{"title":"A distributed algorithm for solving general linear equations over networks","authors":"Mu Yang, Choon Yik Tang","doi":"10.1109/CDC.2015.7402773","DOIUrl":"https://doi.org/10.1109/CDC.2015.7402773","url":null,"abstract":"In this paper, we develop a continuous-time distributed algorithm that allows nodes in an undirected, connected network to cooperatively solve a general system of linear equations, where the only assumption is that each equation is known to at least one node. We show that the algorithm enables the nodes to asymptotically agree on a solution when there are infinitely many solutions, determine the solution when there is exactly one, and discover that no solution exists when there are none. In addition, we prove that the algorithm is globally exponentially convergent, derive an explicit lower bound on its convergence rate, and show that under certain conditions, the larger the network's algebraic connectivity, or the further away from being singular the system of equations, the larger this lower bound.","PeriodicalId":308101,"journal":{"name":"2015 54th IEEE Conference on Decision and Control (CDC)","volume":"475 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123251538","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Output cluster synchronization of heterogeneous linear multi-agent systems","authors":"Zhongchang Liu, W. Wong","doi":"10.1109/CDC.2015.7402649","DOIUrl":"https://doi.org/10.1109/CDC.2015.7402649","url":null,"abstract":"This paper considers the cluster synchronization problem for coupled agents which are described by heterogeneous linear dynamic models. The aim is to synchronize the outputs of the agent systems belonging to the same cluster. This problem is solved by incorporating a common internal reference system into agent systems belonging to the same cluster while in different clusters the internal reference systems are assumed to have nonidentical linear dynamics. This paper proposes a leaderless control law for each agent, and derives a necessary and sufficient algebraic condition which relates parameters from the interaction graph and the internal models. This condition is shown to be satisfied if the interaction graph admits a directed spanning tree in each cluster and the coupling strengths among agents are strong enough.","PeriodicalId":308101,"journal":{"name":"2015 54th IEEE Conference on Decision and Control (CDC)","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125353228","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Progressive time optimal control of reactive systems","authors":"S. Ware, R. Su","doi":"10.1109/CDC.2015.7402767","DOIUrl":"https://doi.org/10.1109/CDC.2015.7402767","url":null,"abstract":"In many practical applications, we need to compute a nonblocking supervisor that not only complies with pre-specified safety requirements but also achieves a certain time optimal performance such as maximum throughput. Previous time optimal synthesis methods have had the significant drawback of only being able to deal with acyclic behavior. In this paper we propose a time optimal synthesis method which can deal with potentially infinite behavior. This is accomplished by dividing a system into progressive behaviors with which the system must be capable of finishing it task within a finite amount of time, and nonprogressive behaviors which can lead to the system having more tasks to complete, and potentially infinite behavior. We also proposed an algorithm with pseudo polynomial time complexity for computing such a supervisor.","PeriodicalId":308101,"journal":{"name":"2015 54th IEEE Conference on Decision and Control (CDC)","volume":"54 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125401753","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A Bayesian approach for model identification of LPV systems with uncertain scheduling variables","authors":"F. Abbasi, J. Mohammadpour, R. Tóth, N. Meskin","doi":"10.1109/CDC.2015.7402326","DOIUrl":"https://doi.org/10.1109/CDC.2015.7402326","url":null,"abstract":"This paper presents a Gaussian Process (GP) based Bayesian method that takes into account the effect of additive noise on the scheduling variables for identification of linear parameter-varying (LPV) models in input-output form. The proposed method approximates the noise-free coefficient functions by a local linear expansion on the observed scheduling variables. Therefore, additive noise on the scheduling variables is reconstructed as a corrective term added to the output noise that is proportional to the squared gradient obtained from the posterior of the Gaussian Process. An iterative procedure is given so that the obtained solution converges to the best estimation of the coefficient functions according to the given measure of fitness. Moreover, the expectation and covariance functions estimated by GP are modified for the noisy scheduling variable case to include the noise contribution on the estimated expectation and covariance functions. The model training procedure identifies noise level in the measurements including outputs and scheduling variables by estimating the noise variances, as well as other defined hyperparameters. Finally, the performance of the proposed method is compared to the standard GP approach through a numerical example.","PeriodicalId":308101,"journal":{"name":"2015 54th IEEE Conference on Decision and Control (CDC)","volume":"55 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125505969","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Zero-delay rate-distortion optimization for partially observable Gauss-Markov processes","authors":"Takashi Tanaka","doi":"10.1109/CDC.2015.7403118","DOIUrl":"https://doi.org/10.1109/CDC.2015.7403118","url":null,"abstract":"In this paper, we consider rate-distortion tradeoff problems for time-varying, multi-dimensional, partially observable Gauss-Markov processes subject to the zero-delay constraint. As a distortion metric, we consider the mean square error between the hidden state process and the reconstructed process. It is shown that an optimal test channel can be realized by a cascade connection of a pre-Kalman filter estimating the hidden state of the Gauss-Markov process, an additive white Gaussian noise channel, and a post-Kalman filter estimating the internal state of the pre-Kalman filter. An optimal test channel can be constructed by semidefinite programming (SDP). We also show that for stationary sources, there exists a time-invariant optimal test channel, which can also be found by SDP.","PeriodicalId":308101,"journal":{"name":"2015 54th IEEE Conference on Decision and Control (CDC)","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126735958","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Computation of the Lyapunov measure for almost everywhere stochastic stability","authors":"U. Vaidya, V. Chinde","doi":"10.1109/CDC.2015.7403329","DOIUrl":"https://doi.org/10.1109/CDC.2015.7403329","url":null,"abstract":"In our recent work [1], we introduced Lyapunov measure as a