Guangwei Zhu

A distributed continuous-time algorithm for network localization using angle-of-arrival information

This paper studies the angle-of-arrival (AOA) localization problem, namely, localizing networks based on the angle-of-arrival measurements between certain neighboring network nodes together with the absolute locations of some anchor nodes. We propose the concepts of stiffness matrix and fixability for the anchored formation graphs modeling the networks, and show that they provide a complete characterization of the AOA localizability as well as an explicit formula for the localization result. Moreover, a distributed continuous-time algorithm is proposed that converges globally to the correct localization result on fixable formation graphs. Performances of the proposed algorithm, e.g.,?convergence rate and robustness to communication delay, are characterized and optimized. Sensitivities of the localization results with respect to errors in AOA measurements and anchor node positions are also analyzed.

Optimizing formation rigidity under connectivity constraints

This paper studies the problem of finding the most rigid formation for a multi-agent system. The worst-case rigidity index (WRI) and the mean rigidity index (MRI) are proposed as the quantitative measures of formation rigidity. From a practical point of view, the values of these indices characterize the stability and robustness of the multi-agent system in maintaining a given formation. An iterative algorithm is presented for finding the most rigid formation through the joint optimization of both the positions of agents and their connection topology. The effectiveness of the algorithm is illustrated through numerical examples.

A study of the generalized input-to-state ℒ 2 -gain of discrete-time switched linear systems

A generalized notion of the input-to-state ℒ2-gains of discrete-time switched linear systems is proposed in this paper. Such gains are then characterized using the radii of convergence of a family of suitably defined functions called the generating functions. Properties of the generating functions are studied and their numerical computation algorithms are developed. Some numerical examples are presented.

Comparative evaluation of model predictive control strategies for a building HVAC system

The paper presents an evaluation procedure for a few promising Model Predictive Control (MPC) based approaches in supervisory control of building heating, ventilation and air-conditioning (HVAC) systems. A case study is established and control trajectories are generated using the proposed solvers. The resulting trajectories are evaluated in terms of benchmark metrics taking energy costs and occupant discomfort into account. A direct approach to incorporate occupant discomfort in the cost function is also proposed. Results indicate potential savings using MPC solvers when compared to the baseline.

Responsiveness and manipulability of formations of multi-robot networks

This paper unifies the previously defined instantaneous measures of responsiveness in multi-agent systems, namely those of stiffness and manipulability. These concepts are used for characterizing how a networked multi-agent system responds to perturbation of agents or to exogenous movements of its leader nodes. The resulting unified notion of a systems responsiveness provides us with a precise characterization of the effect of different choices of leader nodes and interaction topologies have on how easy or hard it is to control the network.

Link resource allocation for maximizing the rigidity of multi-agent formations

In this paper, the problem of optimizing the rigidity of multi-agent formations is formulated and solved using convex optimization methods. Two rigidity indices, the worst-case rigidity index (WRI) and the mean rigidity index (MRI), are proposed to measure the rigidity of formations of multiple agents connected by links with adjustable strengths. Under the assumption of limited total link resources, we develop efficient algorithms that can find the optimal allocation of link resources for maximizing the rigidity indices. Furthermore, through a sensitivity analysis of the optimization problems, the significance (priorities) of the different links are also characterized. Some simulations results are presented.

Distributed network localization using angle-of-arrival information Part I: Continuous-time protocol

In this paper, we propose a distributed continuous-time linear dynamics for solving the localization problem based on signal angle-of-arrival information. We first formulate the AOA localization problem within the framework of formation graph theory, which is an extension of the classical graph theory by incorporating the positional information of the vertices. Solving the AOA localization problem is equivalent to finding the solution to a system of linear equations. To avoid matrix inversion, we propose a continuous-time dynamics whose global asymptotic equilibrium is the desired localization. This dynamics turns out to have a very similar expression to that of the continuous-time consensus dynamics. The convergence and delay performance of the protocol is also studied. We finally argue that through optimizing the condition number of the stiffness matrix, the convergence and delay performance of the protocol can be simultaneously improved.

Distributed network localization using angle-of-arrival information Part II: Discrete-time algorithm and error analysis

In this paper, we propose a discrete-time distributed algorithm for network localization based on angle-of-arrival (AOA) measurements. This algorithm can be viewed as a special case of the averaging consensus algorithm in the two-dimensional space. We also analyze the localization error under inaccurate anchor positions and angles measurements and provide approximate formulae for the error terms. The effectiveness of our localization algorithm and error assessment tools is demonstrated through numerical examples. The main contribution of our paper lies in the theoretical framework for analyzing AOA-based localization processes as well as assessing localization error.

Efficient computation of generalized input-to-state ℒ 2 -gains of discrete-time switched linear systems

This paper proposes an efficient way to compute the ℒ₂-gains of discrete-time switched linear systems. Using the notion of generating functions, generalized versions of ℒ₂-gains under arbitrary switching are studied. An efficient numerical algorithm is formulated by which these generalized ℒ₂-gains can be estimated. The proposed method mitigates the problem of conservative bounds. Numerical examples are provided to illustrate the algorithm.