Algebraic Geometry For Robotics And Control Theory

Laura Menini received the Laurea degree in 1993 and her PhD in 1997 from the University of Rome Tor Vergata, where she is currently Full Professor. She co-authored the books Symmetries and Semi-invariants in the Analysis of Nonlinear Systems (Springer, 2011) and Mathematical Methods for System Theory (World Scientific, 1998). She is Chair of the IFAC Coordinating Committee 2 - Design Method and Senior Editor of the IEEE Control Systems Letters. Corrado Possieri received his Bachelor's and Master's degrees in Medical Engineering and his PhD degree in Computer Science, Control and Geoinformation from the University of Rome Tor Vergata, Italy, in 2011, 2013, and 2016, respectively. In 2016, he visited the University of California, Santa Barbara (UCSB). In 2018, he joined the Dipartimento di Elettronica e Telecomunicazioni at the Politecnico di Torino, where he was an Assistant Professor. Subsequently, in 2019, he joined the Istituto di Analisi dei Sistemi ed Informatica "A Ruberti" of the Consiglio Nazionale delle Ricerche (IASI-CNR), where he is currently a Researcher. He is Associate Editor of the IEEE CSS Conference Editorial Board, the EUCA Conference Editorial Board, and the IFAC Conference Editorial Board. Antonio Tornambè is currently Full Professor of Control Theory at the University of Rome Tor Vergata. His research interests are in control theory for linear and nonlinear systems. He is the co-author of Discrete-Event System Theory: An Introduction (World Scientific, 1995), Mathematical Methods for System Theory (World Scientific, 1998) and Symmetries and Semi-invariants in the Analysis of Nonlinear Systems (Springer, 2011).

Preface; List of Figures; List of Tables; List of Symbols; Algebraic Geometry Notions; Implementations in Macaulay2; The Inverse Kinematics of Robot Arms; Observer Design; Immersions of Polynomial Systems into Linear Ones Up to an Output Injection; Solving Systems of Equations and Inequalities; Motion Planning for Mobile Robots; Computation of the Largest f-Invariant Set Contained in an Affine Variety; Boolean Networks; Multi-Objective Optimization; Distance to Internal Instability of LTI Systems Under Structured Perturbations; Decomposition in Sum of Squares; Bibliography; Index;