows one to…
In this work, we consider optimal control problems for mechanical systems on vector spaces with fixed initial and free final state and a quadratic Lagrange term. Specifically, the dynamics is described by a second order ODE containing an…
This short note shows how to solve optimal control problems using second order sensitivity analysis
A dual control problem is presented for the optimal stochastic control of a system governed by partial differential equations. Relationships between the optimal values of the original and the dual problems are investigated and two duality…
Optimal control of bilinear systems has been a well-studied subject in the area of mathematical control. However, techniques for solving emerging optimal control problems involving an ensemble of structurally identical bilinear systems are…
Starting from an initial pure quantum state, we present a strategy for reaching a target state corresponding to the extremum (maximum or minimum) of a given observable. We show that a sequence of pulses of moderate intensity, applied at…
We study time-optimal protocols for controlling quantum systems which show several avoided level crossings in their energy spectrum. The structure of the spectrum allows us to generate a robust guess which is time-optimal at each crossing.…
We present a simple approach allowing to obtain analytical expressions for laser pulses that can drive a two-level system in an arbitrarily chosen way. The proposed scheme relates every desired population-evolution path to a single resonant…
Recent studies of the dynamically assisted Schwinger effect have shown that particle production is significantly enhanced by a proper choice of the electric field. We demonstrate that optimal control theory provides a systematic means of…
A gradient-based optimization approach combined with automatic differentiation is employed to ensure high accuracy and scalability when working with high-dimensional parameter spaces. Numerical simulations confirm the effectiveness of the…
The mathematical modeling of numerous real-world applications results in hierarchical optimization problems with two decision makers where at least one of them has to solve an optimal control problem of ordinary or partial differential…
The present work deals with quantitative two-phase reach-avoid problems on nonlinear control systems. This class of optimal control problem requires the plant's state to visit two (rather than one) target sets in succession while minimizing…
In this paper, we introduce an optimal control problem for multi-agent systems with non-local cost which favors simultaneous aggregation of particles. This is done introducing a time-dependent notion of multiplicity whose intrinsic…
In this paper, we consider the stochastic optimal control problem for the interacting particle system. We obtain the stochastic maximum principle of the optimal control system by introducing a generalized backward stochastic differential…
Laser cooling of molecules employing broadband optical pumping involves a timescale separation between laser excitation and spontaneous emission. Here, we optimize the optical pumping step using shaped laser pulses. We derive two…
We formulate the problem of a two-level system in a linearly polarized laser field in terms of a nonlinear Riccati-type differential equation and solve the equation analytically in time intervals much shorter than half the optical period.…
Algebraically speaking, linear time-invariant (LTI) systems can be considered as modules. In this framework, controllability is translated as the freeness of the system module. Optimal control mainly relies on quadratic Lagrangians and the…
Using optimal control, we establish and link the ultimate bounds in time (referred to as quantum speed limit) and energy of two- and three-level quantum nonlinear systems which feature 1:2 resonance. Despite the unreachable complete…
Optical techniques for spatiotemporal control can produce laser pulses with custom amplitude, phase, or polarization structure. In nonlinear optics and plasma physics, the use of structured pulses typically follows a forward design…
The aim of various technical applications (for example fusion research) is to control a plasma by magnetic fields in a desired fashion. In our model the plasma is described by the Vlasov-Poisson system that is equipped with an external…