Related papers: Solution to the quantum Zermelo navigation problem
A robust control over quantum dynamics is of paramount importance for quantum technologies. Many of the existing control techniques are based on smooth Hamiltonian modulations involving repeated calculations of basic unitaries resulting in…
This paper addresses an optimal control problem for a robot that has to find and collect a finite number of objects and move them to a depot in minimum time. The robot has fourth-order dynamics that change instantaneously at any pick-up or…
Time symmetry in quantum mechanics, where the current quantum state is determined jointly by both the past and the future, offers a more comprehensive description of physical phenomena. This symmetry facilitates both forward and backward…
This paper aims to establish second order necessary conditions for optimal control in quantum stochastic systems. We employ a variational approach, analogous to methods in classical stochastic control, to analyze systems governed by quantum…
In this paper, we study some control problems that derive from time optimal control of coupled spin dynamics in NMR spectroscopy and quantum information and computation. Time optimal control helps to minimize relaxation losses. The ability…
In this paper, we aim to explore optimal regional trajectory tracking control problems of the anomalous subdiffusion processes governed by time-fractional diffusion systems under the Neumann boundary conditions. Using eigenvalue theory of…
We investigate the existence of solutions of reversible and irreversible port-Hamiltonian systems. To this end, we utilize the associated exergy, a function that is composed of the system's Hamiltonian and entropy, to prove global existence…
The presence of symmetries in a Hamiltonian system usually implies the existence of conservation laws that are represented mathematically in terms of the dynamical preservation of the level sets of a momentum mapping. The symplectic or…
We consider the optimal control problem of determining electromagnetic pulses for implementing logical gates in a closed quantum system, where the Hamiltonian models the dynamics of coupled superconducting qudits. The quantum state is…
In this work, we consider a model of two qubits driven by coherent and incoherent time-dependent controls. The dynamics of the system is governed by a Gorini-Kossakowski-Sudarshan-Lindblad master equation, where coherent control enters into…
Accelerating controlled thermodynamic processes requires an auxiliary Hamiltonian to steer the system into instantaneous equilibrium states. An extra energy cost is inevitably needed in such finite-time operation. We recently develop a…
This paper introduces a novel methodology that leverages the Hamilton-Jacobi solution to enhance non-linear model predictive control (MPC) in scenarios affected by navigational uncertainty. Using Hamilton-Jacobi-Theoretic approach, a…
A method is presented to solve a stochastic, nonlinear optimal control problem representative of spacecraft trajectory design under uncertainty. The problem is reformulated as a chance constrained nonlinear program, or what is known as a…
In order to resolve the measurement problem of Quantum Mechanics, non-unitary time evolution has been derived from the unitarity of standard quantum formalism. New wave functions of free and non-free quantum systems follow from Schroedinger…
In this paper, we propose a Transformer-based framework for approximating solutions to infinite-dimensional optimization problems: calculus of variations problems and optimal control problems. Our approach leverages offline training on data…
Geometric methods have useful application for solving problems in a range of quantum information disciplines, including the synthesis of time-optimal unitaries in quantum control. In particular, the use of Cartan decompositions to solve…
We consider optimal control of fractional in time (subdiffusive, i.e., for $% 0<\gamma <1$) semilinear parabolic PDEs associated with various notions of diffusion operators in an unifying fashion. Under general assumptions on the…
In quantum control, quantum speed limits provide fundamental lower bounds on the time that is needed to implement certain unitary transformations. Using Lie algebraic methods, we link these speed limits to symmetries of the control…
This paper introduces a novel approach to the optimal control of linear discrete-time systems subject to bounded disturbances. Our approach is based on the newly established duality between ellipsoidal approximations of reachable and hardly…
This paper proposes a novel and efficient optimization-based method for generating near time-optimal trajectories for holonomic vehicles navigating through complex but structured environments. The approach aims to solve the problem of…