Search

Image generation and editing have seen a great deal of advancements with the rise of large-scale diffusion models that allow user control of different modalities such as text, mask, depth maps, etc. However, controlled editing of videos still lags behind. Prior work in this area has focused on using 2D diffusion models to globally change the style of an existing video. On the other hand, in many practical applications, editing localized parts of the video is critical. In this work, we propose a method to edit videos using a pre-trained inpainting image diffusion model. We systematically redesign the forward path of the model by replacing the self-attention modules with an extended version of attention modules that creates frame-level dependencies. In this way, we ensure that the edited information will be consistent across all the video frames no matter what the shape and position of the masked area is. We qualitatively compare our results with state-of-the-art in terms of accuracy on several video editing tasks like object retargeting, object replacement, and object removal tasks. Simulations demonstrate the superior performance of the proposed strategy.

Non-intrusive Load Monitoring (NILM) is an established technique for effective and cost-efficient electricity consumption management. The method is used to estimate appliance-level power consumption from aggregated power measurements. This paper presents a hybrid learning approach, consisting of a convolutional neural network (CNN) and a bidirectional long short-term memory (BILSTM), featuring an integrated attention mechanism, all within the context of disaggregating low-frequency power data. While prior research has been mainly focused on high-frequency data disaggregation, our study takes a distinct direction by concentrating on low-frequency data. The proposed hybrid CNN-BILSTM model is adept at extracting both temporal (time-related) and spatial (location-related) features, allowing it to precisely identify energy consumption patterns at the appliance level. This accuracy is further enhanced by the attention mechanism, which aids the model in pinpointing crucial parts of the data for more precise event detection and load disaggregation. We conduct simulations using the existing low-frequency REDD dataset to assess our model performance. The results demonstrate that our proposed approach outperforms existing methods in terms of accuracy and computation time.

In this paper, an efficient deployment strategy is proposed for a network of mobile and static sensors with nonidentical sensing and communication radii. The multiplicatively weighted Voronoi (MW-Voronoi) diagram is used to partition the field and assign the underlying coverage task to each mobile sensor. A gradient-based method is applied to find the best candidate point based on the detected coverage holes and the coverage priority considering the relative distance of the mobile sensor from the static ones and the obstacles in the field. The sensors move to a new position if such a relocation increases their local coverage. The efficiency of the proposed strategy in different scenarios is demonstrated by simulations., Comment: 8 pages, 8 figures, submitted to the 62nd IEEE Conference on Decision and Control

The problem of connectivity assessment in an asymmetric network represented by a weighted directed graph is investigated in this article. A power iteration algorithm in a centralized implementation is developed first to compute the generalized algebraic connectivity of asymmetric networks. After properly transforming the Laplacian matrix of the network, two sequences of one-dimensional and two-dimensional subspaces are generated iteratively, one of which converges to the desired subspace spanned by the eigenvector(s) associated with the eigenvalue(s) representing the network's generalized algebraic connectivity. A distributed implementation of the proposed power iteration algorithm is then developed to compute the generalized algebraic connectivity from the viewpoint of each node, which is scalable to any asymmetric network of any size with a fixed message length per node. The convergence analysis of these algorithms is subsequently provided under some weak assumptions. The efficiency of the developed algorithms in computing the network connectivity is then demonstrated by simulations., Comment: 19 pages, 7 figures

The risk-neutral LQR controller is optimal for stochastic linear dynamical systems. However, the classical optimal controller performs inefficiently in the presence of low-probability yet statistically significant (risky) events. The present research focuses on infinite-horizon risk-constrained linear quadratic regulators in a mean-field setting. We address the risk constraint by bounding the cumulative one-stage variance of the state penalty of all players. It is shown that the optimal controller is affine in the state of each player with an additive term that controls the risk constraint. In addition, we propose a solution independent of the number of players. Finally, simulations are presented to verify the theoretical findings., Comment: Accepted at 62nd IEEE Conference on Decision and Control

