Output-Feedback Boundary Control of a Heat PDE Sandwiched Between Two ODEs

Delay-Compensated Control of Sandwiched ODE-PDE-ODE Hyperbolic Systems for Oil Drilling and Disaster Relief

Motivated by engineering applications of subsea installation by deepwater construction vessels in oil drilling, and of aid delivery by unmanned aerial vehicles in disaster relief, we develop output-feedback boundary control of heterodirectional coupled hyperbolic PDEs sandwiched between two ODEs, where the measurement is the output state of one ODE and suffers a time delay. After rewriting the time-delay dynamics as a transport PDE of which the left boundary connects with the sandwiched system, a state observer is built to estimate the states of the overall system of ODE-heterodirectional coup…

耦合线性常微分方程和双曲型偏微分方程的H$_1$-ISS分析与边界控制设计

H$_1$-ISS Analysis and Boundary Control Design for Coupled Linear ODEs and Hyperbolic PDEs

研究耦合线性ODEs和双曲型PDEs系统的边界控制设计，将基于李雅普诺夫的ISS条件扩展到H$_1$设置，推导稳定性分析和控制设计条件，通过数值例子验证所提方法的有效性和潜力。

Backstepping Control of a Hyperbolic PDE System with Zero Characteristic Speed States

While for coupled hyperbolic PDEs of first order there now exist numerous PDE backstepping designs, systems with zero speed, i.e., without convection but involving infinite-dimensional ODEs, which arise in many applications, from environmental engineering to lasers to manufacturing, have received virtually no attention. In this paper, we introduce single-input boundary feedback designs for a linear 1-D hyperbolic system with two counterconvecting PDEs and $n$ equations (infinite-dimensional ODEs) with zero characteristic speed. The inclusion of zero-speed states, which we refer to as {\em atac…

A Continuation Method for Large-Scale Modeling and Control: from ODEs to PDE, a Round Trip

In this paper we present a continuation method which transforms spatially distributed ODE systems into continuous PDE. We show that this continuation can be performed both for linear and nonlinear systems, including multidimensional, space- and time-varying systems. When applied to a large-scale network, the continuation provides a PDE describing evolution of continuous state approximation that respects the spatial structure of the original ODE. Our method is illustrated by multiple examples including transport equations, Kuramoto equations and heat diffusion equations. As a main example, we p…

借助二次项实现多输入双线性薛定谔方程的小时间局部可控性

Small-Time Local Controllability of the multi-input bilinear Schrödinger equation thanks to a quadratic term

本文研究多输入双线性薛定谔方程在线性化不可控时的小时间局部可控性，明确哪些二次李括号可恢复可控性，并提出基于 Magnus 公式的新证明，将其推广到 PDE 情形。

Representation and Stability Analysis of PDE-ODE Coupled Systems

In this work, we present a scalable Linear Matrix Inequality (LMI) based framework to verify the stability of a set of linear Partial Differential Equations (PDEs) in one spatial dimension coupled with a set of Ordinary Differential Equations (ODEs) via input-output based interconnection. Our approach extends the newly developed state space representation and stability analysis of coupled PDEs that allows parametrizing the Lyapunov function on $L_2$ with multipliers and integral operators using polynomial kernels of semi-separable class. In particular, under arbitrary well-posed boundary condi…