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We consider an unregularized optimal control problem subject to the steady-state Navier-Stokes equations. We derive the existence of optimal solutions and prove first- and second-order optimality conditions. To approximate solutions to the…

Optimal decision-making under partial observability requires reasoning about the uncertainty of the environment's hidden state. However, most reinforcement learning architectures handle partial observability with sequence models that have…

In this article we present an a posteriori error estimator for the spatial-stochastic error of a Galerkin-type discretisation of an initial value problem for a random hyperbolic conservation law. For the stochastic discretisation we use the…

This paper studies the state estimation problem of linear discrete-time systems with stochastic unknown inputs. The unknown input is a wide-sense stationary process while no other prior informaton needs to be known. We propose an…

In this work we consider the two dimensional instationary Navier-Stokes equations with homogeneous Dirichlet/no-slip boundary conditions. We show error estimates for the fully discrete problem, where a discontinuous Galerkin method in time…

Classical discriminant analysis assumes identically distributed training data, yet in many applications observations are collected over time and the class-conditional distributions drift. This population drift renders stationary classifiers…

This paper is concerned with the problem of distributed Kalman filtering in a network of interconnected subsystems with distributed control protocols. We consider networks, which can be either homogeneous or heterogeneous, of linear…

The Kalman filter is extensively used for state estimation for linear systems under Gaussian noise. When non-Gaussian L\'evy noise is present, the conventional Kalman filter may fail to be effective due to the fact that the non-Gaussian…

An optimal estimator of quantum states based on a modified Kalman Filter is presented in this work. Such estimator acts after state measurement, allowing to obtain an optimal estimation of quantum state resulting in the output of any…

The existence of redundant sensors in collaborative state estimation is a common occurrence, yet their true significance remains elusive. This paper comprehensively investigates the effects and optimal design of redundant sensors in sensor…

The input-parameter-state estimation capabilities of a novel unscented Kalman filter is examined herein on both linear and nonlinear systems. The unknown input is estimated in two stages within each time step. Firstly, the predicted dynamic…

The work of Kalman and Bucy has established a duality between filtering and optimal estimation in the context of time-continuous linear systems. This duality has recently been extended to time-continuous nonlinear systems in terms of an…

We devise and analyze a reliable and efficient a posteriori error estimator for a semilinear control-constrained optimal control problem in two and three dimensional Lipschitz, but not necessarily convex, polytopal domains. We consider a…

In this paper we prove optimal error estimates for {solutions with natural regularity} of the equations describing the unsteady motion of incompressible shear-thinning fluids. We consider a full space-time semi-implicit scheme for the…

We study state estimation for discrete-time linear stochastic systems under distributional ambiguity in the initial state, process noise, and measurement noise. We propose a noise-centric distributionally robust Kalman filter (DRKF) based…

We present an a posteriori error analysis for one-dimensional random hyperbolic systems of conservation laws. For the discretization of the random space we consider the Non-Intrusive Spectral Projection method, the spatio-temporal…

This paper studies the distributed state estimation problem for a class of discrete time-varying systems over sensor networks. Firstly, it is shown that a networked Kalman filter with optimal gain parameter is actually a centralized filter,…

This work presents a scalable control framework based on nonlinear Model Predictive Control for high-dimensional dynamical systems. The proposed approach addresses the key challenges of model scalability and partial observability by…

This paper discusses an interval-valued state estimator for linear dynamic systems. In particular, we derive an expression of the tightest possible interval-valued estimator in the sense that it is the intersection of all interval-valued…

Large-scale agent systems have foreseeable applications in the near future. Estimating their macroscopic density is critical for many density-based optimization and control tasks, such as sensor deployment and city traffic scheduling. In…