6533b7dcfe1ef96bd127174a

RESEARCH PRODUCT

Time-Optimal Synthesis for Three Relevant Problems: The Brockett Integrator, the Grushin Plane and the Martinet Distribution

Ugo BoscainDavide BarilariMario SigalottiEnrico Le Donne

subject

EngineeringControl and Optimizationbusiness.industryPlane (geometry)ta111Structure (category theory)Optimal controlControl and Systems Engineering; Modeling and Simulation; Control and OptimizationModeling and simulationControl theoryControl and Systems EngineeringIntegratorModeling and SimulationTrajectoryoptimal control problemsMathematics::Metric GeometryOrder (group theory)Applied mathematics[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]businessDistribution (differential geometry)ComputingMilieux_MISCELLANEOUS

description

We construct the time-optimal synthesis for 3 problems that are linear in the control and with polytopic constraints in the controls. Namely, the Brockett integrator, the Grushin plane, and the Martinet distribution. The main purpose is to illustrate the steps in solving an optimal control problem and in particular the use of second order conditions. The Grushin and the Martinet case are particularly important: the first is the prototype of a rank-varying distribution, the second of a non-equiregular structure.

yearjournalcountryeditionlanguage
2015-12-01
https://inria.hal.science/hal-01216012