Related papers: Probability Density Estimation via Optimal Control
Optimal design of distributed decision policies can be a difficult task, illustrated by the famous Witsenhausen counterexample. In this paper we characterize the optimal control designs for the vector-valued setting assuming that it results…
Consider the following problem: given two arbitrary densities $q_1,q_2$ and a sample-access to an unknown target density $p$, find which of the $q_i$'s is closer to $p$ in total variation. A remarkable result due to Yatracos shows that this…
We consider the inverse multiphase Stefan problem with homogeneous Dirichlet boundary condition on a bounded Lipschitz domain, where the density of the heat source is unknown in addition to the temperature and the phase transition…
We consider optimal control problems involving nonlinear ordinary differential equations with uncertain inputs. Using the sample average approximation, we obtain optimal control problems with ensembles of deterministic dynamical systems.…
This paper considers the relaxed version of the transport problem for general nonlinear control systems, where the objective is to design time-varying feedback laws that transport a given initial probability measure to a target probability…
We study the numerical realisation of optimal consensus control laws for agent-based models. For a nonlinear multi-agent system of Cucker-Smale type, consensus control is cast as a dynamic optimisation problem for which we derive…
The paper is devoted to the study of a new class of optimal control problems governed by discontinuous constrained differential inclusions of the sweeping type with involving the duration of the dynamic process into optimization. We develop…
One key issue in several astrophysical problems is the evaluation of the density probability function underlying an observational discrete data set. We here review two non-parametric density estimators which recently appeared in the…
This paper studies an optimal control problem for continuous-time stochastic systems subject to reachability objectives specified in a subclass of metric interval temporal logic specifications, a temporal logic with real-time constraints.…
The problem of continuous inverse optimal control (over finite time horizon) is to learn the unknown cost function over the sequence of continuous control variables from expert demonstrations. In this article, we study this fundamental…
We consider a simple control problem in which the underlying dynamics depend on a parameter $a$ that is unknown and must be learned. We study three variants of the control problem: Bayesian control, in which we have a prior belief about…
We consider the utilization of a computational model to guide the optimal acquisition of experimental data to inform the stochastic description of model input parameters. Our formulation is based on the recently developed consistent…
Computational aspects of the optimal consumption and investment with the partially observed stochastic volatility of the asset prices are considered. The new quantization approach to filtering - density quantization - is introduced which…
Appropriate time discretization is crucial for real-time applications of numerical optimal control, such as nonlinear model predictive control. However, if the discretization error strongly depends on the applied control input, meeting…
Quantization for probability distributions refers broadly to estimating a given probability measure by a discrete probability measure supported by a finite number of points. We consider general geometric approaches to quantization using…
A novel, non-trivial, probabilistic upper bound on the entropy of an unknown one-dimensional distribution, given the support of the distribution and a sample from that distribution, is presented. No knowledge beyond the support of the…
In this technical note, we deal with a spectrum approximation problem arising in THREE-like multivariate spectral estimation approaches. The solution to the problem minimizes a suitable divergence index with respect to an a priori spectral…
A class of optimal control problems governed by linear fractional diffusion equation with control constraint is considered. We first establish some results on the existence of strong solution to the state equation and the existence of…
A particle filter is introduced to numerically approximate a solution of the global optimization problem. The theoretical significance of this work comes from its variational aspects: (i) the proposed particle filter is a controlled…
This work is concerned with optimal control problems where the objective functional consists of a tracking-type functional and an additional "multibang" regularization functional that promotes optimal control taking values from a given…