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We study a trajectory-planning problem whose solution path evolves by means of a Lie group action and passes near a designated set of target positions at particular times. This is a higher-order variational problem in optimal control,…
The purpose of this work is the design and analysis of a reliable and efficient a posteriori error estimator for the so-called pointwise tracking optimal control problem. This linear-quadratic optimal control problem entails the…
We describe an improved version of the quantum simulation method based on the implementation of a truncated Taylor series of the evolution operator. The idea is to add an extra step to the previously known algorithm which implements an…
In various physical implementations of quantum information processing, qubits are realized in a Lambda type system configuration as two stable lower energy levels coupled indirectly via an unstable higher energy level, that is, in…
The non-linear optimization method developed by Konnov and Krotov [Automation and Remote Control 60, 1427 (1999)] has been used previously to extend the capabilities of optimal control theory from the linear to the non-linear Schr\"odinger…
The first-order optimality conditions for a generic nonlinear optimization problem are generated as part of the terminal transversality conditions of an optimal control problem. It is shown that the Lagrangian of the optimization problem is…
We develop a discrete-time optimal control framework for systems evolving on Lie groups. Our work generalizes the original Differential Dynamic Programming method, by employing a coordinate-free, Lie-theoretic approach for its derivation. A…
Quantum computation is based on implementing selected unitary transformations which represent algorithms. A generalized optimal control theory is used to find the driving field that generates a prespecified unitary transformation. The…
The equations of motion for a Lagrangian mainly refer to the acceleration equations, which can be obtained by the Euler--Lagrange equations. In the post-Newtonian Lagrangian form of general relativity, the Lagrangian systems can only…
This paper addresses the optimal control problem of finite-horizon discrete-time nonlinear systems under state and control constraints. A novel numerical algorithm based on optimal control theory is proposed to achieve superior…
Combinatorial optimization is considered a promising class of problems in which quantum computers can show significant advantages. However, problems of practical relevance typically have more variables than current or foreseeable quantum…
The paper discusses various aspects of time-optimal control of quantum spin systems, modelled as right-invariant systems on a compact Lie group G. The main results are the reduction of such a system to an equivalent system on a homogeneous…
The efficiency of statistical sampling in broad-histogram Monte Carlo simulations can be considerably improved by optimizing the simulated extended ensemble for fastest equilibration. Here we describe how a recently developed feedback…
A family of optimal control problems for a single and two coupled spinning particles in the Euler-Lagrange formalism is discussed. A characteristic of such problems is that the equations controlling the system are implicit and a reduction…
This paper develops numerical methods for optimal control of mechanical systems in the Lagrangian setting. It extends the theory of discrete mechanics to enable the solutions of optimal control problems through the discretization of…
This paper offers a unified perspective on different approaches to the solution of optimal control problems through the lens of constrained sequential quadratic programming. In particular, it allows us to find the relationships between…
We develop a methodology for performing approximate optimal control simulations for quantum systems with multiple interacting degrees of freedom. The quantum dynamics are modeled using the first-order Magnus approximation in the interaction…
We develop a general approach for monitoring and controlling evolution of open quantum systems. In contrast to the master equations describing time evolution of density operators, here, we formulate a dynamical equation for the evolution of…
Solving optimal control problems for transport-dominated partial differential equations (PDEs) can become computationally expensive, especially when dealing with high-dimensional systems. To overcome this challenge, we focus on developing…
We propose a new monotonically convergent algorithm which can enforce spectral constraints on the control field (and extends to arbitrary filters). The procedure differs from standard algorithms in that at each iteration the control field…