Related papers: The topological state derivative: an optimal contr…
Networked systems display complex patterns of interactions between a large number of components. In physical networks, these interactions often occur along structural connections that link components in a hard-wired connection topology,…
Inspired by rational canonical forms, we introduce and analyze two decompositions of dynamic programming (DP) problems for systems with linear dynamics. Specifically, we consider both finite and infinite horizon DP problems in which the…
Nonlinear dynamical systems are complex and typically only simple systems can be analytically studied. In applications, these systems are usually defined with a set of tunable parameters and as the parameters are varied the system response…
We consider universal statistical properties of systems that are characterized by phase states with macroscopic degeneracy of the ground state. A possible topological order in such systems is described by non-linear discrete equations. We…
Smectic order on arbitrary curved substrate can be described by a differential form of rank one (1-form), whose geometric meaning is the differential of the local phase field of the density modulation. The exterior derivative of 1-form is…
A class of non-smooth and non-convex optimization problems with penalty constraints linked to variational inequalities (VI) is studied with respect to its shape differentiability. The specific problem stemming from quasi-brittle fracture…
Many physical systems are well described on domains which are relatively large in some directions but relatively thin in other directions. In this scenario we typically expect the system to have emergent structures that vary slowly over the…
A dual control problem is presented for the optimal stochastic control of a system governed by partial differential equations. Relationships between the optimal values of the original and the dual problems are investigated and two duality…
Traditional solvable optimal control theory predominantly focuses on quadratic costs due to their analytical tractability, yet they often fail to capture critical non-linearities inherent in real-world systems including water, energy,…
In this paper we focus on a general type of mean-field stochastic control problem with partial observation, in which the coefficients depend in a non-linear way not only on the state process $X_t$ and its control $u_t$ but also on the…
A discretization of an optimal control problem of a stochastic parabolic equation driven by multiplicative noise is analyzed. The state equation is discretized by the continuous piecewise linear element method in space and by the backward…
The concept of turnpike connects the solution of long but finite time horizon optimal control problems with steady state optimal controls. A key ingredient of the analysis of the turnpike is the linear quadratic regulator problem and the…
The purpose of this paper is to establish first and second order necessary optimality conditions for optimal control problems of stochastic evolution equations with control and state constraints. The control acts both in the drift and…
We adopt the integral definition of the fractional Laplace operator and study an optimal control problem on Lipschitz domains that involves a fractional elliptic partial differential equation (PDE) as state equation and a control variable…
In this paper we develop automatic shape differentiation techniques for unfitted discretisations and link these to recent advances in shape calculus for unfitted methods. We extend existing analytic shape calculus results to the case where…
In this paper, we consider a class of stochastic control problems for stochastic differential equations with random coefficients. The control domain need not to be convex but the control process is not allowed to enter in diffusion term.…
A surrogate-based topology optimisation algorithm for linear elastic structures under parametric loads and boundary conditions is proposed. Instead of learning the parametric solution of the state (and adjoint) problems or the optimisation…
We consider a noninteracting disordered system designed to model particle diffusion, relaxation in glasses, and impurity bands of semiconductors. Disorder originates in the random spatial distribution of sites. We find strong numerical…
We consider the optimal control of a differential equation that involves the suprema of the state over some part of the history. In many applications, this non-smooth functional dependence is crucial for the successful modeling of…
In this paper, a topology optimization framework utilizing automatic differentiation is presented as an efficient way for solving 2D density-based topology optimization problem by calculating gradients through the fully differentiable…