In this paper, we propose a framework for early-stage malware detection and mitigation by leveraging natural language processing (NLP) techniques and machine learning algorithms. Our primary contribution is presenting an approach for predicting the upcoming actions of malware by treating application programming interface (API) call sequences as natural language inputs and employing text classification methods, specifically a Bi-LSTM neural network, to predict the next API call. This enables proactive threat identification and mitigation, demonstrating the effectiveness of applying NLP principles to API call sequences. The Bi-LSTM model is evaluated using two datasets. %The model achieved an accuracy of 93.6\% and 88.8\% for the %first and second dataset respectively. Additionally, by modeling consecutive API calls as 2-gram and 3-gram strings, we extract new features to be further processed using a Bagging-XGBoost algorithm, effectively predicting malware presence at its early stages. The accuracy of the proposed framework is evaluated by simulations.

A key question in the problem of 3D reconstruction is how to train a machine or a robot to model 3D objects. Many tasks like navigation in real-time systems such as autonomous vehicles directly depend on this problem. These systems usually have limited computational power. Despite considerable progress in 3D reconstruction systems in recent years, applying them to real-time systems such as navigation systems in autonomous vehicles is still challenging due to the high complexity and computational demand of the existing methods. This study addresses current problems in reconstructing objects displayed in a single-view image in a faster (real-time) fashion. To this end, a simple yet powerful deep neural framework is developed. The proposed framework consists of two components: the feature extractor module and the 3D generator module. We use point cloud representation for the output of our reconstruction module. The ShapeNet dataset is utilized to compare the method with the existing results in terms of computation time and accuracy. Simulations demonstrate the superior performance of the proposed method. Index Terms-Real-time 3D reconstruction, single-view reconstruction, supervised learning, deep neural network, Comment: 1- The paper has 8 pages 2- The paper has already been accepted in IEEE International Conference on Machine Learning and Applications (ICMLA) 2022 and it will appear in IEEE ICMLA 2022 proceedings

A novel semi-analytical method is proposed to develop the pseudo-rigid-body~(PRB) model of robots made of highly flexible members (HFM), such as flexures and continuum robots, with no limit on the degrees of freedom of the PRB model. The proposed method has a simple formulation yet high precision. Furthermore, it can describe HFMs with variable curvature and stiffness along their length. The method offers a semi-analytical solution for the highly coupled nonlinear constrained optimization problem of PRB modeling and can be extended to variable-length robots comprised of HFM, such as catheter and concentric tube robots. We also show that this method can obtain a PRB model of uniformly stiff HFMs, with only three parameters. The versatility of the method is investigated in various applications of HFM in continuum robots. Simulations demonstrate substantial improvement in the precision of the PRB model in general and a reduction in the complexity of the formulation., Comment: 10 pages and 8 figures

In this paper, a new numerical method to solve the forward kinematics (FK) of a parallel manipulator with three-limb spherical-prismatic-revolute (3SPR) structure is presented. Unlike the existing numerical approaches that rely on computation of the manipulator's Jacobian matrix and its inverse at each iteration, the proposed algorithm requires much less computations to estimate the FK parameters. A cost function is introduced that measures the difference of the estimates from the actual FK values. At each iteration, the problem is decomposed into two steps. First, the estimates of the platform orientation from the heave estimates are obtained. Then, heave estimates are updated by moving in the gradient direction of the proposed cost function. To validate the performance of the proposed algorithm, it is compared against a Jacobian-based (JB) approach for a 3SPR parallel manipulator.

