0000000000385854

AUTHOR

Davide Barilari

0000-0002-8676-7362

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

2015

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.

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
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