# Rotational controls and uniqueness of constrained viscosity solutions of Hamilton-Jacobi PDE

@inproceedings{Colombo2021RotationalCA, title={Rotational controls and uniqueness of constrained viscosity solutions of Hamilton-Jacobi PDE}, author={Giovanni Colombo and Nathalie T. Khalil and Franco Rampazzo}, year={2021} }

The classical inward pointing condition (IPC) for a control system whose state x is constrained in the closure C ∶= Ω̄ of an open set Ω prescribes that at each point of the boundary x ∈ ∂Ω the intersection between the dynamics and the interior of the tangent space of Ω̄ at x is nonempty. Under this hypothesis, for every system trajectory x(.) on a time-interval [0, T ], possibly violating the constraint, one can construct a new system trajectory x̂(.) that satisfies the constraint and whose…

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