{"title":"On applications of the spectral theory of the Koopman operator in dynamical systems and control theory","authors":"I. Mezić","doi":"10.1109/CDC.2015.7403328","DOIUrl":"https://doi.org/10.1109/CDC.2015.7403328","url":null,"abstract":"Recent contributions have extended the applicability of Koopman operator theory from dynamical systems to control. Stability theory got reformulated in terms of spectral properties of the Koopman operator [1], providing a nice link between the way we treat linear systems and nonlinear systems and opening the door for the use of classical linear e.g. pole placement theory in the fully nonlinear setting. New concepts such as isostables proved useful in the context of optimal control. Here, using Kato Decomposition we develop Koopman expansion for general LTI systems. We also interpret stable and unstable subspaces in terms of zero level sets of Koopman eigenfunctions. We then utilize conjugacy properties of Koopman eigenfunctions to extend these results to globally stable systems. In conclusion, we discuss how the classical Hamilton-Jacobi-Bellman setting for optimal control can be reformulated in operator-theoretic terms and point the applicability of spectral operator theory in max-plus algebra to it. Geometric theories such as differential positivity have been also related to spectral theories of the Koopman operator [2], in cases when the attractor is a fixed point or a limit cycle, pointing the way to the more general case of quasiperiodic and chaotic attractors.","PeriodicalId":308101,"journal":{"name":"2015 54th IEEE Conference on Decision and Control (CDC)","volume":"38 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":"116683457","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":"An iterative scheme to hierarchically structured optimal energy management of a microgrid","authors":"D. Ioli, A. Falsone, M. Prandini","doi":"10.1109/CDC.2015.7403037","DOIUrl":"https://doi.org/10.1109/CDC.2015.7403037","url":null,"abstract":"In this paper we address the optimal energy management of a microgrid composed of multiple sub-units, each one including one or more buildings sharing some common resources. The goal of the microgrid operator is to match a given electrical energy profile agreed with the operator of the main grid. We propose a decentralized solution scheme based on a hierarchical structure involving three layers: single building, sub-unit, and microgrid operator. At the level of each building, thermal and electrical energy requests are minimized while guaranteeing a certain comfort and quality of service to the building occupants. Optimization of the use of common resources (storages and technological devices) is performed by each sub-unit based on the energy requests of the buildings composing the sub-unit and the cost signal received by the microgrid operator. Each sub-unit minimizes its electrical energy cost as computed based on its own cost signal, while the microgrid operator updates all cost signals based on the outcome of the decentralized optimization, so as to coordinate the sub-units and match the given reference profile. A numerical example shows the efficacy of the approach.","PeriodicalId":308101,"journal":{"name":"2015 54th IEEE Conference on Decision and Control (CDC)","volume":"48 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":"117269559","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":"Computing all minimal transition-based sensor activation policies for centralized supervisory control","authors":"Weilin Wang, Chaohui Gong","doi":"10.1109/CDC.2015.7402004","DOIUrl":"https://doi.org/10.1109/CDC.2015.7402004","url":null,"abstract":"A controller activates sensors to acquire information in order to correctly implement a supervisory control law. Sensor activation is costly because systems often operate in restrictive environments with limited resources. In order to reduce unnecessary sensor activation, along with controlling the system, the supervisory controller continuously adjusts its selecting information in response to its observation of changing circumstances. Building upon existing methods for computing a transition-based minimal sensor activation policy, this paper presents algorithms for computing all minimal transition-based sensor activation policies. This result is also extended for minimizing the numerical sensor activation cost for systems modeled by stochastic automata.","PeriodicalId":308101,"journal":{"name":"2015 54th IEEE Conference on Decision and Control (CDC)","volume":"92 9","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120842297","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":"Decomposition of multi-agent planning under distributed motion and task LTL specifications","authors":"Jana Tumova, Dimos V. Dimarogonas","doi":"10.1109/CDC.2015.7403396","DOIUrl":"https://doi.org/10.1109/CDC.2015.7403396","url":null,"abstract":"The aim of this work is to introduce an efficient procedure for discrete multi-agent planning under local complex temporal logic behavior specifications. While the first part of an agent's behavior specification constraints the agent's trace and is independent, the second part of the specification expresses the agent's tasks in terms of the services to be provided along the trace and may impose requests for the other agents' collaborations. To fight the extreme computational complexity of centralized multi-agent planning, we propose a two-phase automata-based solution, where we systematically decouple the planning procedure for the two types of specifications. At first, we only consider the former specifications in a fully decentralized way and we compactly represent each agents' admissible traces by abstracting away the states that are insignificant for the satisfaction of their latter specifications. Second, the synchronized planning procedure uses only the compact representations. The satisfaction of the overall specification is guaranteed by construction for each agent.","PeriodicalId":308101,"journal":{"name":"2015 54th IEEE Conference on Decision and Control (CDC)","volume":"64 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":"121098875","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":"Online fault diagnosis of modular discrete-event systems","authors":"F. G. Cabral, M. V. Moreira, O. Diene","doi":"10.1109/CDC.2015.7402914","DOIUrl":"https://doi.org/10.1109/CDC.2015.7402914","url":null,"abstract":"In general, systems are formed by the composition of several modules, local components or subsystems, and may exhibit a large number of states. The growth of the global system model with the number of system components leads to high computational costs for diagnosis techniques based on the global model. In order to circumvent this problem, several works in the literature address the problem of modular fault diagnosis of discrete event systems. In these works, the computation of the global system model is avoided, and the diagnosability of the language of the system is inferred from the behavior of its components. In this paper, a new approach to