The Role of Human-Automation Consensus in Multiple Unmanned Vehicle Scheduling

Objective: This study examined the impact of increasing automation replanning rates on operator performance and workload when supervising a decentralized network of heterogeneous unmanned vehicles. Background: Futuristic unmanned vehicles systems will invert the operator-to-vehicle ratio so that one operator can control multiple dissimilar vehicles connected through a decentralized network. Significant human-automation collaboration will be needed because of automation brittleness, but such collaboration could cause high workload. Method: Three increasing levels of replanning were tested on an existing multiple unmanned vehicle simulation environment that leverages decentralized algorithms for vehicle routing and task allocation in conjunction with human supervision. Results: Rapid replanning can cause high operator workload, ultimately resulting in poorer overall system performance. Poor performance was associated with a lack of operator consensus for when to accept the automation’s suggested prompts for new plan consideration as well as negative attitudes toward unmanned aerial vehicles in general. Participants with video game experience tended to collaborate more with the automation, which resulted in better performance. Conclusion: In decentralized unmanned vehicle networks, operators who ignore the automation’s requests for new plan consideration and impose rapid replans both increase their own workload and reduce the ability of the vehicle network to operate at its maximum capacity. Application: These findings have implications for personnel selection and training for futuristic systems involving human collaboration with decentralized algorithms embedded in networks of autonomous systems.Aurora Flight Sciences Corp.United States. Office of Naval Researc

Existence of positive solutions for a singular nonlinear fractional differential equation with integral boundary conditions involving fractional derivatives

In this article, by using the spectral analysis of the relevant linear operator and Gelfand’s formula, some properties of the first eigenvalue of a fractional differential equation are obtained. Based on these properties and through the fixed point index theory, the singular nonlinear fractional differential equations with Riemann–Stieltjes integral boundary conditions involving fractional derivatives are considered under some appropriate conditions, and the nonlinearity is allowed to be singular in regard to not only time variable but also space variable and it includes fractional derivatives. The existence of positive solutions for boundary conditions involving fractional derivatives is established. Finally, an example is given to demonstrate the validity of our main results

Hölder continuity of weak solutions of p-Laplacian PDEs with VMO coefficients

We consider solutions u∈W 1,p (Ω;R N ) of the p-Laplacian PDE ∇⋅(a(x)|Du| p−2 Du)=0,for x∈Ω⊆R n , where Ω is open and bounded. More generally, we consider solutions of the elliptic system ∇⋅a(x)g ′ (a(x)|Du|)[Formula presented]=0,x∈Ωas well as minimizers of the functional ∫ Ω g(a(x)|Du|)dx.In each case, the coefficient map a:Ω→R is only assumed to be of class VMO(Ω)∩L ∞ (Ω), which means that it may be discontinuous. Without assuming that x↦a(x) has any weak differentiability, we show that u∈C loc 0,α (Ω) for each 0<α<1. The preceding results are, in fact, a corollary of a much more general result, which applies to the functional ∫ Ω f(x,u,Du)dx in case f is only asymptotically convex. © 2019 Elsevier Lt

Partial regularity of solutions to p(x)-Laplacian PDEs with discontinuous coefficients

For Ω⊆Rn an open and bounded region we consider solutions u∈Wloc 1,p(x)(Ω;RN), with N>1, of the p(x)-Laplacian system ∇⋅(a(x)|Du|p(x)−2Du)=0, a.e. x∈Ω, where concerning the coefficient function x↦a(x) we assume only that a∈W1,q(Ω)∩L∞(Ω), where q>1 is essentially arbitrary. This implies that the coefficient in the PDE can be highly irregular, and yet in spite of this we still recover that u∈Cloc 0,α(Ω0), for each 0<α<1, where Ω0⊆Ω is a set of full measure. Due to the variational methodology that we employ, our results apply to the more general question of the regularity of the integral functional ∫Ωa(x)|Du|p(x)dx. © 2019 Elsevier Inc