In this article, we introduce decentralized Kalman filters for linear quadratic deep structured teams. The agents in deep structured teams are coupled in dynamics, costs and measurements through a set of linear regressions of the states and actions (also called deep states and deep actions). The information structure is decentralized, where every agent observes a noisy measurement of its local state and the global deep state. Since the number of agents is often very large in deep structured teams, any naive approach to finding an optimal Kalman filter suffers from the curse of dimensionality. Moreover, due to the decentralized nature of information structure, the resultant optimization problem is non-convex, in general, where non-linear strategies can outperform linear ones. However, we prove that the optimal strategy is linear in the local state estimate as well as the deep state estimate and can be efficiently computed by two scale-free Riccati equations and Kalman filters. We propose a bi-level orthogonal approach across both space and time levels based on a gauge transformation technique to achieve the above result. We also establish a separation principle between optimal control and optimal estimation. Furthermore, we show that as the number of agents goes to infinity, the Kalman gain associated with the deep state estimate converges to zero at a rate inversely proportional to the number of agents. This leads to a fully decentralized approximate strategy where every agent predicts the deep state by its conditional and unconditional expected value, also known as the certainty equivalence approximation and (weighted) mean-field approximation, respectively.

In this paper, a deep structured tracking problem is introduced for a large number of decision-makers. The problem is formulated as a linear quadratic deep structured team, where the decision-makers wish to track a global target cooperatively while considering their local targets. For the unconstrained setup, the gauge transformation technique is used to decompose the resultant optimization problem in order to obtain a low-dimensional optimal control strategy in terms of the local and global Riccati equations. For the constrained case, however, the feasible set is not necessarily decomposable by the gauge transformation. To overcome this hurdle, we propose a family of local and global receding horizon control problems, where a carefully constructed linear combination of their solutions provides a feasible solution for the original constrained problem. The salient property of the above solutions is that they are tractable with respect to the number of decision-makers and can be implemented in a distributed manner. In addition, the main results are generalized to cases with multiple sub-populations and multiple features, including leader-follower setup, cohesive cost function and soft structural constraint. Furthermore, a class of cyber-physical attacks is proposed in terms of perturbed influence factors. A numerical example is presented to demonstrate the efficacy of the results.

This paper investigates a soft-constrained MinMax control problem of a leader-follower network. The network consists of one leader and an arbitrary number of followers that wish to reach consensus with minimum energy consumption in the presence of external disturbances. The leader and followers are coupled in the dynamics and cost function. Two non-classical information structures are considered: mean-field sharing and intermittent mean-field sharing, where the mean-field refers to the aggregate state of the followers. In mean-field sharing, every follower observes its local state, the state of the leader and the mean field while in the intermittent mean-field sharing, the mean-field is only observed at some (possibly no) time instants. A social welfare cost function is defined, and it is shown that a unique saddle-point strategy exists which minimizes the worst-case value of the cost function under mean-field sharing information structure. The solution is obtained by two scalable Riccati equations, which depend on a prescribed attenuation parameter, serving as a robustness factor. For the intermittent mean-field sharing information structure, an approximate saddle-point strategy is proposed, and its converges to the saddle-point is analyzed. Two numerical examples are provided to demonstrate the efficacy of the obtained results., Comment: Proceedings of IEEE IEEE Control Systems Letters, 2020

Motivated by demand-side management in smart grids, a decentralized controlled Markov chain formulation is proposed to model a homogeneous population of users with binary demands (i.e., off or on). The binary demands often arise in scheduling applications such as plug-in hybrid vehicles. Normally, an independent service operator (ISO) has a finite number of options when it comes to providing the users with electricity. The options represent various incentive means, generation resources, and price profiles. The objective of the ISO is to find optimal options in order to keep the distribution of demands close to a desired level (which varies with time, in general) by imposing the minimum price on the users. A Bellman equation is developed here to identify the globally team-optimal strategy. The proposed strategy is fair for all users and also protects the privacy of users. Moreover, its computational complexity increases linearly (rather than exponentially) with the number of users. A numerical example with 100 users is presented for peak-load management., Comment: Proceedings of American Control Conference, 2018

