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In this paper, we investigate the structure of reachable sets from a given point q0 for a class of analytic control affine systems characterized, among other things, by possessing two singular trajectories initiating at q0. The aim of the paper is to establish the connection between the minimal number of analytic functions needed for describing reachable sets and the number of geometrically optimal singular trajectories. The paper is written in a language of the sub-Lorentzian geometry. Also, the sub-Lorentzian geometry methods are used to prove theorems.

journal of dynamical and control systems

The Structure of Reachable Sets and Geometric Optimality of Singular Trajectories for Certain Affine Control Systems in ℝ3. The Sub-Lorentzian Approach