Related papers: Dynamic optimization and its relation to classical…
Most classical mechanical systems are based on dynamical variables whose values are real numbers. Energy conservation is then guaranteed if the dynamical equations are phrased in terms of a Hamiltonian function, which then leads to…
Hybrid optimal control problems are studied for a general class of hybrid systems where autonomous and controlled state jumps are allowed at the switching instants and in addition to terminal and running costs switching between discrete…
The distributed system $\mathcal{S}_D$ described by the Dirac equation is investigated simply as a dynamic system, i.e. without usage of quantum principles. The Dirac equation is described in terms of hydrodynamic variables: 4-flux $j^{i}$,…
In this paper, we present an application of the optimal control theory to orbital transfer of Low Earth Orbit satellites. The optimal control problem is treated with Dynamic Programming techniques which require solving the…
We extend some aspects of the Hamilton-Jacobi theory to the category of stochastic Hamiltonian dynamical systems. More specifically, we show that the stochastic action satisfies the Hamilton-Jacobi equation when, as in the classical…
In Stochastic Optimal Control (SOC) one minimizes the average cost-to-go, that consists of the cost-of-control (amount of efforts), cost-of-space (where one wants the system to be) and the target cost (where one wants the system to arrive),…
In this work, we present a second-order numerical scheme to address the solution of optimal control problems constrained by the evolution of nonlinear Fokker-Planck equations arising from socio-economic dynamics. In order to design an…
Quantum coherence inherently affects the dynamics and the performances of a quantum machine. Coherent control can, at least in principle, enhance the work extraction and boost the velocity of evolution in an open quantum system. Using…
This paper proposes a new framework to model control systems in which a dynamic friction occurs. The model consists in a controlled differential inclusion with a discontinuous right hand side, which still preserves existence and uniqueness…
For a sequence of dynamic optimization problems, we aim at discussing a notion of consistency over time. This notion can be informally introduced as follows. At the very first time step $t_0$, the decision maker formulates an optimization…
We consider piecewise-deterministic optimal control problems in which the environment randomly switches among several deterministic modes, and the goal is to optimize the expected cost up to the termination while taking the likelihood of…
In this paper, we study an optimal stopping problem in the presence of model uncertainty and regime switching. The max-min formulation for robust control and the dynamic programming approach are adopted to establish a general theoretical…
In this work, we investigate a stochastic control framework for global optimization over both Euclidean spaces and the Wasserstein space of probability measures, where the objective function may be non-convex and/or non-differentiable. In…
The effective approach to quantum dynamics allows a reformulation of the Dirac quantization procedure for constrained systems in terms of an infinite-dimensional constrained system of classical type. For semiclassical approximations, the…
The purpose of this paper is to describe the numerical solution of the Hamilton-Jacobi-Bellman (HJB) for an optimal control problem for quantum spin systems. This HJB equation is a first order nonlinear partial differential equation defined…
We show that necessary and sufficient conditions of optimality in periodic optimization problems can be stated in terms of a solution of the corresponding HJB inequality, the latter being equivalent to a max-min type variational problem…
In this paper we investigate possible approaches to study general time-inconsistent optimization problems without assuming the existence of optimal strategy. This leads immediately to the need to refine the concept of time-consistency as…
The quest for real-time dynamic optimization solutions in the process industry represents a formidable computational challenge, particularly within the realm of applications like model-predictive control, where rapid and reliable…
In this paper, we introduce a model-based deep-learning approach to solve finite-horizon continuous-time stochastic control problems with jumps. We iteratively train two neural networks: one to represent the optimal policy and the other to…
We introduce a transformation of the quantum phase $S'=S+\frac{\hbar}{2}\log\rho$, which converts the deterministic equations of quantum mechanics into the Lagrangian reference frame of stochastic particles. We show that the quantum…