The First Five Years of a Phase Theory for Complex Systems and Networks

In this paper,we review the development of a phase theory for systems and networks in its first five years,represented by a trilogy:Matrix phases and their properties;The MIMO LTI system phase response,its physical interpretations,the small phase theorem,and the sectored real lemma;The synchronization of a multi-agent network using phase alignment.Towards the end,we also summarize a list of ongoing research on the phase theory and speculate what will happen in the next five years.

On convergence of covariance matrix of empirical Bayes hyper-parameter estimator

Regularized system identification has become the research frontier of system identification in the past decade.One related core subject is to study the convergence properties of various hyper-parameter estimators as the sample size goes to infinity.In this paper,we consider one commonly used hyper-parameter estimator,the empirical Bayes(EB).Its convergence in distribution has been studied,and the explicit expression of the covariance matrix of its limiting distribution has been given.However,what we are truly interested in are factors contained in the covariance matrix of the EB hyper-parameter estimator,and then,the convergence of its covariance matrix to that of its limiting distribution is required.In general,the convergence in distribution of a sequence of random variables does not necessarily guarantee the convergence of its covariance matrix.Thus,the derivation of such convergence is a necessary complement to our theoretical analysis about factors that influence the convergence properties of the EB hyper-parameter estimator.In this paper,we consider the regularized finite impulse response(FIR)model estimation with deterministic inputs,and show that the covariance matrix of the EB hyper-parameter estimator converges to that of its limiting distribution.Moreover,we run numerical simulations to demonstrate the efficacy of ourtheoretical results.

A Primal-Dual SGD Algorithm for Distributed Nonconvex Optimization

The distributed nonconvex optimization problem of minimizing a global cost function formed by a sum of n local cost functions by using local information exchange is considered.This problem is an important component of many machine learning techniques with data parallelism,such as deep learning and federated learning.We propose a distributed primal-dual stochastic gradient descent(SGD)algorithm,suitable for arbitrarily connected communication networks and any smooth(possibly nonconvex)cost functions.We show that the proposed algorithm achieves the linear speedup convergence rate O(1/(√nT))for general nonconvex cost functions and the linear speedup convergence rate O(1/(nT)) when the global cost function satisfies the Polyak-Lojasiewicz(P-L)condition,where T is the total number of iterations.We also show that the output of the proposed algorithm with constant parameters linearly converges to a neighborhood of a global optimum.We demonstrate through numerical experiments the efficiency of our algorithm in comparison with the baseline centralized SGD and recently proposed distributed SGD algorithms.

Hidden Markov Models:Inverse Filtering,Belief Estimation and Privacy Protection

A hidden Markov model(HMM)comprises a state with Markovian dynamics that can only be observed via noisy sensors.This paper considers three problems connected to HMMs,namely,inverse filtering,belief estimation from actions,and privacy enforcement in such a context.First,the authors discuss how HMM parameters and sensor measurements can be reconstructed from posterior distributions of an HMM filter.Next,the authors consider a rational decision-maker that forms a private belief(posterior distribution)on the state of the world by filtering private information.The authors show how to estimate such posterior distributions from observed optimal actions taken by the agent.In the setting of adversarial systems,the authors finally show how the decision-maker can protect its private belief by confusing the adversary using slightly sub-optimal actions.Applications range from financial portfolio investments to life science decision systems.

Finite-time consensus protocols for multi-dimensional multi-agent systems

A fnite.-time consensus protocol is proposed for multi -dimensional multi- agent systems, using direction peserving signumcontrols. Flipp solutions and nonsmooh analysis tehniques are adopted to handle discontinuities. Suficient and ncessaryconditions are provided to guarantee infinte time convergence and boundedness of the solutions. It turns out that the numberof agents which have cotinuous contol law plays an ssenan role in fnite-tine conerence In adidio it is shown thatthe unit bals itoduced bylp, norms. where p ∈[1,∞] , are inariat for the closed lop.

Consistent Kalman flters for nonlinear uncertain systems over sensor networks

In this paper,we study how to design filters for nonlinear uncertain systems over sensor networks.We intoduce two Kalmantype nonlinear fitrs in centralied and dstrbute frameworks.Moreover,the tuning method for the parameters of the filteres is established to ensure the consistency,i.e..the mean square error is upper bounded by a known parameter matrix at each time.We apply the consistent fiters to the track to-track association analysis of multi targets with uncertain dynamics.A novel track to-track asocaion algoritm is proposed to idenify whether two tracks are from the same target.It is proven that the resulting probability of mis.asociation is lower than the desired threshold.Numerical simulations on track.to track association are given to show the ffetives of the methods.

WARA-PS:a research arena for public safety demonstrations and autonomous collaborative rescue robotics experimentation

A research arena(WARA-PS)for sensing,data fusion,user interaction,planning and control of collaborative autonomous aerial and surface vehicles in public safety applications is presented.The objective is to demonstrate scientific discoveries and to generate new directions for future research on autonomous systems for societal challenges.The enabler is a computational infrastructure with a core system architecture for industrial and academic collaboration.This includes a control and command system together with a framework for planning and executing tasks for unmanned surface vehicles and aerial vehicles.The motivating application for the demonstration is marine search and rescue operations.A state-of-art delegation framework for the mission planning together with three specific applications is also presented.The first one concerns model predictive control for cooperative rendezvous of autonomous unmanned aerial and surface vehicles.The second project is about learning to make safe real-time decisions under uncertainty for autonomous vehicles,and the third one is on robust terrain-aided navigation through sensor fusion and virtual reality tele-operation to support a GPS-free positioning system in marine environments.The research results have been experimentally evaluated and demonstrated to industry and public sector audiences at a marine test facility.It would be most difficult to do experiments on this large scale without the WARA-PS research arena.Furthermore,these demonstrator activities have resulted in effective research dissemination with high public visibility,business impact and new research collaborations between academia and industry.