This paper studies a large number of homogeneous Markov decision processes where the transition probabilities and costs are coupled in the empirical distribution of states (also called mean-field). The state of each process is not known to others, which means that the information structure is fully decentralized. The objective is to minimize the average cost, defined as the empirical mean of individual costs, for which a sub-optimal solution is proposed. This solution does not depend on the number of processes, yet it converges to the optimal solution of the so-called mean-field sharing as the number of processes tends to infinity. Under some mild conditions, it is shown that the convergence rate of the proposed decentralized solution is proportional to the square root of the inverse of the number of processes. Finding this sub-optimal solution involves a non-smooth non-convex optimization problem over an uncountable set, in general. To overcome this drawback, a combinatorial optimization problem is introduced that achieves the same rate of convergence., Comment: Proceedings of IEEE Conference on Decision and Control, 2017

In this paper, we study a fault-tolerant control for systems consisting of multiple homogeneous components such as parallel processing machines. This type of system is often more robust to uncertainty compared to those with a single component. The state of each component is either in the operating mode or faulty. At any time instant, each component may independently become faulty according to a Bernoulli probability distribution. If a component is faulty, it remains so until it is fixed. The objective is to design a fault-tolerant system by sequentially choosing one of the following three options: (a) do nothing at zero cost; b) detect the number of faulty components at the cost of inspection, and c) fix the system at the cost of repairing faulty components. A Bellman equation is developed to identify a near-optimal solution for the problem. The efficacy of the proposed solution is verified by numerical simulations., Comment: Proceedings of IEEE International Midwest Symposium on Circuits and Systems, 2018

In this paper, a decentralized stochastic control system consisting of one leader and many homogeneous followers is studied. The leader and followers are coupled in both dynamics and cost, where the dynamics are linear and the cost function is quadratic in the states and actions of the leader and followers. The objective of the leader and followers is to reach consensus while minimizing their communication and energy costs. The leader knows its local state and each follower knows its local state and the state of the leader. The number of required links to implement this decentralized information structure is equal to the number of followers, which is the minimum number of links for a communication graph to be connected. In the special case of leaderless, no link is required among followers, i.e., the communication graph is not even connected. We propose a near-optimal control strategy that converges to the optimal solution as the number of followers increases. One of the salient features of the proposed solution is that it provides a design scheme, where the convergence rate \edit{as well as} the collective behavior of the followers can be designed by choosing appropriate cost functions. In addition, the computational complexity of the proposed solution does not depend on the number of followers. Furthermore, the proposed strategy can be computed in a distributed manner, where the leader solves one Riccati equation and each follower solves two Riccati equations to calculate their strategies. Two numerical examples are provided to demonstrate the effectiveness of the results in the control of multi-agent systems., Comment: Proceedings of IEEE Conference on Decision and Control, 2018

In this paper, a stochastic dynamic control strategy is presented to prevent the spread of an infection over a homogeneous network. The infectious process is persistent, i.e., it continues to contaminate the network once it is established. It is assumed that there is a finite set of network management options available such as degrees of nodes and promotional plans to minimize the number of infected nodes while taking the implementation cost into account. The network is modeled by an exchangeable controlled Markov chain, whose transition probability matrices depend on three parameters: the selected network management option, the state of the infectious process, and the empirical distribution of infected nodes (with not necessarily a linear dependence). Borrowing some techniques from mean-field team theory the optimal strategy is obtained for any finite number of nodes using dynamic programming decomposition and the convolution of some binomial probability mass functions. For infinite-population networks, the optimal solution is described by a Bellman equation. It is shown that the infinite-population strategy is a meaningful sub-optimal solution for finite-population networks if a certain condition holds. The theoretical results are verified by an example of rumor control in social networks., Comment: Proceedings of American Control Conference, 2019

