Related papers: Dual Representations and $H_{\infty}$-Optimal Cont…
We adopt the integral definition of the fractional Laplace operator and analyze an optimal control problem for a fractional semilinear elliptic partial differential equation (PDE); control constraints are also considered. We establish the…
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 analyzes the motion of solutions to non-homogeneous linear differential equations. It further clarifies that a proportional-integral-derivative (PID) controller essentially comprises two parts: a homogeneous controller and a…
We consider robust optimal experimental design (ROED) for nonlinear Bayesian inverse problems governed by partial differential equations (PDEs). An optimal design is one that maximizes some utility quantifying the quality of the solution of…
This paper considers the problem of finite dimensional output feedback H-infinity control for a class of nonlinear spatially distributed processes (SDPs) described by highly dissipative partial differential equations (PDEs), whose state is…
Ordinary and partial differential equations (ODEs/PDEs) play a paramount role in analyzing and simulating complex dynamic processes across all corners of science and engineering. In recent years machine learning tools are aspiring to…
We propose and analyze a posteriori error estimators for an optimal control problem that involves an elliptic partial differential equation as state equation and a control variable that enters the state equation as a coefficient; pointwise…
We present an efficient method for computing A-optimal experimental designs for infinite-dimensional Bayesian linear inverse problems governed by partial differential equations (PDEs). Specifically, we address the problem of optimizing the…
A magnetizable piezoelectric beam model, free at both ends, is considered. Piezoelectric materials have a strong interaction of electromagnetic and acoustic waves, whose wave propagation speeds differ substantially. The corresponding…
In this paper the notion of bisimulation relation for linear input-state-output systems is extended to general linear differential-algebraic (DAE) systems. Geometric control theory is used to derive a linear-algebraic characterization of…
This paper proposes a stabilizing state-feedback control law for vector-valued state systems with a scalar control input, governed by a general class of integral difference equations that incorporate both pointwise and distributed input…
This work deals with optimal control problems as a strategy to drive bifurcating solution of nonlinear parametrized partial differential equations towards a desired branch. Indeed, for these governing equations, multiple solution…
The modeling and control of single-phase flow systems governed by Partial Differential Equations (PDEs) present challenges, especially under transient conditions. In this work, we extend the Physics-Informed Neural Nets for Control (PINC)…
This paper develops a probabilistic numerical method for solution of partial differential equations (PDEs) and studies application of that method to PDE-constrained inverse problems. This approach enables the solution of challenging inverse…
We present designs for exponential stabilization of an ODE-heat PDE-ODE coupled system where the control actuation only acts in one ODE. The combination of PDE backstepping and ODE backstepping is employed in a state-feedback control law…
Parabolic partial differential equations (PDEs) appear in many disciplines to model the evolution of various mathematical objects, such as probability flows, value functions in control theory, and derivative prices in finance. It is often…
A class of evolution variational inequalities (EVIs), which comprises ordinary differential equations (ODEs) coupled with variational inequalities (VIs) associated with time-varying set-valued mappings, is proposed in this paper. We first…
Model discrepancy, defined as the difference between model predictions and reality, is ubiquitous in computational models for physical systems. It is common to derive partial differential equations (PDEs) from first principles physics, but…
In this paper we propose a variation of the widely popular Interconnection-and-Damping-Assigment Passivity-Based Control (IDA-PBC) based on Poincare's Lemma to design output feedback globally stabilizing controllers for two dimensional…
This article describes a new, efficient way of finding control and state trajectories in optimal control problems by reformulation as a system of differential-algebraic equations (DAEs). The optimal control and state vectors can be obtained…