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• W3011729723 abstract "The development of inexpensive and fast computers, coupled with the discovery of ecientalgorithms for dealing with polynomial equations, gave rise to some exciting new applicationsof algebraic geometry and commutative algebra.One of the main goals of this work is to show how some tools borrowed from these two eldscan be eciently employed to solve relevant control problem, as, for instance, nonlinearobserver design, fault detection and isolation, motion planning of mobile robots, optimalcontrol and game theory.In order to do this, a brief introduction to some algebraic objects and techniques is given inChapter 1, where concepts that nd useful applications in control theory are highlighted.To keep the exposition reasonably short, the classical results in algebraic geometry are givenwithout proofs, although complete references are given.Such tools and methodologies are then applied to a wide variety of topics concerning controltheory, as detailed in the following. In Chapter 2, a procedure that, coupled with classical control techniques, allows toeasily design nonlinear observers is proposed, with a particular attention on switchingand switched nonlinear systems and on disturbance identication. In Chapter 3, a model{based tool is given to design fault detectors. In Chapter 4, it is shown how algebraic geometry can be eciently employed to designnonlinear systems having an ane variety as attractive and invariant set, with a focuson how these techniques can be employed to plan the motion of mobile robots. In Chapter 5, a method to build a Boolean network able to represent the dynamics ofa continuous{time system is given. A procedure to compute a nite{horizon optimalpolicy for a Boolean network is given and a tool to apply the optimal control to thecontinuous{time system is reported.i In Chapter 6, a novel approach for robust model predictive control (MPC) for constrainedlinear discrete{time systems with bounded time{varying structural uncertaintiesis presented. In Chapter 7, a novel algorithm to compute the set of all the solutions to a polynomialsystem of equalities is given. Such an algorithm is then employed in three relevantcontrol applications: the static output feedback stabilization of a linear parametricallyvarying plant, the dead{beat regulation of mechanical juggling systems, and thesolution to Linear Quadratic dierential games. In Chapter 8, by exploiting some tools borrowed from algebraic geometry, interestinggame{theoretical results are given.An attempt has been made to keep the exposition as self{contained as possible, by reportingproofs of the new results that, sometimes, provide a deeper understanding of the topic andof its relationship with other results presented in the literature." @default.
• W3011729723 created "2020-03-23" @default.
• W3011729723 creator A5072322964 @default.
• W3011729723 date "2016-01-01" @default.
• W3011729723 modified "2023-09-24" @default.
• W3011729723 title "Using algebraic geometry for control probems: from observer design to game theory" @default.
• W3011729723 hasPublicationYear "2016" @default.
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