arXiv subjects

Peter Dower

Publications and source records attributed to Peter Dower.

3 recordsLinked to original sources

arXiv2025

GMM-Based Time-Varying Coverage Control

In coverage control problems that involve time-varying density functions, the coverage control law depends on spatial integrals of the time evolution of the density function. The latter is often neglected, replaced with an upper bound or calculated as a numerical approximation of the spatial integrals involved. In this paper, we consider a special case of time-varying density functions modeled as Gaussian Mixture Models (GMMs) that evolve with time via a set of time-varying sources (with known corresponding velocities). By imposing this structure, we obtain an efficient time-varying coverage controller that fully incorporates the time evolution of the density function. We show that the induced trajectories under our control law minimise the overall coverage cost. We elicit the structure of the proposed controller and compare it with a classical time-varying coverage controller, against which we benchmark the coverage performance in simulation. Furthermore, we highlight that the computationally efficient and distributed nature of the proposed control law makes it ideal for multi-vehicle robotic applications involving time-varying coverage control problems. We employ our method in plume monitoring using a swarm of drones. In an experimental field trial we show that drones guided by the proposed controller are able to track a simulated time-varying chemical plume in a distributed manner.

eess.SY↗

arXiv2024

Bidirectional Adversarial Autoencoders for the design of Plasmonic Metasurfaces

Deep Learning has been a critical part of designing inverse design methods that are computationally efficient and accurate. An example of this is the design of photonic metasurfaces by using their photoluminescent spectrum as the input data to predict their topology. One fundamental challenge of these systems is their ability to represent nonlinear relationships between sets of data that have different dimensionalities. Existing design methods often implement a conditional Generative Adversarial Network in order to solve this problem, but in many cases the solution is unable to generate structures that provide multiple peaks when validated. It is demonstrated that in response to the target spectrum, the Bidirectional Adversarial Autoencoder is able to generate structures that provide multiple peaks on several occasions. As a result the proposed model represents an important advance towards the generation of nonlinear photonic metasurfaces that can be used in advanced metasurface design.

physics.optics↗

arXiv2017

Perspectives on characteristics based curse-of-dimensionality-free numerical approaches for solving Hamilton-Jacobi equations

This paper extends the considerations of the works [1, 2] regarding curse-of-dimensionality-free numerical approaches to solve certain types of Hamilton-Jacobi equations arising in optimal control problems, differential games and elsewhere. A rigorous formulation and justification for the extended Hopf-Lax formula of [2] is provided together with novel theoretical and practical discussions including useful recommendations. By using the method of characteristics, the solutions of some problem classes under convexity/concavity conditions on Hamiltonians (in particular, the solutions of Hamilton-Jacobi-Bellman equations in optimal control problems) are evaluated separately at different initial positions. This allows for the avoidance of the curse of dimensionality, as well as for choosing arbitrary computational regions. The corresponding feedback control strategies are obtained at selected positions without approximating the partial derivatives of the solutions. The results of numerical simulations demonstrate the high potential of the proposed techniques. It is also pointed out that, despite the indicated advantages, the related approaches still have a limited range of applicability, and their extensions to Hamilton-Jacobi-Isaacs equations in zero-sum two-player differential games are currently developed only for sufficiently narrow classes of control systems. That is why further extensions are worth investigating.

math.OC↗