The focus of this paper is directed towards optimal control of multi-agent systems consisting of one leader and a number of followers in the presence of noise. The dynamics of every agent is assumed to be linear, and the performance index is a quadratic function of the states and actions of the leader and followers. The leader and followers are coupled in both dynamics and cost. The state of the leader and the average of the states of all followers (called mean-field) are common information and known to all agents; however, the local state of the followers are private information and unknown to other agents. It is shown that the optimal distributed control strategy is linear time-varying, and its computational complexity is independent of the number of followers. This strategy can be computed in a distributed manner, where the leader needs to solve one Riccati equation to determine its optimal strategy while each follower needs to solve two Riccati equations to obtain its optimal strategy. This result is subsequently extended to the case of the infinite horizon discounted and undiscounted cost functions, where the optimal distributed strategy is shown to be stationary. A numerical example with $100$ followers is provided to demonstrate the efficacy of the results., Comment: Proceedings of Canadian Conference on Electrical and Computer Engineering, 2018

We study model-based and model-free policy optimization in a class of nonzero-sum stochastic dynamic games called linear quadratic (LQ) deep structured games. In such games, players interact with each other through a set of weighted averages (linear regressions) of the states and actions. In this paper, we focus our attention to homogeneous weights; however, for the special case of infinite population, the obtained results extend to asymptotically vanishing weights wherein the players learn the sequential weighted mean-field equilibrium. Despite the non-convexity of the optimization in policy space and the fact that policy optimization does not generally converge in game setting, we prove that the proposed model-based and model-free policy gradient descent and natural policy gradient descent algorithms globally converge to the sub-game perfect Nash equilibrium. To the best of our knowledge, this is the first result that provides a global convergence proof of policy optimization in a nonzero-sum LQ game. One of the salient features of the proposed algorithms is that their parameter space is independent of the number of players, and when the dimension of state space is significantly larger than that of the action space, they provide a more efficient way of computation compared to those algorithms that plan and learn in the action space. Finally, some simulations are provided to numerically verify the obtained theoretical results., Comment: Proceedings of Conference on Decision and Control, 2020

In this paper, we study the global convergence of model-based and model-free policy gradient descent and natural policy gradient descent algorithms for linear quadratic deep structured teams. In such systems, agents are partitioned into a few sub-populations wherein the agents in each sub-population are coupled in the dynamics and cost function through a set of linear regressions of the states and actions of all agents. Every agent observes its local state and the linear regressions of states, called deep states. For a sufficiently small risk factor and/or sufficiently large population, we prove that model-based policy gradient methods globally converge to the optimal solution. Given an arbitrary number of agents, we develop model-free policy gradient and natural policy gradient algorithms for the special case of risk-neutral cost function. The proposed algorithms are scalable with respect to the number of agents due to the fact that the dimension of their policy space is independent of the number of agents in each sub-population. Simulations are provided to verify the theoretical results., Comment: Proceedings of IEEE Conference on Decision and Control, 2020

In this paper, we consider Markov chain and linear quadratic models for deep structured teams with discounted and time-average cost functions under two non-classical information structures, namely, deep state sharing and no sharing. In deep structured teams, agents are coupled in dynamics and cost functions through deep state, where deep state refers to a set of orthogonal linear regressions of the states. In this article, we consider a homogeneous linear regression for Markov chain models (i.e., empirical distribution of states) and a few orthonormal linear regressions for linear quadratic models (i.e., weighted average of states). Some planning algorithms are developed for the case when the model is known, and some reinforcement learning algorithms are proposed for the case when the model is not known completely. The convergence of two model-free (reinforcement learning) algorithms, one for Markov chain models and one for linear quadratic models, is established. The results are then applied to a smart grid., Comment: This version corrects some typographical errors

