46 citations · 79 across the 28 of their papers we have counts for
29 papers
Input-to-State Stabilization of a Coupled ODE-PDE System with Time-Varying Coefficients via Composite Boundary Control
Yongchun Bi, Jun Zheng, Guchuan Zhu +1
This paper proposes a novel composite boundary feedback control law that ensures input-to-state stability (ISS) for a coupled ODE-parabolic PDE system with time-varying coefficient…
Robust synchronization for multi-agent systems governed by PDEs with observable and unobservable disturbances
Yongchun Bi, Jun Zheng, Guchuan Zhu +1
This paper investigates robust synchronization for multi-agent systems (MASs) governed by parabolic partial differential equations in the presence of both observable and unobservab…
Unified Lyapunov Method for ISS of PDEs: A Tutorial on Constructing Generalized Lyapunov Functionals for Parabolic and Hyperbolic Equations
Jun Zheng, Guchuan Zhu
This tutorial provides an overview of the generalized Lyapunov method (GLM) for analyzing input-to-state stability (ISS) of partial differential equations (PDEs). We begin by revis…
A Spectral-based ISS small-gain theorem for boundary control systems with infinite couplings
Yassine El Gantouh, Jun Zheng, Guchuan Zhu +1
We study the input-to-state stability (ISS) of boundary control systems allowing for infinitely many boundary couplings. Using semigroup perturbation theory and the theory of posit…
Well-posedness of boundary control systems and application to ISS for coupled heat equations with boundary disturbances and delays
Yassine El Gantouh, Jun Zheng, Guchuan Zhu
This paper studies the existence of solutions and, in particular, the well-posedness of a class of boundary control systems. Our main result provides explicit and verifiable condit…
Input-to-state stabilization of an ODE cascaded with a parabolic equation involving Dirichlet-Robin boundary disturbances
Yongchun Bi, Jun Zheng, Guchuan Zhu
This paper focuses on the input-to-state stabilization problem for an ordinary differential equation (ODE) cascaded by parabolic partial differential equation (PDE) in the presence…
Local integral input-to-state stability for non-autonomous infinite-dimensional systems
Yongchun Bi, Panyu Deng, Jun Zheng +1
In this paper, we prove comparison principles for nonlinear differential equations with time-varying coefficients and develop Lyapunov analytical tools for the integral input-to-st…
Finite-time input-to-state stability for infinite-dimensional systems
Xiaorong Sun, Jun Zheng, Guchuan Zhu
In this paper, we extend the notion of finite-time input-to-state stability (FTISS) for finite-dimensional systems to infinite-dimensional systems. More specifically, we first prov…
Input-to-state stabilization of -D parabolic equations with Dirichlet boundary disturbances under boundary fixed-time control
Jun Zheng, Guchuan Zhu
This paper addresses the problem of stabilization of -D parabolic equations with destabilizing terms and Dirichlet boundary disturbances. By using the method of backstepping and…
Input-to-State Stabilization of 1-D Parabolic PDEs under Output Feedback Control
Yongchun Bi, Jun Zheng, Guchuan Zhu
This paper addresses the problem of input-to-state stabilization for a class of parabolic equations with time-varying coefficients, as well as Dirichlet and Robin boundary disturba…
Power Tracking Control of Heterogeneous Populations of TCLs with Partially Measured States
Zhenhe Zhang, Jun Zheng, Guchuan Zhu
This paper presents a new aggregate power tracking control scheme for populations of thermostatically controlled loads (TCLs). The control design is performed in the framework of p…
Power Tracking Control of Heterogeneous TCL Populations with Modeling Uncertainties and Communication Restrictions
Zhenhe Zhang, Jun Zheng, Guchuan Zhu
This paper presents a new aggregate power tracking control scheme for populations of thermostatically controlled loads (TCLs). The control design is carried out in the framework of…
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''
Qiaoling Chen, Jun Zheng, Guchuan Zhu
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…
Exponential stabilization and continuous dependence of solutions on initial data in different norms for space-time-varying linear parabolic PDEs
Qiaoling Chen, Jun Zheng, Guchuan Zhu
For an arbitrary parameter , we consider the problem of exponential stabilization in the spatial -norm, and -norm, respectively, for a class of an…
A PDE--based Power Tracking Control of Heterogeneous TCL Populations
Jun Zheng, Guchuan Zhu, Meng Li
This chapter presents the development and the analysis of a scheme for aggregate power tracking control of heterogeneous populations of thermostatically controlled loads (TCLs) bas…
Relative Stability in the Sup-norm and Input-to-state Stability in the Spatial Sup-norm for Parabolic PDEs
Jun Zheng, Guchuan Zhu, Sergey Dashkovskiy
In this paper, we introduce the notion of relative -equi-stability (RKES) to characterize the uniformly continuous dependence of (weak) solutions on external disturban…
Approximations of Lyapunov functions for ISS analysis of a class of nonlinear parabolic PDEs
Jun Zheng, Guchuan Zhu
This paper addresses the input-to-state stability (ISS) and integral input-to-state stability (iISS) for a class of nonlinear higher dimensional parabolic partial differential equa…
A Note on the Maximum Principle-based Approach for ISS Analysis of Higher Dimensional Parabolic PDEs with Variable Coefficients
Jun Zheng, Guchuan Zhu
This paper presents a maximum principle-based approach in the establishment of input-to-state stability (ISS) for a class of nonlinear parabolic partial differential equations (PDE…
A weak maximum principle-based approach for input-to-state stability analysis of nonlinear parabolic PDEs with boundary disturbances
Jun Zheng, Guchuan Zhu
In this paper, we introduce a weak maximum principle-based approach to input-to-state stability (ISS) analysis for certain nonlinear partial differential equations (PDEs) with boun…
Aggregate Power Control of Heterogeneous TCL Populations Governed by Fokker-Planck Equations
Jun Zheng, Gabriel Laparra, Guchuan Zhu +1
This paper addresses the modeling and control of heterogeneous populations of thermostatically controlled loads (TCLs) operated by model predictive control (MPC) schemes at level o…
A De Giorgi Iteration-based Approach for the Establishment of ISS Properties for Burgers' Equation with Boundary and In-domain Disturbances
Jun Zheng, Guchuan Zhu
This note addresses input-to-state stability (ISS) properties with respect to (w.r.t.) boundary and in-domain disturbances for Burgers' equation. The developed approach is a combin…
ISS with Respect to Boundary and In-domain Disturbances for a Coupled Beam-String System
Jun Zheng, Hugo Lhachemi, Guchuan Zhu +1
This paper addresses the robust stability of a boundary controlled system coupling two partial differential equations (PDEs), namely beam and string equations, in the presence of b…
Regularity in the two-phase free boundary problems under non-standard growth conditions
Jun Zheng
In this paper, we prove several regularity results for the heterogeneous, two-phase free boundary problems $\mathcal {J}_γ(u)=\int_Ω\big(f(x,\nabla u)+λ_{+} (u^{+})^γ+λ_{-}(u^{-})^…
A minimum problem with free boundary and subcritical growth in Orlicz spaces
Jun Zheng, Leandro S. Tavares, Claudianor O. Alves
The aim of this paper is to study the heterogeneous optimization problem \begin{align*} \mathcal {J}(u)=\int_Ω(G(|\nabla u|)+qF(u^+)+hu+λ_{+}χ_{\{u>0\}} )\text{d}x\rightarrow\text{…