NDLI: Observer-based dynamic local piecewise control of a linear parabolic PDE using non-collocated local piecewise observation

Content Provider	IET Digital Library
Author	Wang, Jun Wei Liu, Ya Qiang Sun, Chang Yin
Abstract	This paper employs the observer-based output feedback control technique to study the problem of local piecewise control for a linear parabolic partial differential equation(PDE) using non-collocated local piecewise observation. By the non-collocated local piecewise observation, a Luenberger-type PDE observer is first constructed to exponentially track the state of the PDE in the sense of both L 2 norm and H 1 norm. Based on the estimated state, a collocated local piecewise state feedback controller is then proposed for exponential stabilisation of the PDE. Sufficient conditions on exponential stabilisation of the PDE by the suggested feedback controller in the sense of both L 2 norm and H 1 norm are developed by utilising Lyapunov direct method, integration by parts, Wirtinger's inequality, and first mean value theorem for definite integrals, and presented in terms of standard linear matrix inequalities. The well-posedness is also analysed for both open-loop and resulting closed-loop PDE by using C 0 -semigroup approach. Finally, numerical simulation results are presented to show the effectiveness of the proposed design method.
Starting Page	346
Ending Page	358
Page Count	13
ISSN	17518644
Volume Number	12
e-ISSN	17518652
Issue Number	Issue 3, Feb (2018)
Alternate Webpage(s)	https://digital-library.theiet.org/content/journals/iet-cta/12/3
Alternate Webpage(s)	https://digital-library.theiet.org/content/journals/10.1049/iet-cta.2017.0797
Journal	IET Control Theory & Applications
Publisher Date	2017-11-15
Access Restriction	Open
Rights Holder	© The Institution of Engineering and Technology
Subject Keyword	Asymptotic Stability C0-semigroup Approach Closed Loop System Closed-loop Collocated Local Piecewise State Feedback Controller Control System Analysis Control System Synthesis Design Method Differential Equation (numerical Analysis) Dynamic Local Piecewise Control Exponential Stabilisation First Mean Value Theorem H1 Norm Integrals L2 Norm Linear Algebra Linear Matrix Inequalities Linear Parabolic PDE Luenberger-type Observer Lyapunov Direct Method Lyapunov Method Modelling And Identification Noncollocated Local Piecewise Observation Numerical Analysis Numerical Simulation Observers Open Loop System Open-loop Output Feedback Control Technique Partial Differential Equation Simulation Stability in Control Theory Standard Linear Matrix Inequalities State Feedback Synthesis Method Wirtinger Inequality
Content Type	Text
Resource Type	Article
Subject	Control and Optimization Control and Systems Engineering Human-Computer Interaction Electrical and Electronic Engineering Computer Science Applications

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