相关论文: Fekete points, formation control, and the balancin…

We geometrically describe optimal control problems in terms of Morse families in the Hamiltonian framework. These geometric structures allow us to recover the classical first order necessary conditions for optimality and the starting point…

We propose a mean-field optimal control problem for the parameter identification of a given pattern. The cost functional is based on the Wasserstein distance between the probability measures of the modeled and the desired patterns. The…

We outline a method for controlling the location of stable and unstable manifolds in the following sense. From a known location of the stable and unstable manifolds in a steady two-dimensional flow, the primary segments of the manifolds are…

Inspired by biological systems, we introduce a general framework for quasi-static shape control of human-scale structures under slowly varying external actions or requirements. In this setting, shape control aims to traverse the stable…

An experimental method has been developed to locate unstable equilibria of nonlinear structures quasi-statically. The technique involves loading a structure by application of either a force or a displacement at a main actuation point, while…

This paper examines stability properties of distance-based formation control when the underlying topology consists of a rigid graph and a flex node addition. It is shown that the desired equilibrium set is locally asymptotically stable but…

Ensemble control offers rich and diverse opportunities in mathematical systems theory. In this paper, we present a new paradigm of ensemble control, referred to as distributional control, for ensemble systems. We shift the focus from…

Conventional affine formation control (AFC) empowers a network of agents with flexible but collective motions - a potential which has not yet been exploited for large-scale swarms. One of the key bottlenecks lies in the design of an…

Angle-constrained formation control has attracted much attention from control community due to the advantage that inter-edge angles are invariant under uniform translations, rotations, and scalings of the whole formation. However, almost…

We propose a semi-discrete numerical scheme and establish well-posedness of a class of parabolic systems. Such systems naturally arise while studying the optimal control of grain boundary motions. The latter is typically described using a…

A crucial problem in shape deformation analysis is to determine a deformation of a given shape into another one, which is optimal for a certain cost. It has a number of applications in particular in medical imaging. In this article we…

Given a control system on a manifold that is embedded in Euclidean space, it is sometimes convenient to use a single global coordinate system in the ambient Euclidean space for controller design rather than to use multiple local charts on…

Given an ensemble of autonomous agents and a task to achieve cooperatively, how much do the agents need to know about the state of the ensemble and about the task in order to achieve it? We introduce new methods to understand these aspects…

Motivated by the ubiquity of control-affine systems in optimal control theory, we investigate the geometry of point-affine control systems with metric structures in dimensions two and three. We compute local isometric invariants for…

We consider the problem of controlling the group behavior of a large number of dynamic systems that are constantly interacting with each other. These systems are assumed to have identical dynamics (e.g., birds flock, robot swarm) and their…

This work investigates an elliptic optimal control problem defined on uncertain domains and discretized by a fictitious domain finite element method and cut elements. Key ingredients of the study are to manage cases considering the usually…

The construction of feedback-like control fields for a kinetic model in phase space is investigated. The purpose of these controls is to drive an initial density of particles in the phase space to reach a desired cyclic trajectory and…

This paper presents an angle-based approach for distributed formation shape stabilization of multi-agent systems in the plane. We develop an angle rigidity theory to study whether a planar framework can be determined by angles between…

The ability of a soft robot to perform specific tasks is determined by its contact configuration, and transitioning between configurations is often necessary to reach a desired position or manipulate an object. Based on this observation, we…

This manuscript considers the problem of ensuring stability and safety during formation control with distributed multi-agent systems in the presence of parametric uncertainty in the dynamics and limited communication. We propose an…