A class of nonzero-sum stochastic dynamic games with imperfect information structure is investigated. The game involves an arbitrary number of players, modeled as homogeneous Markov decision processes, aiming to find a sequential Nash equilibrium. The players are coupled in both dynamics and cost functions through the empirical distribution of states and actions of players. Two non-classical information structures are considered: deep state sharing and no-sharing, where deep state refers to the empirical distribution of the states of players. In the former, each player observes its local state as well as the deep state while in the latter each player observes only its local state. For both finite- and infinite-horizon cost functions, a sequential equilibrium, called deep Nash equilibrium, is identified, where the dynamics of deep state resembles a convolutional neural network. In addition, an approximate sequential equilibrium, called sequential mean-field equilibrium, under no-sharing information structure is proposed, whose performance converges to that of the deep Nash equilibrium despite the fact that the strategy is not necessarily continuous with respect to the deep state. The proposed strategies are robust to trembling-hand imperfection in both microscopic and macroscopic levels. Finally, the extension to multiple sub-populations and arbitrarily-coupled (asymmetric) cost functions are demonstrated.

In this paper, we investigate a class of nonzero-sum dynamic stochastic games, where players have linear dynamics and quadratic cost functions. The players are coupled in both dynamics and cost through a linear regression (weighted average) as well as a quadratic regression (weighted covariance matrix) of the states and actions, where the linear regression of states is called deep state. We study collaborative and non-collaborative games under three information structures: perfect sharing, deep state sharing, and no sharing for three different types of weights: positive, homogeneous and asymptotically vanishing weights. For perfect and deep state sharing information structures, we propose a transformation-based technique to solve for the best-response equations of players and identify a few sufficient conditions under which a unique subgame perfect Nash equilibrium exists. The equilibrium is linear in the local state and deep state, and the corresponding gains are obtained by solving a novel non-standard Riccati equation (whose dimension is independent of the number of players, thus making the solution scalable). When the information structure is no-sharing and the number of players is asymptotically large, one approximate population-size-dependent equilibrium and one approximate population-size-independent equilibrium (also called sequential weighted mean-field equilibrium) are proposed, and their convergence to the infinite-population limits are established. In addition, the main results are extended to infinite-horizon cost function, and generalized to multiple orthogonal linear regressions and heterogeneous sub-populations. A numerical example is provided to demonstrate the difference between the two proposed approximate equilibria., Comment: Extended version with 22 pages. To appear in Automatica. Initial draft was submitted in 2018

Inspired by the concepts of deep learning in artificial intelligence and fairness in behavioural economics, we introduce deep teams in this paper. In such systems, agents are partitioned into a few sub-populations so that the dynamics and cost of agents in each sub-population is invariant to the indexing of agents. The goal of agents is to minimize a common cost function in such a manner that the agents in each sub-population are not discriminated or privileged by the way they are indexed. Two non-classical information structures are studied. In the first one, each agent observes its local state as well as the empirical distribution of the states of agents in each sub-population, called deep state, whereas in the second one, the deep states of a subset (possibly all) of sub-populations are not observed. Novel dynamic programs are developed to identify globally optimal and sub-optimal solutions for the first and second information structures, respectively. The computational complexity of finding the optimal solution in both space and time is polynomial (rather than exponential) with respect to the number of agents in each sub-population and is linear (rather than exponential) with respect to the control horizon. This complexity is further reduced in time by introducing a forward equation, that we call deep Chapman-Kolmogorov equation, described by multiple convolutional layers of Binomial probability distributions. Two different prices are defined for computation and communication, and it is shown that under mild assumptions they converge to zero as the quantization level and the number of agents tend to infinity. In addition, the main results are extended to the infinite-horizon discounted model and arbitrarily asymmetric cost function. Finally, a service-management example with 200 users is presented., Comment: To appear in IEEE Transaction on Automatic Control, 16 pages

