Regular synthesis for time-optimal control of single-input real analytic systems in the plane
SIAM Journal on Control and Optimization
Mathematical control theory: deterministic finite dimensional systems (2nd ed.)
Mathematical control theory: deterministic finite dimensional systems (2nd ed.)
Subanalyticity of the Sub-Riemannian Distance
Journal of Dynamical and Control Systems
Optimal Control with State Constraints and the Space Shuttle Re-entry Problem
Journal of Dynamical and Control Systems
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Let T 0 be fixed. We consider the optimal control problem for analytic affine systems: \dot{x} = f_{0}(x) + \sum\limits_{i=1}^{m} u_{i} f_{i} (x), with a cost of the form: C(u) = \int\limits_{0}^{T} \sum\limits_{i=1}^{m} u_{i}^{2} (t) dt. For this kind of systems we prove that if there are no minimizing abnormal extremals then the value function S is subanalytic. Second, we prove that if there exists an abnormal minimizer of corank 1, then the set of endpoints of minimizers at cost fixed is tangent to a given hyperplane. We illustrate this situation in sub-Riemannian geometry.