Guojie Zheng

• PhD
• Henan Normal University

This article is concerned with the unique continuation and observability of a semi-linear parabolic system in a bounded domain Ω with homogeneous Dirichlet boundary conditions. We first study the existence and uniqueness of the L[[EQUATION]]-solution to the system when the initial value belongs to L[[EQUATION]](Ω)2. We then build up some observatio...

This paper studies the 2nd-moment exponential stability of a class of infinite-dimensional linear stochastic switched systems comprising two unstable subsystems. We first construct an algebraic sufficient condition on the existence of multiple Lyapunov functions. Then, two switching strategies are designed to stabilize infinite-dimensional linear s...

This paper investigates the stabilization of an unstable stochastic heat equation. By the backstepping technique, a boundary feedback control is designed to stabilize the unstable stochastic system, including the 2nd-moment and almost-sure exponential stabilization. We also prove that the system with a disturbance in the control channel possesses g...

This paper studies the quantitative unique continuation for a semi-linear parabolic-elliptic coupled system on a bounded domain Ω. This system is a simplified version of the chemotaxis model introduced by Keller and Segel in [14]. With the aid of priori L∞-estimates (for solutions of the system) built up in this paper, we treat the semi-linear para...

This paper investigates an observability estimate for the parabolic equations with inverse square potential in a $ C^2 $ bounded domain $ \Omega\subset\mathbb{R}^d $, which contains $ 0 $. The observation region is a product set of a subset $ E\subset(0, T] $ with positive measure and a non-empty open subset $ \omega\subset\Omega $ with $ 0\notin\o...

This paper studies the quantitative unique continuation for a semi-linear parabolic-elliptic coupled system on a bounded domain. This system is a simplified version of the chemotaxis model introduced by Keller and Segel. With the aid of priori L^infty-estimates (for solutions of the system) built up in this paper, we treat the semi-linear parabolic...

In this paper, we investigate the stabilization for infinite dimensional switched linear systems comprising two unstable subsystems. From the algebraic structure of the state space, two switching strategies are designed to stabilize the infinite dimensional switched linear systems. Under these strategies and suitable assumptions, the systems with t...

This article is concerned with the unique continuation property of a forward differential inequality abstracted from parabolic equations proposed on a convex domain $\Omega$ prescribed with some regularity and growth conditions. Our result shows that the value of the solutions can be determined uniquely by its value on an arbitrary open subset $\om...

In this paper, we consider stabilization for a multi-dimensional heat equation with internal control matched disturbance. The active disturbance rejection control approach is adopted in this work. First of all, we estimate the disturbance in terms of the output. Then we cancel the disturbance by its approximation. In the end, we design some control...

In this paper, we study the controllability of the semi-discrete internally controlled 1-D wave equation by using the finite difference method. In the discrete setting of the finite difference method, we derive the observability inequality and get the exact controllability for the semi-discrete internally controlled wave equation in the one-dimensi...

This paper is devoted to study the abstract functional differential equation (FDE) of the following form (u) over dot(t) - Au(t) + Phi u(t), where A generates a C-regularized semigroup, which is the generalization of C-0-semigroup and can be applied to deal with many important differential operators that the C-0-semigroup can not be used to. We fir...

This paper is devoted to study the abstract functional differential equation (FDE) of the following form where A generates a C-regularized semigroup, which is the generalization of C0-semigroup and can be applied to deal with many important differential operators that the C0-semigroup can not be used to. We first show that the C-well-posedness of a...

In this paper, we study the stability of the anti-stable 1-D heat equation with uncertain disturbance on the boundary. We first estimate the disturbance in terms of the output. Then, we design some control strategy to stabilize the anti-stable system.

This paper deals with the stabilization problem of first-order hyperbolic partial differential equations (PDEs) with spatial-temporal actuation over the full physical domains. We assume that the interior actuator can be decomposed into a product of spatial and temporal components, where the spatial component satisfies a specific ordinary differenti...

We establish an observability estimate for the fractional order parabolic equations evolved in a bounded domain Ω of ℝ n . The observation region is F × ω , where ω and F are measurable subsets of Ω and (0, T ), respectively, with positive measure. This inequality is equivalent to the null controllable property for a linear controlled...

In this paper, we study the optimal time for a time optimal control problem (P), governed by an internally controlled semi-linear heat equation. By projecting the original problem via the finite element method, we obtain another time optimal control problem (Ph) governed by a semi-linear system of ordinary differential equations. Here, h is the mes...

In this paper, we study the controllability problem of the semi-discrete internally controlled one-dimensional wave equation with the finite element method. We derive the observability inequality and prove the exact controllability for the semi-discrete internally controlled wave equation, with the controls taken from a finite dimensional space. M...

This article studies a time optimal control problem for some switching controlled systems. We first prove the existence of time optimal controls to the problem . Then, we derive the bang-bang property for time optimal controls to this problem, through utilizing the Pontryagin maximum principle. AMS Classification: 49K20; 35J65.

In this paper, we study the optimal time for a time optimal control problem $(\mathcal{P})$, where the state system is an internally controlled heat equation. By projecting the original problem via the finite element method, we obtain another time optimal control problem $(\mathcal{P}_{hl})$ governed by a linear system of ordinary differential equa...

This paper concerns an optimal control problem governed by a linear evolution system with a small perturbation in the system conductivity. The system without any perturbation is assumed to have such a periodic property that it holds a periodic solution. In general, the perturbed system dose not enjoy this periodic property again, even though the pe...