English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

The classical inward pointing condition (IPC) for a control system whosestate $x$ is constrained in the closure $C:=\bar\Omega$ of an open set $\Omega$prescribes that at each point of the boundary $x\in \partial \Omega$ theintersection between the dynamics and the interior of the tangent space of$\bar \Omega$ at $x$ is nonempty. Under this hypothesis, for every systemtrajectory $x(.)$ on a time-interval $[0,T]$, possibly violating theconstraint, one can construct a new system trajectory $\hat x(.)$ thatsatisfies the constraint and whose distance from $x(.)$ is bounded by aquantity proportional to the maximal deviation$d:=\mathrm{dist}(\Omega,x([0,T]))$. When (IPC) is violated, the constructionof such a constrained trajectory is not possible in general. However, for acontrol system of the form $\dot{x}=f_1(x)u_1+f_2(x)u_2$, we prove in thispaper that a "higher order" inward pointing condition involving Lie brackets ofthe dynamics' vector fields allows for a novel construction of a constrainedtrajectory $\hat x(.)$ whose distance from the reference trajectory $x(.)$ isbounded by a quantity proportional to $\sqrt{d}$. Our method requires a furtherassumption of non-positiveness of a sort of curvature and is based on theimplementation of a suitable "rotating" control strategy. As an application, weestablish the continuity up to the boundary of the value function $V$ of aclassical optimal control problem, a continuity that allows to regard $V$ asthe unique constrained viscosity solution of the corresponding Bellmanequation.

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