online diagnosis of modular systems is presented. The method is based on the computation of a Petri net diagnoser, called as synchronized Petri net diagnoser (SPND), that is constructed from the nonfaulty behavior of the modules of the system. We also introduce the definition of synchronous diagnosability of the language of a modular system with respect to the languages of its modules, and present an algorithm to verify this property.","PeriodicalId":308101,"journal":{"name":"2015 54th IEEE Conference on Decision and Control (CDC)","volume":"24 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":"121099614","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":"Approximately optimal linear strategies for static teams with ‘big’ non-Gaussian noise","authors":"Ankur A. Kulkarni","doi":"10.1109/CDC.2015.7403351","DOIUrl":"https://doi.org/10.1109/CDC.2015.7403351","url":null,"abstract":"We study stochastic team problems with static information structure where we assume controllers have linear information and quadratic cost but allow the noise to be from a non-Gaussian class. When the noise is Gaussian, it is well known that these problems admit a linear optimal controller. We show that if the noise has a log-concave density, then for `most' problems of this kind, linear strategies are approximately optimal. The quality of the approximation improves as length of the noise vector grows. We show that if the optimal strategies for problems with log-concave noise converge pointwise, they converge to the (linear) optimal strategy for the problem with Gaussian noise. And we derive an error bound on the difference between the optimal cost for the non-Gaussian problem and the best cost obtained under linear strategies.","PeriodicalId":308101,"journal":{"name":"2015 54th IEEE Conference on Decision and Control (CDC)","volume":"104 15 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":"127437424","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":"Network semantics of dynamical systems","authors":"V. Chetty, S. Warnick","doi":"10.1109/CDC.2015.7402432","DOIUrl":"https://doi.org/10.1109/CDC.2015.7402432","url":null,"abstract":"Dynamical systems enjoy a rich variety of mathematical representations, from interconnections of convolution operators or rational functions of a complex variable to systems of (possibly stochastic) differential or differential-algebraic equations. Although many of these representations can describe the same behavior, i.e. represent the same constraints on manifest variables, each one may characterize a different notion of system structure. This paper introduces a method for interpreting the semantics of different representations of a network system by exploring the set of realizations consistent with each. We then focus on signal structure, extending its definition, and demonstrate that its semantics differ from other network representations in important and useful ways. In particular, the information cost for identifying a system's signal structure from data can be considerably less than that needed for identifying a system's subsystem structure.","PeriodicalId":308101,"journal":{"name":"2015 54th IEEE Conference on Decision and Control (CDC)","volume":"38 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":"127472313","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":"On notions and sufficient conditions for forward invariance of sets for hybrid dynamical systems","authors":"Jun Chai, R. Sanfelice","doi":"10.1109/CDC.2015.7402652","DOIUrl":"https://doi.org/10.1109/CDC.2015.7402652","url":null,"abstract":"Forward invariance for hybrid dynamical systems modeled by differential and difference inclusions with state-depending conditions enabling flows and jumps is studied. Several notions of forward invariance are considered and sufficient conditions in terms of the objects defining the system are introduced. In particular, we study forward invariance notions that apply to systems with nonlinear dynamics for which not every solution is unique or may exist for arbitrary long hybrid time. Such behavior is very common in hybrid systems. Lyapunov-based conditions are also proposed for the estimation of invariant sets. Applications and examples are given to illustrate the results. In particular, the results are applied to the estimation of weakly forward invariant sets, which is an invariance property of interest when employing invariance principles to study convergence of solutions.","PeriodicalId":308101,"journal":{"name":"2015 54th IEEE Conference on Decision and Control (CDC)","volume":"136 3 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":"125816184","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":"Reconstruction of promoter activity statistics from reporter protein population snapshot data","authors":"E. Cinquemani","doi":"10.1109/CDC.2015.7402418","DOIUrl":"https://doi.org/10.1109/CDC.2015.7402418","url":null,"abstract":"A critical step in the analysis of the dynamics of gene expression and regulation from protein reporter data is the reconstruction of promoter activity. While devoted significant attention in a population-average setting, the problem has not been addressed in much detail for stochastic models and individual cell data. In this work we address the reconstruction of time profiles of promoter activity statistics, such as population mean and variance, from the corresponding statistics of reporter protein abundance in cell samples collected at subsequent times. Based on the so-called random telegraph model of gene expression, we address the problem both in terms of structural and practical identifiability of the model parameters and of the direct reconstruction of promoter activity mean and variance profiles via regularized deconvolution, providing analysis tools, theoretical results and application of our methods to the in silico analysis of a relevant example.","PeriodicalId":308101,"journal":{"name":"2015 54th IEEE Conference on Decision and Control (CDC)","volume":"56 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":"126041825","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 to hybrid fault detection and isolation","authors":"Shuo Zhang, M. Baric","doi":"10.1109/CDC.2015.7402917","DOIUrl":"https://doi.org/10.1109/CDC.2015.7402917","url":null,"abstract":"Fault diagnosis is a crucial component in aircraft control. Fast detection and effective isolation of faults is desired for both manned and unmanned aircrafts to take correct actions when a fault has occurred. This paper proposes a hybrid algorithm for helicopter fault detection and isolation (FDI), which systematically integrates the two paradigms in FDI - model based and data based methodologies - in the Bayesian framework. This hybrid FDI approach has been tested against a helicopter model [1] and excellent FDI performance has been observed.","PeriodicalId":308101,"journal":{"name":"2015 54th IEEE Conference on Decision and Control (CDC)","volume":"6 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":"126078592","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}