Non-Linear Model Predictive Control with Adaptive Time-Mesh Refinement

In this paper, we present a novel solution for real-time, Non-Linear Model Predictive Control (NMPC) exploiting a time-mesh refinement strategy. The proposed controller formulates the Optimal Control Problem (OCP) in terms of flat outputs over an adaptive lattice. In common approximated OCP solutions, the number of discretization points composing the lattice represents a critical upper bound for real-time applications. The proposed NMPC-based technique refines the initially uniform time horizon by adding time steps with a sampling criterion that aims to reduce the discretization error. This enables a higher accuracy in the initial part of the receding horizon, which is more relevant to NMPC, while keeping bounded the number of discretization points. By combining this feature with an efficient Least Square formulation, our solver is also extremely time-efficient, generating trajectories of multiple seconds within only a few milliseconds. The performance of the proposed approach has been validated in a high fidelity simulation environment, by using an UAV platform. We also released our implementation as open source C++ code.Comment: In: 2018 IEEE International Conference on Simulation, Modeling, and Programming for Autonomous Robots (SIMPAR 2018

Minimum-time trajectory generation for quadrotors in constrained environments

In this paper, we present a novel strategy to compute minimum-time trajectories for quadrotors in constrained environments. In particular, we consider the motion in a given flying region with obstacles and take into account the physical limitations of the vehicle. Instead of approaching the optimization problem in its standard time-parameterized formulation, the proposed strategy is based on an appealing re-formulation. Transverse coordinates, expressing the distance from a frame path, are used to parameterise the vehicle position and a spatial parameter is used as independent variable. This re-formulation allows us to (i) obtain a fixed horizon problem and (ii) easily formulate (fairly complex) position constraints. The effectiveness of the proposed strategy is proven by numerical computations on two different illustrative scenarios. Moreover, the optimal trajectory generated in the second scenario is experimentally executed with a real nano-quadrotor in order to show its feasibility.Comment: arXiv admin note: text overlap with arXiv:1702.0427

Mean Field Limits for Interacting Diffusions in a Two-Scale Potential

In this paper we study the combined mean field and homogenization limits for a system of weakly interacting diffusions moving in a two-scale, locally periodic confining potential, of the form considered in~\cite{DuncanPavliotis2016}. We show that, although the mean field and homogenization limits commute for finite times, they do not, in general, commute in the long time limit. In particular, the bifurcation diagrams for the stationary states can be different depending on the order with which we take the two limits. Furthermore, we construct the bifurcation diagram for the stationary McKean-Vlasov equation in a two-scale potential, before passing to the homogenization limit, and we analyze the effect of the multiple local minima in the confining potential on the number and the stability of stationary solutions

Kinetic Intersections as a Source of Information on Rate Coefficients

C

Homogenization of a locally periodic oscillating boundary

This paper deals with the homogenization of a mixed boundary value problem for the Laplace operator in a domain with locally periodic oscillating boundary. The Neumann condition is prescribed on the oscillating part of the boundary, and the Dirichlet condition on a separate part. It is shown that the homogenization result holds in the sense of weak $L^2$ convergence of the solutions and their flows, under natural hypothesis on the regularity of the domain. The strong $L^2$ convergence of average preserving extensions of the solutions and their flows is also considered.Comment: 30 pages, 5 figures, 1 tabl