This paper considers a real-time algorithm for performance optimization of switched-mode hybrid dynamical systems. The controlled parameter consists of the switching times between the modes, and the cost criterion has the form of the integral of a performance function defined on the system's state trajectory. The dynamic response functions (state equations) associated with the modes are not known in advance; rather, at each time t, they are estimated for all future times s ≥ t. A first-order algorithm is proposed and its behavior is analyzed in terms of its convergence rate. Finally, an example of a mobile robot tracking a moving target while avoiding obstacles is presented.

This paper describes an adaptive-precision algorithm for solving a general optimal mode-scheduling problem in switched-mode dynamical systems. The problem is complicated by the fact that the controlled variable has discrete and continuous components, namely the sequence of modes and the switching times between them. Recently we developed a gradient-descent algorithm whose salient feature is that its descent at a given iteration is independent of the length (number of modes) of the schedule, hence it is suitable to situations where the schedule-lengths at successive iterations grow unboundedly. The computation of the descent direction requires grid-based approximations to solve differential equations as well as minimize certain functions on uncountable sets. However, the algorithm's convergence analysis assumes exact computations, and it breaks down when approximations are used, because the descent directions are discontinuous in the problem parameters. The purpose of the present paper is to overcome this theoretical gap and its computational implications by developing an implementable, adaptive-precision algorithm that controls the approximation levels by balancing precision with computational workloads. Its asymptotic convergence is proved, and simulation results are provided to support the theoretical developments.

Abstract-Heterogeneous multi-agent systems have previously been studied and deployed to solve a number of different tasks. Despite this, we still lack a basic understanding of just what "heterogeneity" really is. For example, what makes one team of agents more heterogeneous than another? In this paper, we address this issue by proposing a measure of heterogeneity. This measure takes both the complexity and disparity of a system into account by combining different notions of entropy. The result is a formulation that is both easily computable and makes intuitive sense. An overview is given of existing metrics for diversity found in various fields such as biology, economics, as well as robotics, followed by a discussion of their relative merits and demerits. We show how our proposed measure of heterogeneity overcomes problematic issues identified across the previous metrics. Finally, we discuss how to apply the new measure of heterogeneity specifically to multi-agent systems by using the notion of a common task-space to compare agents with different capabilities.

This paper addresses an aspect of controllability in a single-leader network when the agents are homogeneous. In such a network, indices are not assigned to the individual agents and controllability, which is typically a point to point property, now becomes a point to set property, where the set consists of all permutations of the target point. Agent homogeneity allows for choice of the optimal target point permutation that minimizes the distance to the system's reachable subspace, which we show is equivalent to finding a minimum sum-of-squares clustering with constraints on the cluster sizes. However, finding the optimal permutation is NP-hard. Methods are presented to find suboptimal permutations in the general case and the optimal permutation when the agent positions are 1-D.

FAA's NextGen program aims at increasing the capacity of the national airspace, while ensuring the safety of aircraft. This paper provides a distributed merging and spacing algorithm that maximizes the throughput at the terminal phase of flight using the information provided through the ADS-B framework. Using dual decomposition, aircraft negotiate with each other and reach an agreement on optimal merging times, with respect to an associated cost, that ensures proper inter-aircraft spacing. We provide a feasibility analysis that gives sufficient conditions to guarantee that proper spacing is achievable and derive maximum throughput controllers based on the air traffic characteristics of the merging flight paths.