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In this note, we present some complementary results on the infinite horizon optimal control for linear time-delay systems. We formally establish some properties of the matrices arising in the Bellman functional, and we prove that no…
We introduce the delayed Mittag-Leffler type matrix functions, delayed fractional cosine, delayed fractional sine and use the Laplace transform to obtain an analytical solution to the IVP for a Hilfer type fractional linear time-delay…
We consider optimization of nonlinear objective functions that balance $d$ linear criteria over $n$-element independence systems presented by linear-optimization oracles. For $d=1$, we have previously shown that an $r$-best approximate…
This paper studies the construction of symbolic abstractions for nonlinear control systems via feedback refinement relation. Both the delay-free and time-delay cases are addressed. For the delay-free case, to reduce the computational…
Time-invariant finite-dimensional systems, under reasonable continuity assumptions, exhibit the property that if solutions exist for all future times, the set of vectors reachable from a bounded set of initial conditions over bounded time…
We consider nonlocal nonlinear potentials and estimate the rate of convergence of time stepping schemes to the peridynamic equation of motion. We begin by establishing the existence of $H^2$ solutions over any finite time interval. Here…
We address the problem of verifying timed properties of Markovian models of large populations of interacting agents, modelled as finite state automata. In particular, we focus on time-bounded properties of (random) individual agents…
We prove the convergence of an incremental projection numerical scheme for the time-dependent incompressible Navier--Stokes equations, without any regularity assumption on the weak solution. The velocity and the pressure are discretised in…
In this manuscript we consider a class optimal control problem for stochastic differential delay equations. First, we rewrite the problem in a suitable infinite-dimensional Hilbert space. Then, using the dynamic programming approach, we…
The 't Hooft model, i.e. the two-dimensional quantum chromodynamics in the limit of infinite number of colors, is interpolated by an angle parameter $\delta$ between $\delta=0$ for the instant form dynamics (IFD) and $\delta=\pi/4$ for the…
In this paper, we accomplish two objectives: First, we provide a new mathematical characterization of the value function for impulse control problems with implementation delay and present a direct solution method that differs from its…
Quantum speed-ups for dynamical simulation usually demand unitary time-evolution, whereas the large ODE/PDE systems encountered in realistic physical models are generically non-unitary. We present a universal moment-fulfilling dilation that…
This article studies the solutions of time-dependent differential inclusions which is motivated by their utility in the modeling of certain physical systems. The differential inclusion is described by a time-dependent set-valued mapping…
An approximate equation for the effective conductivity sigma_eff of systems with a finite maximal scale of inhomogeneities is deduced. An exact solution of this equation is found and its physical meaning is discussed. A two-phase randomly…
We develop new methods for approximating conformal blocks as positive functions times polynomials, with applications to the numerical bootstrap. We argue that to obtain accurate bootstrap bounds, conformal block approximations should…
An important class of dynamical systems with several practical applications is linear systems with quadratic outputs. These models have the same state equation as standard linear time-invariant systems but differ in their output equations,…
Several methods have been developed for the simulation of the Hawkes process. The oldest approach is the inverse sampling transform (ITS) suggested in \citep{ozaki1979maximum}, but rapidly abandoned in favor of more efficient alternatives.…
We revisit the problem of real-time verification with dense dynamics using timeout and calendar based models and simplify this to a finite state verification problem. To overcome the complexity of verification of real-time systems with…
A classical approach for solving discrete time nonlinear control on a finite horizon consists in repeatedly minimizing linear quadratic approximations of the original problem around current candidate solutions. While widely popular in many…
Optimizing conversions is crucial in modern online advertising systems, enabling advertisers to deliver relevant products to users and drive business outcomes. However, accurately predicting conversion events remains challenging due to…