Mohammad Pirani

On the Smallest Eigenvalue of Grounded Laplacian Matrices

We provide bounds on the smallest eigenvalue of grounded Laplacian matrices (which are obtained by removing certain rows and columns of the Laplacian matrix of a given graph). The gap between our upper and lower bounds depends on the ratio of the smallest and largest components of the eigenvector corresponding to the smallest eigenvalue of the grounded Laplacian. We provide a graph-theoretic bound on this ratio, and subsequently obtain a tight characterization of the smallest eigenvalue for certain classes of graphs. Specifically, for weighted Erdos-Renyi random graphs, we show that when a (sufficiently small) set S of rows and columns is removed from the Laplacian, and the probability p of adding an edge is sufficiently large, the smallest eigenvalue of the grounded Laplacian asymptotically almost surely approaches μw|S|p, where μw is the mean edge weight. We also show that for weighted random d-regular graphs with a single row and column removed, the smallest eigenvalue is Θ(1/n), where n is the number of nodes in the network. Our bounds have applications to the study of the convergence rate in consensus dynamics with stubborn or leader nodes.

Spectral properties of the grounded Laplacian matrix with applications to consensus in the presence of stubborn agents

We study linear consensus and opinion dynamics in networks that contain stubborn agents. Previous work has shown that the convergence rate of such dynamics is given by the smallest eigenvalue of the grounded Laplacian induced by the stubborn agents. Building on this, we define a notion of centrality for each node in the network based upon the smallest eigenvalue obtained by removing that node from the network. We show that this centrality can deviate from other well known centralities. We then characterize certain properties of the smallest eigenvalue and corresponding eigenvector of the grounded Laplacian in terms of the graph structure and the expected absorption time of a random walk on the graph.

Coherence and convergence rate in networked dynamical systems

We study two metrics in stochastic consensus dynamics with leaders or stubborn agents: network coherence (defined in terms of the system ℋ2 and ℋ∞ norms), and convergence rate. We allow each agent to maintain an individual level of stubbornness in deviating from its initial values. We give bounds on the convergence rate and present sufficient conditions under which the bounds become tight. Moreover we study the effect of the level of stubbornness of the agents on network coherence and convergence rate. We then characterize these two metrics in random regular graphs and Erdos-Renyi random graphs. From a leader selection point of view, we show that maximizing ℋ∞ coherence is equivalent to maximizing convergence rate. Moreover we study conditions under which the optimal leader for maximizing ℋ2 coherence differs from the optimal leader for maximizing convergence rate, and conversely, provide sufficient conditions on the network for a single leader to maximize both metrics simultaneously.

Integrated estimation structure for the tire friction forces in ground vehicles

This paper presents a novel corner-based force estimation method to monitor tire capacities required for the traction and stability control systems. This is entailed for more advanced vehicle stability systems in harsh maneuvers. A novel estimation structure is proposed in this paper for the longitudinal, lateral, and vertical tire forces robust to the road friction condition. A nonlinear and a Kalman observer is utilized for estimation of the longitudinal and lateral friction forces. The stability and performance of the time-varying estimators are explored and it is shown that the developed integrated structure is robust to model uncertainties and does not require knowledge of the road friction. The proposed method is experimentally tested in several maneuvers on different road surface conditions and the results illustrate the accuracy and robustness of the state estimators.

A comprehensive study on the stability analysis of vehicle dynamics with pure/combined-slip tyre models

ABSTRACT In this paper, a vehicles lateral dynamic model is developed based on the pure and the combined-slip LuGre tyre models. Conventional vehicles lateral dynamic methods derive handling models utilising linear tyres and pure-slip assumptions. The current article proposes a general lateral dynamic model, which takes the linear and nonlinear behaviours of the tyre into account using the pure and combined-slip assumptions separately. The developed methodology also incorporates various normal loads at each corner and provides a proper tyre–vehicle platform for control and estimation applications. Steady-state and transient LuGre models are also used in the model development and their responses are compared in different driving scenarios. Considering the fact that the vehicle dynamics is time-varying, the stability of the suggested time-varying model is investigated using an affine quadratic stability approach, and a novel approach to define the critical longitudinal speed is suggested and compared with that of conventional lateral stability methods. Simulations have been conducted and the results are used to validate the proposed method.

