Weiwei Hu

EXPONENTIAL STABILITY OF A REPARABLE MULTI-STATE DEVICE

The exponential stability of a multi-state device is discussed in this paper. We present that the C0-semigroup generated by the system operator is quasi-compact and irreducible. It is known that 0 is a simple eigenvalue of the system operator. In combination with this, we obtain that the time-dependent solution exponentially converges to the steady-state solution, which is the positive eigenfuction corresponding to the simple eigenvalue 0.

Availability optimisation of repairable system with preventive maintenance policy

This article investigates the steady availability of the repairable system with preventive maintenance policy. By total probability formula, we describe the system as an abstract mathematical model and present the steady-state solution. Then we get the steady availability formula of the system. By analyzing the different monotonicity of the failure rate function, we discuss the well-posedness of the optimal time interval of executing the preventive maintenance. As a result, the steady availability of the system is optimized. Some numerical examples are given to show the effectiveness of the method presented in the article.

Modelling and analysis of repairable systems with preventive maintenance

The time-dependent solution of a kind of repairable system with preventive maintenance is investigated in the paper. With total probability formula, we show that the behavior of the system can be described as a group of ordinary differential equations coupled with partial differential equations, which can be formulated as a time delay equation in an appropriate Banach space. Based on the time-delay equation, this paper presents a difference scheme as an approximating method to solve the time-dependent solution which is necessary for analyzing the instantaneous availability of the repairable system. Some numerical examples are shown to illustrate the effectiveness of this approach.

Feedback stabilization of a thermal fluid system with mixed boundary control

We consider the problem of local exponential stabilization of the nonlinear Boussinesq equations with control acting on portion of the boundary. In particular, given a steady state solution on an bounded and connected domain ź ź R 2 , we show that a finite number of controls acting on a part of the boundary through Neumann/Robin boundary conditions is sufficient to stabilize the full nonlinear equations in a neighborhood of this steady state solution. Dirichlet boundary conditions are imposed on the rest of the boundary. We prove that a stabilizing feedback control law can be obtained by solving a Linear Quadratic Regulator (LQR) problem for the linearized Boussinesq equations. Numerical result are provided for a 2D problem to illustrate the ideas.

Approximation methods for boundary control of the Boussinesq equations

In this paper we discuss an approximation method for dealing with Dirichlet boundary control of thermal-fluid systems. The physics of displacement ventilation and buoyancy-driven flows are described by the Boussinesq equations. We first develop a computational algorithm for solving the corresponding LQR control problem for the Boussinesq equations with general Robin boundary conditions. This scheme is combined with a finite element method that generalizes Nitsches perturbation theory for approximating Dirichlet boundary conditions. Using this approach we are able to avoid imposing the “compatibility condition” that is required for Dirichlet boundary control in 3D problems. Numerical examples are presented to illustrate the computational algorithm.

Control of the Boussinesq equations with implications for sensor location in energy efficient buildings

In this paper we consider the problem of computing feedback functional gains for control problem governed by the Boussinesq equations. These gains and the corresponding feedback laws provide insight into determining good spatial location of sensors for optimal operation of energy efficient buildings. Theoretical and numerical results are presented to illustrate the ideas and to suggest areas for future research.

Optimal control design for a reparable multi-state system

In this paper, we consider the problem of optimal distributed control of a multi-state reparable system. A Linear Quadratic Regulator (LQR) design is proposed in order to accelerate the convergence of the system to its steady-state availability under a preassigned rate. The feedback law provides insights into designing the optimal system maintenance strategy. Finite difference is used to approximate the system and numerical experiments are presented to demonstrate the efficacy of the proposed method.

Sensor location in a controlled thermal fluid

We investigate different criteria for locating sensors for the state estimation in a controlled thermal fluid modeled by the Boussinesq equations. This paper focuses on the linearized Boussinesq equation. We combine optimal sensor location with observer design to obtain a sensor placement. One way to locate sensors is to minimize the covariance of the estimation error. Another way is based on the geometric structure of the feedback functional gain. The controllers are finite dimensional and act on a portion of the boundary through Neumann/Robin boundary conditions. Dirichlet boundary conditions are imposed on the rest of the boundary. A lower order observer is constructed by using the LQG balanced truncation for the linearized controlled system. Computer simulations are presented to compare the effectiveness of different sensor locations.

Numerical analysis of a reparable multi-state device

A numerical scheme is formulated for approximating the dynamic behavior of a reparable multi-state device, which can be described as a distributed parameter system of coupled partial and ordinary hybrid equations. The convergence issues are established by applying the Trotter-Kato Theorem, and simulation results show the effectiveness of the proposed scheme.