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- W3208629196 abstract "The classical inward pointing condition (IPC) for a control system whose state $x$ is constrained in the closure $C:=barOmega$ of an open set $Omega$ prescribes that at each point of the boundary $xin partial Omega$ the intersection between the dynamics and the interior of the tangent space of $bar Omega$ 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 $hat x(.)$ that satisfies the constraint and whose distance from $x(.)$ is bounded by a quantity proportional to the maximal deviation $d:=mathrm{dist}(Omega,x([0,T]))$. When (IPC) is violated, the construction of such a constrained trajectory is not possible in general. However, for a control system of the form $dot{x}=f_1(x)u_1+f_2(x)u_2$, we prove in this paper that a higher order inward pointing condition involving Lie brackets of the dynamics' vector fields allows for a novel construction of a constrained trajectory $hat x(.)$ whose distance from the reference trajectory $x(.)$ is bounded by a quantity proportional to $sqrt{d}$. Our method requires a further assumption of non-positiveness of a sort of curvature and is based on the implementation of a suitable rotating control strategy. As an application, we establish the continuity up to the boundary of the value function $V$ of a classical optimal control problem, a continuity that allows to regard $V$ as the unique constrained viscosity solution of the corresponding Bellman equation." @default.
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- W3208629196 date "2021-10-16" @default.
- W3208629196 modified "2023-09-23" @default.
- W3208629196 title "Rotational controls and uniqueness of constrained viscosity solutions of Hamilton-Jacobi PDE" @default.
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