05/03/2004, 15:00 — 16:00 — Sala P8, Pavilhão de Matemática, IST
Andrés García and Diogo Gomes, ISR/IST and CAM/IST
"The Concept of Controlled Eigenvectors for Affine Non-Linear Systems Applied to Vehicle Formations Control" and "Optimal Control and Viscosity Solutions"
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Andrés García - The concept of Controlled Eigenvectors for Affine Non-Linear Systems Applied to Vehicle Formations Control
Abstract: Affine non-linear control systems arise naturally in vehicle formation control as a result of the formulation of the requirements for the formation goals (keeping formation, initialization, reach the target location). One alternative approach to describe the desired requirements for a formation control framework is to express non-holonomic constraints in an Analytical Mechanics framework. These two related technics yield a novel methodology to control a vehicle formation similar to pole placement in linear control systems, which we call eigenvector placement, through the calculation of one additional constraint, allowing the analysis of stability issues as well. The methodology is directly exploited for non-linear affine control systems and it is presented together with some representative examples for single vehicles and multivehicle formations.
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Diogo Gomes - Optimal Control and Viscosity Solutions
Abstract: We present the theory of viscosity solutions of Hamilton-Jacobi equations as a tool to study optimal control problems even when Halmilton-Jacobi equations fail to have smooth solutions.