new tool to verify weaker set-theoretic notion of almost everywhere stability of stochastic nonlinear systems. A Linear transfer Perron-Frobenius operator for stochastic systems was used to provide an explicit formula for the Lyapunov measure, verifying almost everywhere almost sure stability of stochastic systems. The focus of this paper is on the computational aspect of the Lyapunov measure for stochastic systems. We used set-oriented numerical methods for the finite dimensional approximation of the linear operator and the Lyapunov measure. Stability results in the finite dimensional approximation space are also presented. In particular, we show the finite dimensional approximation leads to a further weaker notion of stability referred to as coarse stability.","PeriodicalId":308101,"journal":{"name":"2015 54th IEEE Conference on Decision and Control (CDC)","volume":"119 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116024018","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Dynamic state estimation in the presence of compromised sensory data","authors":"Yorie Nakahira, Yilin Mo","doi":"10.1109/CDC.2015.7403132","DOIUrl":"https://doi.org/10.1109/CDC.2015.7403132","url":null,"abstract":"In this article, we consider the state estimation problem of a linear time invariant system in adversarial environment. We assume that the process noise and measurement noise of the system are l∞ functions. The adversary compromises at most γ sensors, the set of which is unknown to the estimation algorithm, and can change their measurements arbitrarily. We first prove that if after removing a set of 2γ sensors, the system is undetectable, then there exists a destabilizing noise process and attacker's input to render the estimation error unbounded. For the case that the system remains detectable after removing an arbitrary set of 2γ sensors, we construct a resilient estimator and provide an upper bound on the l∞ norm of the estimation error. Finally, a numerical example is provided to illustrate the effectiveness of the proposed estimator design.","PeriodicalId":308101,"journal":{"name":"2015 54th IEEE Conference on Decision and Control (CDC)","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116231274","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Representing externally positive systems through minimal eventually positive realizations","authors":"C. Altafini","doi":"10.1109/CDC.2015.7403225","DOIUrl":"https://doi.org/10.1109/CDC.2015.7403225","url":null,"abstract":"In order to investigate the cases in which an externally positive discrete-time system fails to have a minimal positive realization, in this paper we introduce the notion of minimal eventually positive realization, for which the state update matrix becomes positive after a certain power. This property captures the idea that in the impulse response of an externally positive system the state of a minimal realization may fail to be positive, but only transiently. It is shown in the paper that whenever a minimal eventually positive realization exists, then the sequence of Markov parameters of the impulse response admits decimated subsequences for which minimal positive realizations exist and can be obtained by downsampling the eventually positive realization.","PeriodicalId":308101,"journal":{"name":"2015 54th IEEE Conference on Decision and Control (CDC)","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116422952","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Optimal sensor transmission energy allocation for linear control over a packet dropping link with energy harvesting","authors":"S. Knorn, S. Dey","doi":"10.1109/CDC.2015.7402374","DOIUrl":"https://doi.org/10.1109/CDC.2015.7402374","url":null,"abstract":"This paper studies a closed loop linear control system. The sensor computes a state estimate and sends it to the controller/actuator in the receiver block over a randomly fading packet dropping link. The receiver sends an ACK/NACK packet to the transmitter over a link. It is assumed that the transmission energy per packet at the sensor depletes a battery of limited capacity, replenished by an energy harvester. The objective is to design an optimal energy allocation policy and an optimal control policy so that a finite horizon LQG control cost is minimized. It is shown that in case the receiver to sensor feedback channel is free of errors, a separation principle holds. Hence, the optimal LQG controller is linear, the Kalman filter is optimal and the optimal energy allocation policy is obtained via solving a backward dynamic programming equation. In case the feedback channel is erroneous, the separation principle does not hold. In this case, we propose a suboptimal policy where the controller still uses a linear control, and the transmitter minimizes an expected sum of the trace of an “estimated” receiver state estimation error covariance matrix. Simulations are used to illustrate the relative performance of the proposed algorithms and various heuristic algorithms for both the perfect and imperfect feedback cases. It is seen that the dynamic programming based policies outperform the simple heuristic policies by a margin.","PeriodicalId":308101,"journal":{"name":"2015 54th IEEE Conference on Decision and Control (CDC)","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116452248","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Robust taxi dispatch under model uncertainties","authors":"Fei Miao, Shuo Han, Shan Lin, George J. Pappas","doi":"10.1109/CDC.2015.7402643","DOIUrl":"https://doi.org/10.1109/CDC.2015.7402643","url":null,"abstract":"In modern taxi networks, large amount of real-time taxi occupancy and location data are collected from networked in-vehicle sensors. They provide knowledge of system models on passenger demand and taxi supply for efficient dispatch control and coordinating strategies. Such dispatch approaches face a new challenge: how to deal with future customer demand uncertainties while fulfilling system's performance requirements, such as balancing service across the whole city and minimizing taxis' total idle cruising distance. To address this problem, we present a novel robust optimization method for taxis dispatch problems to consider polytope model uncertainties of highly spatiotemporally correlated demand and supply models. An objective function concave over the uncertain demand parameters and convex over the variables is formulated according to the design requirements. We transform the robust optimization problem to an equivalent convex optimization form by strong duality and minimax theorem, and computational tractability is guaranteed. By Monte-Carlo simulations, we show that the robust taxi dispatch solutions in this work are less probable to get large costs compared with non-robust results.","PeriodicalId":308101,"journal":{"name":"2015 54th IEEE Conference on Decision and Control (CDC)","volume":"140 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122349220","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}