Opinion Dynamics-Based Vehicle Velocity Estimation and Diagnosis

An opinion dynamics approach is proposed to enhance the reliability of the vehicle velocity estimators, which are required for autonomous driving as well as advanced vehicle active safety systems, such as traction and stability control. The corners’ estimates of a velocity observer, which is formed by combining the kinematic and model-based estimation schemes, are used as opinions with different levels of confidence in the developed algorithm. This is to find more reliable estimates robust to disturbances and time delay via solving a convex optimization problem. To bypass the effect of failure in velocity estimation, a fault rejection policy is used concurrently with the opinion dynamics. Road tests confirm the validity and robustness of the algorithm on slippery and dry roads independent of the powertrain configuration in different driving scenarios, especially for combined-slip and low-excitation maneuvers, which are demanding for the current vehicle state estimators.

Cooperative road condition estimation for an adaptive model predictive collision avoidance control strategy

This paper proposes a model predictive collision avoidance scheme for use in autonomous driving, based on cooperative on-line estimation of unknown and time varying road conditions. The autonomous vehicle is linearly modelled with constraints dependent on the road condition parameter. The proposed model predictive controller (MPC) is designed to be adaptive to this parameter. To accommodate this adaptive design, a particular method is developed for estimating the road friction coefficient cooperatively, by disseminating individual estimates in a vehicular network and using a consensus algorithm to converge these estimates to the maximum likelihood value. Presented simulation results demonstrate that the cooperative consensus scheme improves estimation significantly, and accordingly, the adaptive MPC incorporates road condition properly in collision avoidance planning.

Cooperative Least Square Parameter Identification by Consensus within the Network of Autonomous Vehicles

In this paper, a consensus framework for cooperative parameter estimation within the vehicular network is presented. It is assumed that each vehicle is equipped with a dedicated short range communication (DSRC) device and connected to other vehicles. The improvement achieved by the consensus for parameter estimation in presence of sensor’s noise is studied, and the effects of network nodes and edges on the consensus performance is discussed. Finally, the simulation results of the introduced cooperative estimation algorithm for estimation of the unknown parameter of road condition is presented. It is shown that due to the faster dynamic of network communication, single agents’ estimation converges to the least square approximation of the unknown parameter properly.

Resilient Corner-Based Vehicle Velocity Estimation

This paper presents longitudinal and lateral velocity estimators by considering the effect of the suspension compliance (SC) at each corner (tire) for ground vehicles. The estimators are developed to be resilient to sensor measurement inaccuracies, model and tire parameter uncertainties, switchings in observer gains, and measurement failures. More particularly, the stability of the observer is investigated, and its robustness to road condition uncertainties and sensor noises is analyzed. The sensitivity of the observers’ stability and performance to the model parameter changes is discussed. Moreover, the stability of the velocity observers for two cases of arbitrary and stochastic switching gains is investigated. The stochastic stability of the observer in the presence of faulty measurements is also studied, and it is shown that if the probability of a faulty measurement occurring is less than a certain threshold, the observer error dynamics will remain stochastically stable. The performance of the observer and the effect of the SC are validated via several road experiments.

Spectral and structural properties of random interdependent networks

Abstract Random interdependent networks consist of a group of subnetworks where each edge between two different subnetworks is formed independently with probability p . In this paper, we investigate certain spectral and structural properties of such networks, with corresponding implications for certain variants of consensus and diffusion dynamics on those networks. We start by providing a characterization of the isoperimetric constant in terms of the inter-network edge formation probability p . We then analyze the algebraic connectivity of such networks, and provide an asymptotically tight rate of growth of this quantity for a certain range of inter-network edge formation probabilities. Next, we give bounds on the smallest eigenvalue of the grounded Laplacian matrix (obtained by removing certain rows and columns of the Laplacian matrix) of random interdependent networks for the case where the removed rows and columns correspond to one of the subnetworks. Finally, we study a property known as r -robustness, which is a strong indicator of the ability of a network to tolerate structural perturbations and dynamical attacks. Our results yield new insights into the structure and robustness properties of random interdependent networks.