Related papers: Introduction to the Pontryagin Maximum Principle f…
A Hamiltonian algorithm, both theoretical and numerical, to obtain the reduced equations implementing Pontryagine's Maximum Principle for singular linear-quadratic optimal control problems is presented. This algorithm is inspired on the…
In this short communication, we first recall a version of the Pontryagin maximum principle for general finite-dimensional nonlinear optimal sampled-data control problems. This result was recently obtained in [L. Bourdin and E. Tr{\'e}lat ,…
The Chantasri-Dressel-Jordan (CDJ) stochastic path integral formalism (Chantasri et al. 2013 and 2015) characterizes the statistics of the readouts and the most likely conditional evolution of continuously monitored quantum systems. In our…
This paper explains some fundamental ideas of {\em feedback} control of quantum systems through the study of a relatively simple two-level system coupled to optical field channels. The model for this system includes both continuous and…
We consider an optimal control problem for a system of local continuity equations on a space of probability measures. Such systems can be viewed as macroscopic models of ensembles of non-interacting particles or homotypic individuals,…
We consider a state-constrained optimal control problem of a system of two non-local partial-differential equations, which is an extension of the one introduced in a previous work in mathematical oncology. The aim is to minimize the tumor…
Quantum mechanical systems exhibit an inherently probabilistic nature upon measurement. Using a quantum noise model to describe the stochastic evolution of the open quantum system and working in parallel with classical indeterministic…
For a class of stochastic delay evolution equations driven by cylindrical $Q$-Wiener process, we study the Pontryagin's maximum principle for the stochastic recursive optimal control problem. The delays are given as moving averages with…
Simple, precise, and robust control is demanded for operating a large quantum information processor. However, existing routes to high-fidelity quantum control rely heavily on arbitrary waveform generators that are difficult to scale up.…
Optimal control theory deals with finding protocols to steer a system between assigned initial and final states, such that a trajectory-dependent cost function is minimized. The application of optimal control to stochastic systems is an…
In this paper we formulate a risk-sensitive optimal control problem for continuously monitored open quantum systems modelled by quantum Langevin equations. The optimal controller is expressed in terms of a modified conditional state, which…
We provide an improvement of the maximum principle of Pontryagin of the Optimal Control problems. We establish differentiability properties of the value function of problems of Optimal Control with assumptions as low as possible. Notably,…
Quantum Optimal Control (QOC) enables the realization of accurate operations, such as quantum gates, and support the development of quantum technologies. To date, many QOC frameworks have been developed but those remain only naturally…
We present a quantum optimal control problem which exhibits a chattering phenomenon. This is the first instance of such a process in quantum control. Using the Pontryagin Maximum Principle and a general procedure due to V. F. Borisov and M.…
Optimal control of closed quantum systems is a well studied geometrically elegant set of computational theory and techniques that have proven pivotal in the implementation and understanding of quantum computers. The design of a circuit…
We consider distributed-order non-local fractional optimal control problems with controls taking values on a closed set and prove a strong necessary optimality condition of Pontryagin type. The possibility that admissible controls are…
We present variational theory for optimal control over a finite time interval in quantum systems with relaxation. The corresponding Euler-Lagrange equations determining the optimal control field are derived. In our theory the optimal…
We apply advanced methods of control theory to open quantum systems and we determine finite-time processes which are optimal with respect to thermodynamic performances. General properties and necessary conditions characterizing optimal…
We address Newton-type problems of minimal resistance from an optimal control perspective. It is proven that for Newton-type problems the Pontryagin maximum principle is a necessary and sufficient condition. Solutions are then computed for…
The problem concerning the minimum time for an initial state to evolve up to a target state plays an important role in the Classic Optimal Control theory. In the quantum context, as quantum states are so sensitive to environmental…