Output Feedback Control of Inhomogeneous Parabolic PDEs with Point Actuation and Point Measurement using SOS and Semi-Separable Kernels
Illinois Institute of Technology（伊利诺伊理工学院）；Grenoble Image Parole Signal Automatique Lab., Université Joseph Fourier/Centre National de la Recherche Scientifique（格勒诺布尔图像语音信号自动实验室，约瑟夫·傅立叶大学/法国国家科学研究中心）；School of Engineering of Matter, Transport and Energy at Arizona State University（亚利桑那州立大学物质、运输与能源工程学院）
In this paper we use SOS and SDP to design output feedback controllers for a class of one-dimensional parabolic partial differential equations with point measurements and point actuation. Our approach is based on the use of SOS to search for positive quadratic Lyapunov functions, controllers and observers. These Lyapunov functions, controllers and observers are parameterized by linear operators which are defined by SOS polynomials. The main result of the paper is the development of an improved class of observer-based controllers and evidence which indicates that when the system is controllable and observable, these methods will find a observer-based controller for sufficiently high polynomial degree (similar to well-known results from backstepping).
A Convex Approach to Output Feedback Control of Parabolic PDEs Using Sum-of-Squares
Illinois Institute of Technology（伊利诺伊理工学院）；Grenoble Image Parole Signal Automatique Lab., Université Joseph Fourier/Centre National de la Recherche Scientifique（格勒诺布尔图像语音信号自动化实验室，约瑟夫·傅立叶大学/法国国家科学研究中心）；School of Engineering of Matter, Transport and Energy at Arizona State University（亚利桑那州立大学物质、运输与能源工程学院）
A Convex Optimization Approach for Backstepping PDE Design: Volterra and Fredholm Operators
University of Warwick（华威大学）；Imperial College London（帝国理工学院）；Università di Roma “Tor Vergata”（罗马托维加塔大学）；KIOS Research and Innovation Centre of Excellence, University of Cyprus（塞浦路斯大学KIOS卓越研究与创新中心）；University of Trieste（的里雅斯特大学）
