Related papers: Calculus of Variation and Path-Integrals with Non-…
We derive It\^o-type change of variable formulas for smooth functionals of irregular paths with non-zero $p-$th variation along a sequence of partitions where $p \geq 1$ is arbitrary, in terms of fractional derivative operators, extending…
The present paper represents a continuation of our previous one. There, a continuous dependence result for the solution of an elliptic variational-hemivariational inequality was obtained and then used to prove the existence of optimal pairs…
We define a deterministic integral with respect to irregular paths as a limit of standard line integrals and completely describe a class of all paths for which this integral exists for functions with H\"older exponent in the range of (0,1].…
An optimal control problem with an infinite horizon quadratic cost functional for a linear system with a known additive disturbance is considered. The feature of this problem is that a weight matrix of the control cost in the cost…
Motivated by recent developments in Hamiltonian variational principles, Hamiltonian variational integrators, and their applications such as to optimization and control, we present a new Type II variational approach for Hamiltonian systems,…
We develop a non-anticipating calculus of variations for functionals on a space of laws of continuous semi-martingales, which extends the classical one. We extend Hamilton's least action principle and Noether's theorem to this generalized…
We consider a nonlinear control system depending on two controls u and v, with dynamics affine in the (unbounded) derivative of u, and v appearing initially only in the drift term. Recently, motivated by applications to optimization…
We develop the path integral formalism for studying cosmological perturbations in multi-field inflation, which is particularly well suited to study quantum theories with gauge symmetries such as diffeomorphism invariance. We formulate the…
We consider a nonlinear control system with vector-valued measures as controls and with dynamics depending on time delayed states. First, we introduce a notion of discontinuous, bounded variation solution associated with this system and…
A path integral formalism for non-equilibrium systems is proposed based on a manifold of quasi-equilibrium densities. A generalized Boltzmann principle is used to weight manifold paths with the exponential of minus the information…
In this paper, we provide a generalized framework for Variational Inference-Stochastic Optimal Control by using thenon-extensive Tsallis divergence. By incorporating the deformed exponential function into the optimality likelihood function,…
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…
A key problem in the attempt to quantize the gravitational field is the choice of boundary conditions. These are mixed, in that spatial and normal components of metric perturbations obey different sets of boundary conditions. In the…
Optimal control for switch-based dynamical systems is a challenging problem in the process control literature. In this study, we model these systems as hybrid dynamical systems with finite number of unknown switching points and reformulate…
We apply path integrals to study nonequilibrium work theorems in the context of Brownian dynamics, deriving in particular the equations of motion governing the most typical and most dominant trajectories. For the analytically soluble cases…
For thermal equilibrium systems it is shown, how the Kubo-Martin-Schwinger boundary condition may be used to factorize the generating functional of Green functions at least on the level of the full two-point function. Genuine…
We present a unified framework for path-parametric planning and control. This formulation is universal as it standardizes the entire spectrum of path-parametric techniques -- from traditional path following to more recent contouring or…
We consider some boundary value tracking optimal control problem constrained by a Neumann boundary value problem for some elliptic partial differential equation where the control acts as right-hand side. This optimal control problem can be…
Using a path integral approach, we derive an analytical solution of a nonlinear and singular Langevin equation, which has been introduced previously by P.-G. de Gennes as a simple phenomenological model for the stick-slip motion of a solid…
The path integral formulation of quantum mechanics constructs the propagator by evaluating the action S for all classical paths in coordinate space. A corresponding momentum path integral may also be defined through Fourier transforms in…