9-11 July 2018
Ho Chi Minh City University of Science
Asia/Ho_Chi_Minh timezone

Robust controllers for parabolic systems using the Galerkin approximation

9 Jul 2018, 14:45
30m
Ho Chi Minh City University of Science

Ho Chi Minh City University of Science

227 Nguyễn Văn Cừ, Phường 4, T.P. Hồ Chí Minh

Speaker

Dr Duc Duy PHAN (Tampere University of Technology)

Description

This is a joint work with Lassi Paunonen and Petteri Laakkonen, Tampere University of Technology. We consider the robust output tracking problem on state space $H$ $$ \dot{x} (t) = A x(t) + B u(t),$$ $$ y(t) = C x(t) + D u(t),$$ where $x$ is the state, $u$ is the input (control), and $y$ is the output (observation). Our goal is to design a dynamic feedback controller of the form $$\dot{z}(t) = \mathcal{G}_1 z(t) + \mathcal{G}_2 e(t),$$ $$u(t) = K z(t),$$ where $e(t) = y(t)- y_{ref}(t)$ is the regulation error in such a way that the output $y(t)$ of the system converges asymptotically to a given reference signal $y_{ref}(t)$. We propose a new way of designing finite-dimensional robust controllers based on Galerkin approximations of infinite-dimensional controllers presented before in [Pau16]. For a class of sesquilinear form $A$ and assumptions of approximation schemes proposed in [BI88,BI97,Mor94], we prove that the finite dimensional controllers solve the Robust Output Regulation Problem. \\ [BI88] H. T. Banks and K. Ito. A unified framework for approximation in inverse problems for distributed parameter systems. Control Theory Adv. Tech., 1988. [BI97] H. T. Banks and K. Ito. Approximation in LQR Problems for Infinite Dimensional Systems With Unbounded Input Operators. J. Math. Systems Estim. Control, 1997. [Mor94] K. A. Morris. Design of finite-dimensional controllers for infinite-dimensional systems by approximation. J. Math. Systems Estim. Control, 4(2):30, 1994. [Pau16] L. Paunonen. Controller Design for Robust Output Regulation of Regular Linear Systems. IEEE Transactions on Automatic Control}, 61(10):2974--2986, Oct 2016.

Primary author

Dr Duc Duy PHAN (Tampere University of Technology)

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