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We present the calculation of the Feynman path integral in real time for tunneling in quantum mechanics and field theory, including the first quantum corrections. For this purpose, we use the well-known fact that Euclidean saddle points in…
A systematic derivation is given of the worldline path integrals for the effective action of a multiplet of Dirac fermions interacting with general matrix-valued classical background scalar, pseudoscalar, and vector gauge fields. The first…
In this paper, we describe a constrained Lagrangian and Hamiltonian formalism for the optimal control of nonholonomic mechanical systems. In particular, we aim to minimize a cost functional, given initial and final conditions where the…
Applying robust optimization often requires selecting an appropriate uncertainty set both in shape and size, a choice that directly affects the trade-off between average-case and worst-case performances. In practice, this calibration is…
Without exact knowledge of the true system dynamics, optimal control of non-linear continuous-time systems requires careful treatment under epistemic uncertainty. In this work, we translate a probabilistic interpretation of the Pontryagin…
In this work, we present a new diagrammatic method for computing the effective Hamiltonian of driven nonlinear oscillators. At the heart of our method is a self-consistent perturbation expansion developed in phase space, which establishes a…
We propose a scalable, policy-centric framework for continuous-time multi-asset portfolio-consumption optimization under inequality constraints. Our method integrates neural policies with Pontryagin's Maximum Principle (PMP) and enforces…
This paper investigates optimal trading strategies in a financial market with multidimensional stock returns where the drift is an unobservable multivariate Ornstein-Uhlenbeck process. Information about the drift is obtained by observing…
This paper investigates the optimal control problem for a class of nonlinear fully coupled forward-backward stochastic difference equations (FBS$\Delta$Es). Under the convexity assumption of the control domain, we establish a variational…
Extension of Feynman's path integral to quantum mechanics of noncommuting spatial coordinates is considered. The corresponding formalism for noncommutative classical dynamics related to quadratic Lagrangians (Hamiltonians) is formulated.…
We discuss non-Euclidean deterministic and stochastic algorithms for optimization problems with strongly and uniformly convex objectives. We provide accuracy bounds for the performance of these algorithms and design methods which are…
We propose a novel approach to input design for identification of nonlinear state space models. The optimal input sequence is obtained by maximizing a scalar cost function of the Fisher information matrix. Since the Fisher information…
Devising optimal interventions for constraining stochastic systems is a challenging endeavour that has to confront the interplay between randomness and nonlinearity. Existing methods for identifying the necessary dynamical adjustments…
In this paper, we consider a formulation of nonlinear constrained optimization problems. We reformulate it as a time-varying optimization using continuous-time parametric functions and derive a dynamical system for tracking the optimal…
This paper tackles the multi-objective optimization of the cost functional of a path-following model predictive control for vehicle longitudinal and lateral control. While the inherent optimal character of the model predictive control and…
We consider the problem of optimal path planning on a manifold which is the image of a smooth function. Optimal path-planning is of crucial importance for motion planning, image processing, and statistical data analysis. In this work, we…
We consider a model of optimal investment and consumption with both habit formation and partial observations in incomplete It\^{o} processes market. The investor chooses his consumption under the addictive habits constraint while only…
This paper focuses on optimal control problem for a class of discrete-time nonlinear systems. In practical applications, computation time is a crucial consideration when solving nonlinear optimal control problems, especially under real-time…
We study a class of monotone inclusions called "self-concordant inclusion" which covers three fundamental convex optimization formulations as special cases. We develop a new generalized Newton-type framework to solve this inclusion. Our…
We identify generic protocols achieving optimal power extraction from a single active particle subject to continuous feedback control under the assumption that its spatial trajectory, but not its instantaneous self-propulsion force, is…