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By means of a direct and constructive method based on the theory of semiglobal $C^2$ solution, the local exact boundary observability is shown for nonautonomous 1-D quasilinear wave equations. The essential difference between nonautonomous…
In this work, we broadly connect kernel-based filtering (e.g. approaches such as the bilateral filters and nonlocal means, but also many more) with general variational formulations of Bayesian regularized least squares, and the related…
Approximate stationarity conditions provide necessary optimality conditions without requiring additional assumptions by demanding that a perturbed stationarity system possesses solutions as the involved perturbations tend to zero. Together…
We present a general approach to prove existence of solutions for optimal control problems not based on typical convexity conditions which quite often are very hard, if not impossible, to check. By taking advantage of several relaxations of…
Quantum Optimal Control (QOC) is the field devoted to the production of external control protocols that actively guide quantum dynamics. Solutions to QOC problems were shown to constitute continuous submanifolds of control space. A solution…
We consider a problem of optimal control of an infinite horizon system governed by forward-backward stochastic differential equations with delay. Sufficient and necessary maximum principles for optimal control under partial information in…
The periodic standing wave (PSW) method for the binary inspiral of black holes and neutron stars computes exact numerical solutions for periodic standing wave spacetimes and then extracts approximate solutions of the physical problem, with…
We study stochastic optimal control problems for (possibly degenerate) McKean-Vlasov controlled diffusions and obtain discrete-time as well as finite interacting particle approximations. (i) Under mild assumptions, we first prove the…
We lift the constraint of a diagonal representation of the Hamiltonian by searching for square integrable bases that support an infinite tridiagonal matrix representation of the wave operator. The class of solutions obtained as such…
Asymptotic stability in receding horizon control is obtained under a strict pre-dissipativity assumption, in the presence of suitable state constraints. In this paper we analyze how terminal constraints can be replaced by suitable terminal…
This paper considers the problem of finding near-optimal Markovian randomized (MR) policies for finite-state-action, infinite-horizon, constrained risk-sensitive Markov decision processes (CRSMDPs). Constraints are in the form of standard…
The inverse linear-quadratic optimal control problem is a system identification problem whose aim is to recover the quadratic cost function and hence the closed-loop system matrices based on observations of optimal trajectories. In this…
In this article we study a finite horizon optimal control problem with monotone controls. We consider the associated Hamilton-Jacobi-Bellman (HJB) equation which characterizes the value function. We consider the totally discretized problem…
We show a connection between global unconstrained optimization of a continuous function $f$ and weak KAM theory for an eikonal-type equation arising also in ergodic control. A solution $v$ of the critical Hamilton-Jacobi equation is built…
Precise variational solutions are given for problems involving diverse fermionic and bosonic $N=2-7$-body systems. The trial wave functions are chosen to be combinations of correlated Gaussians, which are constructed from products of the…
This paper investigates the infinite horizon optimal control problem (OCP) for space applications characterized by nonlinear dynamics. The proposed approach divides the problem into a finite horizon OCP with a regularized terminal cost,…
We study optimality conditions for various types of control problems like the standard optimal control problem, optimal multiprocesses, problems with infinite horizon or the control of Volterra integral equations. To derive necessary…
This is the first in a series of papers devoted to an analogue of the metaplectic representation, namely, the minimal unitary representation of an indefinite orthogonal group; this representation corresponds to the minimal nilpotent…
We consider a bilinear control problem for the wave equation on a torus of arbitrary dimension. We show that the system is globally approximately controllable in arbitrarily small times from a dense family of initial states. The control…
The numerical solution of the many-body problem of interacting electrons and ions is a key challenge in condensed matter physics, chemistry, and materials science. Traditional methods to solve the multi-component quantum Hamiltonian are…