Motivated by the recent developments in artificial intelligence, we introduce linear quadratic deep structured teams in this paper. Two notions of equivariant and partially equivariant systems are defined, and it is shown that such systems can be partitioned into a few sub-populations of decision makers, where every decision maker in each sub-population is coupled in both dynamics and cost function through a set of linear regressions of the states and actions of all decision makers. Two non-classical information structures are considered: deep-state sharing and partial deep-state sharing, where deep state refers to the linear regression of the states of the decision makers in each sub-population. For a risk-sensitive cost function with deep-state sharing structure, a closed-form low-complexity representation of the globally optimal strategy is obtained, whose computational complexity is independent of the number of decision makers in each sub-population. In addition, it is shown that the risk-sensitive solution converges to the risk-neutral one as the number of decision makers increases to infinity. Moreover, two sub-optimal sequential strategies under partial deep-state sharing information structure are proposed by introducing two Kalman-like filters, one based on the finite-population model and the other one based on the infinite-population model. It is proved that the prices of information associated with the above sub-optimal solutions converge to zero as the number of decision makers goes to infinity. Furthermore, a class of feed-forward deep neural networks with multiple layers of weighted sums and products is introduced wherein the optimal weights and biases are explicitly obtained. A supply-chain management example is presented to demonstrate the efficacy of the obtained results.

An important question that often arises in the operation of networked systems is whether to collect the real-time data or to estimate them based on the previously collected data. Various factors should be taken into account such as how informative the data are at each time instant for state estimation, how costly and credible the collected data are, and how rapidly the data vary with time. The above question can be formulated as a dynamic decision making problem with imperfect information structure, where a decision maker wishes to find an efficient way to switch between data collection and data estimation while the quality of the estimation depends on the previously collected data (i.e., duality effect). In this paper, the evolution of the state of each node is modeled as an exchangeable Markov process for discrete features and equivariant linear system for continuous features, where the data of interest are defined in the former case as the empirical distribution of the states, and in the latter case as the weighted average of the states. When the data are collected, they may or may not be credible, according to a Bernoulli distribution. Based on a novel planning space, a Bellman equation is proposed to identify a near-optimal strategy. A reinforcement learning algorithm is developed for the case when the model is not known exactly, and its convergence to the near-optimal solution is shown subsequently. In addition, a certainty threshold is introduced that determines when data estimation is more desirable than data collection, as the number of nodes increases. For the special case of linear dynamics, a separation principle is constructed wherein the optimal estimate is computed by a Kalman-like filter, irrespective of the probability distribution of random variables..., Comment: IEEE Transactions on Network Science and Engineering, 16 pages

In this paper, structural controllability of a leader-follower multi-agent system with multiple leaders is studied from a graph-theoretic point of view. The problem of preservation of structural controllability under simultaneous failures in both the communication links and the agents is investigated. The effects of the loss of agents and communication links on the controllability of an information flow graph are previously studied. In this work, the corresponding results are exploited to introduce some useful indices and importance measures that help characterize and quantify the role of individual links and agents in the controllability of the overall network. Existing results are then extended by considering the effects of losses in both links and agents at the same time. To this end, the concepts of joint (r,s)-controllability and joint t-controllability are introduced as quantitative measures of reliability for a multi-agent system, and their important properties are investigated. Lastly, the class of jointly critical digraphs is introduced and it is stated that if a digraph is jointly critical, then joint t-controllability is a necessary and sufficient condition for remaining controllable following the failure of any set of links and agents, with cardinality less than t. Various examples are exploited throughout the paper to elaborate on the analytical findings.

In this work, the ability to distinguish digraphs from the output response of some observing agents in a multi-agent network under the agreement protocol has been studied. Given a fixed observation point, it is desired to find sufficient graphical conditions under which the failure of a set of edges in the network information flow digraph is distinguishable from another set. When the latter is empty, this corresponds to the detectability of the former link set given the response of the observing agent. In developing the results, a powerful extension of the all-minors matrix tree theorem in algebraic graph theory is proved which relates the minors of the transformed Laplacian of a directed graph to the number and length of the shortest paths between its vertices. The results reveal an intricate relationship between the ability to distinguish the responses of a healthy and a faulty multi-agent network and the inter-nodal paths in their information flow digraphs. The results have direct implications for the operation and design of multi-agent systems subject to multiple link losses. Simulations and examples are presented to illustrate the analytic findings.