Related papers: Feedback Linearization of Hyperbolic PDEs with Vol…
We present a methodology for stabilization of general nonlinear systems with actuator dynamics governed by general, quasilinear, first-order hyperbolic PDEs. Since for such PDE-ODE cascades the speed of propagation depends on the PDE state…
This paper gives an overview of the control of distributed-parameter systems using normal forms. Considering linear controllable PDE-ODE systems of hyperbolic type, two methods derive tracking controllers by mapping the system into a form…
This paper presents a methodology for the construction of simple Control Lyapunov Functionals (CLFs) for boundary controlled parabolic Partial Differential Equations (PDEs). The proposed methodology provides functionals that contain only…
We introduce a finite dimensional version of backstepping controller design for stabilizing solutions of PDEs from boundary. Our controller uses only a finite number of Fourier modes of the state of solution, as opposed to the classical…
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…
This paper is devoted to a simple and new proof on the optimal finite control time for general linear coupled hyperbolic system by using boundary feedback on one side. The feedback control law is designed by first using a Volterra…
The paper provides results for a non-standard, hyperbolic, 1-D, nonlinear traffic flow model on a bounded domain. The model consists of two first-order PDEs with a dynamic boundary condition that involves the time derivative of the…
In this article, we detail the design of an output feedback stabilizing control law for an underactuated network of N subsystems of n + m heterodirectional linear first-order hyperbolic Partial Differential Equations interconnected through…
We provide a detailed proof of Proposition 3.1 in the paper titled ``Backstepping control of a class of space-time-varying linear parabolic PDEs via time invariant kernel functions''. In the paper titled ``Backstepping control of a class of…
For quasilinear parabolic partial differential equations (PDEs) that exhibit finite-time blow up in open loop, i.e., under null boundary conditions, we provide an estimate of the region of attraction under cubic feedback laws applied at the…
We present a novel approach to control design for nonlinear systems which leverages model-free policy optimization techniques to learn a linearizing controller for a physical plant with unknown dynamics. Feedback linearization is a…
This paper presents a systematic approach to nonlinear state-feedback control design that has three main advantages: (i) it ensures exponential stability and $ \mathcal{L}_2 $-gain performance with respect to a user-defined set of reference…
A large class of hyperbolic and advection-dominated PDEs can have solutions with discontinuities. This paper investigates, both theoretically and empirically, the operator learning of PDEs with discontinuous solutions. We rigorously prove,…
The recently introduced DeepONet operator-learning framework for PDE control is extended from the results for basic hyperbolic and parabolic PDEs to an advanced hyperbolic class that involves delays on both the state and the system output…
This paper proposes a backstepping boundary control design for robust stabilization of linear first-order coupled hyperbolic partial differential equations (PDEs) with Markov-jumping parameters. The PDE system consists of 4 X 4 coupled…
In this paper, we consider the inverse problem of determining some coefficients within a coupled nonlinear parabolic system, through boundary observation of its non-negative solutions. In the physical setup, the non-negative solutions…
This paper deals with the problem of boundary stabilization of first-order n\times n inhomogeneous quasilinear hyperbolic systems. A backstepping method is developed. The main result supplements the previous works on how to design…
Research on stabilization of coupled hyperbolic PDEs has been dominated by the focus on pairs of counter-convecting ("heterodirectional") transport PDEs with distributed local coupling and with controls at one or both boundaries. A recent…
The overarching goal of this work is to develop an accurate, robust, and stable methodology for finite deformation modeling using strong-form peridynamics (PD) and the correspondence modeling framework. We adopt recently developed methods…
This paper explores a fully discrete approximation for a nonlinear hyperbolic PDE-constrained optimization problem (P) with applications in acoustic full waveform inversion. The optimization problem is primarily complicated by the…