Related papers: Actuator design for parabolic distributed paramete…
In this paper we study robust output tracking and disturbance rejection of linear partial differential equation (PDE) models. We focus on demonstrating how the abstract internal model based controller design methods developed for "regular…
In this paper we consider multi-dimensional partial differential equations of parabolic type involving divergence form operators that possess a discontinuous coefficient matrix along some smooth interface. The solution of the equation is…
In this paper, we study the tracking controllability of a 1D parabolic type equation. Notably, with controls acting on the boundary, we seek to approximately control the solution of the equation on specific points of the domain. We prove…
In this paper, we propose an efficient exponential integrator finite element method for solving a class of semilinear parabolic equations in rectangular domains. The proposed method first performs the spatial discretization of the model…
In this work we introduce an approach for modeling and analyzing collective behavior of a group of agents using moments. We represent the group of agents via their distribution and derive a method to estimate the dynamics of the moments. We…
It is shown that an explicit oblique projection nonlinear feedback controller is able to stabilize semilinear parabolic equations, with time-dependent dynamics and with a polynomial nonlinearity. The actuators are typically modeled by a…
This paper considers the problem of designing a dynamical system to solve constrained optimization problems in a distributed way and in an anytime fashion (i.e., such that the feasible set is forward invariant). For problems with separable…
In this paper, we consider a class of time-optimal control problems governed by linear parabolic equations with mixed control-state constraints and end-point constraints, and without Tikhonov regularization term in the objective function.…
Coordination of distributed agents is required for problems arising in many areas, including multi-robot systems, networking and e-commerce. As a formal framework for such problems, we use the decentralized partially observable Markov…
Parareal algorithms are studied for semilinear parabolic stochastic partial differential equations. These algorithms proceed as two-level integrators, with fine and coarse schemes, and have been designed to achieve a `parallel in real time'…
In this work, we will investigate the question of optimal control for bilinear systems with constrained endpoint. The optimal control will be characterized through a set of unconstrained minimization problems that approximate the former.…
The ParaDiag family of algorithms solves differential equations by using preconditioners that can be inverted in parallel through diagonalization. In the context of optimal control of linear parabolic PDEs, the state-of-the-art ParaDiag…
The paper focuses on unconditionally optimal error analysis of the fully discrete Galerkin finite element methods for a general nonlinear parabolic system in $\R^d$ with $d=2,3$. In terms of a corresponding time-discrete system of PDEs as…
We present a systematic approach to the optimal placement of finitely many sensors in order to infer a finite-dimensional parameter from point evaluations of the solution of an associated parameter-dependent elliptic PDE. The quality of the…
We propose a numerical method to solve parameter-dependent hyperbolic partial differential equations (PDEs) with a moment approach, based on a previous work from Marx et al. (2020). This approach relies on a very weak notion of solution of…
This work considers two boundary correction techniques to mitigate the reduction in the temporal order of convergence in PDE sense (i.e., when both the space and time resolutions tend to zero independently of each other) of $d$ dimension…
Space-time finite element discretizations of time-optimal control problems governed by linear parabolic PDEs and subject to pointwise control constraints are considered. Optimal a priori error estimates are obtained for the control variable…
This paper is concerned with the optimal control problem governed by a linear parabolic equation and subjected to box constraints on control variables. This type of problem has important applications in heating and cooling systems. By…
We analyze the dynamics of multi-agent collective behavior models and their control theoretical properties. We first derive a large population limit to parabolic diffusive equations. We also show that the non-local transport equations…
This paper investigates the differentiable dynamic modeling of mobile manipulators to facilitate efficient motion planning and physical design of actuators, where the actuator design is parameterized by physically meaningful motor geometry…