This paper puts forth an infrastructure-free cooperative relative localization (RL) for unmanned aerial vehicles (UAVs) in global positioning system (GPS)-denied environments. Instead of estimating relative coordinates with vision-based methods, an onboard ultra-wideband (UWB) ranging and communication (RCM) network is adopted to both sense the inter-UAV distance and exchange information for RL estimation in 2-D spaces. Without any external infrastructures prepositioned, each agent cooperatively performs a consensus-based fusion, which fuses the obtained direct and indirect RL estimates, to generate the relative positions to its neighbors in real time despite the fact that some UAVs may not have direct range measurements to their neighbors. The proposed RL estimation is then applied to formation control. Extensive simulations and real-world flight tests corroborate the merits of the developed RL algorithm.

This article investigates the distributed online optimization problem over a multi-agent network subject to local set constraints and coupled inequality constraints, which has a lot of applications in many areas, such as wireless sensor networks, power systems, and plug-in electric vehicles. In this problem, the cost function at each time step is the sum of local cost functions with each of them being gradually revealed to its corresponding agent, and meanwhile only local functions in coupled inequality constraints are accessible to each agent. To address this problem, a modified primal-dual algorithm, called distributed online primal-dual push-sum algorithm, is developed in this article, which does not rest on any assumption on parameter boundedness and is applicable to unbalanced networks. It is shown that the proposed algorithm is sublinear for both the dynamic regret and the violation of coupled inequality constraints. Finally, the theoretical results are supported by a simulation example.

Distributed bandit online convex optimization with time-varying coupled inequality constraints is considered, motivated by a repeated game between a group of learners and an adversary. The learners attempt to minimize a sequence of global loss functions and at the same time satisfy a sequence of coupled constraint functions, where the constraints are coupled across the distributed learners at each round. The global loss and the coupled constraint functions are the sum of local convex loss and constraint functions, respectively, which are adaptively generated by the adversary. The local loss and constraint functions are revealed in a bandit manner, i.e., only the values of loss and constraint functions are revealed to the learners at the sampling instance, and the revealed function values are held privately by each learner. Both one- and two-point bandit feedback are studied with the two corresponding distributed bandit online algorithms used by the learners. We show that sublinear expected regret and constraint violation are achieved by these two algorithms, if the accumulated variation of the comparator sequence also grows sublinearly. In particular, we show that $\mathcal {O}(T^{\theta })$ expected static regret and $\mathcal {O}(T^{7/4-\theta })$ constraint violation are achieved in the one-point bandit feedback setting, and $\mathcal {O}(T^{\max \lbrace \kappa,1-\kappa \rbrace })$ expected static regret and $\mathcal {O}(T^{1-\kappa /2})$ constraint violation in the two-point bandit feedback setting, where $\theta \in (3/4,5/6]$ and $\kappa \in (0,1)$ are user-defined tradeoff parameters. Finally, the tightness of the theoretical results is illustrated by numerical simulations of a simple power grid example, which also compares the proposed algorithms to algorithms existing in the literature.

This article proposes a new framework for distributed optimization, called distributed aggregative optimization, which allows local objective functions to be dependent not only on their own decision variables, but also on the sum of functions of decision variables of all the agents. To handle this problem, a distributed algorithm, called distributed aggregative gradient tracking, is proposed and analyzed, where the global objective function is strongly convex, and the communication graph is balanced and strongly connected. It is shown that the algorithm can converge to the optimal variable at a linear rate. A numerical example is provided to corroborate the theoretical result.

This article investigates distributed online convex optimization in the presence of an aggregative variable without any global/central coordinators over a multiagent network. In this problem, each individual agent is only able to access partial information of time-varying global loss functions, thus requiring local information exchanges between neighboring agents. Motivated by many applications in reality, the considered local loss functions depend not only on their own decision variables, but also on an aggregative variable, such as the average of all decision variables. To handle this problem, an online distributed gradient tracking algorithm (O-DGT) is proposed with exact gradient information and it is shown that the dynamic regret is upper bounded by three terms: 1) a sublinear term; 2) a path variation term; and 3) a gradient variation term. Meanwhile, the O-DGT algorithm is also analyzed with stochastic/noisy gradients, showing that the expected dynamic regret has the same upper bound as the exact gradient case. To our best knowledge, this article is the first to study online convex optimization in the presence of an aggregative variable, which enjoys new characteristics in comparison with the conventional scenario without the aggregative variable. Finally, a numerical experiment is provided to corroborate the obtained theoretical results.