Related papers: $H_2$-Optimal Estimation of Linear Delayed and PDE…
Physics-Informed Neural Networks (PINNs) have proven effective in solving partial differential equations (PDEs), especially when some data are available by seamlessly blending data and physics. However, extending PINNs to high-dimensional…
We consider the linear matrix inequality (LMI) problem of $H_\infty$ output feedback control problem for a generalized plant whose control input, measured output, disturbance input, and controlled output are scalar. We provide an explicit…
This paper studies the problem of state estimation for linear time-invariant descriptor systems in their most general form. The estimator is a system of ordinary differential equations (ODEs). We introduce the notion of partial causal…
We present a control design for semilinear and quasilinear 2x2 hyperbolic partial differential equations with the control input at one boundary and a nonlinear ordinary differential equation coupled to the other. The controller can be…
In this paper we establish the interpolatory model reduction framework for optimal approximation of MIMO dynamical systems with respect to the $\mathcal{H}_2$ norm over a finite-time horizon, denoted as the $\mathcal{H}_2(t_f)$ norm. Using…
This paper addresses the end-to-end sample complexity bound for learning in closed loop the state estimator-based robust H2 controller for an unknown (possibly unstable) Linear Time Invariant (LTI) system, when given a fixed state-feedback…
Hybrid High-Order methods for elliptic diffusion problems have been originally formulated for loads in the Lebesgue space $L^2(\Omega)$. In this paper we devise and analyze a variant thereof, which is defined for any load in the dual…
A multi-variable PI (proportional integrating) controller is proved to be optimal for an important class of control problems where performance is specified in terms of frequency weighted H-infinity norms. The problem class includes…
We prove an L2 recovery bound for a family of sparse estimators defined as minimizers of some empirical loss functions -- which include hinge loss and logistic loss. More precisely, we achieve an upper-bound for coefficients estimation…
This paper develops an optimal relative output-feedback based solution to the containment control problem of linear heterogeneous multi-agent systems. A distributed optimal control protocol is presented for the followers to not only assure…
In this paper, we simultaneously determine the optimal sensor precision and the observer gain, which achieves the specified accuracy in the state estimates. Along with the unknown observer gain, the formulation parameterizes the scaling of…
Ordinary Differential Equations are a simple but powerful framework for modeling complex systems. Parameter estimation from times series can be done by Nonlinear Least Squares (or other classical approaches), but this can give…
This paper investigates the state estimation problem for linear systems subject to Gaussian noise, where the model parameters are unknown. By formulating and solving an optimization problem that incorporates both offline and online system…
We explore the use of a Neural Ratio Estimator (NRE) to determine the Hubble constant ($H_0$) in the context of time delay cosmography. Assuming a Singular Isothermal Ellipsoid (SIE) mass profile for the deflector, we simulate time delay…
Despite all the benefits of automated hyperparameter optimization (HPO), most modern HPO algorithms are black-boxes themselves. This makes it difficult to understand the decision process which leads to the selected configuration, reduces…
A novel approach to solve the problem of distributed state estimation of linear time-invariant systems is proposed in this paper. It relies on the application of parameter estimation-based observers, where the state observation task is…
We investigate an algorithm named histogram transform ensembles (HTE) density estimator whose effectiveness is supported by both solid theoretical analysis and significant experimental performance. On the theoretical side, by decomposing…
This paper is concerned with the state estimation problem for two-dimensional systems with asynchronous multichannel delays and energy harvesting constraints. In the system, each smart sensor has a certain probability of harvesting energy…
We propose machine learning methods for solving fully nonlinear partial differential equations (PDEs) with convex Hamiltonian. Our algorithms are conducted in two steps. First the PDE is rewritten in its dual stochastic control…
We consider constrained bilinear optimal control of second-order linear evolution partial differential equations (PDEs) with a reaction term on the half line, where control arises as a time-dependent reaction coefficient and constraints are…