Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userGlobal Structure Identifiability and Reconstructibility of an NDS with Descriptor Subsystems
85
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
This paper investigates requirements on a networked dynamic system (NDS) such that its subsystem interactions can be solely determined from experiment data or reconstructed from its overall model. The NDS is constituted from several subsystems whose dynamics are described through a descriptor form. Except regularity on each subsystem and the whole NDS, no other restrictions are put on either subsystem dynamics or subsystem interactions. A matrix rank based necessary and sufficient condition is derived for the global identifiability of subsystem interactions, which leads to several conclusions about NDS structure identifiability when there is some a priori information. This matrix also gives an explicit description for the set of subsystem interactions that can not be distinguished from experiment data only. In addition, under a well-posedness assumption, a necessary and sufficient condition is obtained for the reconstructibility of subsystem interactions from an NDS descriptor form model. This condition can be verified with each subsystem separately and is therefore attractive in the analysis and synthesis of a large-scale NDS. Simulation results show that rather than increases monotonically with the distance of subsystem interactions to the undifferentiable set, the magnitude of the external output differences between two NDSs with distinct subsystem interactions increases much more rapidly when one of them is close to be unstable. In addition, directions of probing signals are also very important in distinguishing external outputs of distinctive NDSs.These findings are expected to be helpful in identification experiment designs, etc.
rate research
Read More
Requirements on subsystems have been made clear in this paper for a linear time invariant (LTI) networked dynamic system (NDS), under which subsystem interconnections can be estimated from external output measurements. In this NDS, subsystems may have distinctive dynamics, and subsystem interconnections are arbitrary. It is assumed that system matrices of each subsystem depend on its (pseudo) first principle parameters (FPPs) through a linear fractional transformation (LFT). It has been proven that if in each subsystem, the transfer function matrix (TFM) from its internal inputs to its external outputs is of full normal column rank (FNCR), while the TFM from its external inputs to its internal outputs is of full normal row rank (FNRR), then the structure of the NDS is identifiable. Moreover, under some particular situations like there are no direct information transmission from an internal input to an internal output in each subsystem, a necessary and sufficient condition is established for NDS structure identifiability. A matrix valued polynomial (MVP) rank based equivalent condition is further derived, which depends affinely on subsystem (pseudo) FPPs and can be independently verified for each subsystem. From this condition, some necessary conditions are obtained for both subsystem dynamics and its (pseudo) FPPs, using the Kronecker canonical form (KCF) of a matrix pencil.
Requirements are investigated in this paper for each descriptor form subsystem, with which a causal/impulse free networked dynamic system (NDS) can be constructed. For this purpose, a matrix rank based necessary and sufficient condition is at first derived for the causality/impulse freeness of an NDS, in which the associated matrix depends affinely on subsystem connections. From this result, a necessary and sufficient condition is derived for each subsystem, such that there exists a subsystem connection matrix that leads to a causal/impulse free NDS. This condition further leads to a necessary and sufficient condition for the existence of a local static output feedback that guarantees the construction of a causal/impulse free NDS. A prominent property of these conditions are that all the involved numerical computations are performed independently on each individual subsystem, which is quite attractive in reducing computation costs and improving numerical stability for large scale NDS analysis and synthesis. Situations have also been clarified in which NDS causality/impulse freeness is independent of subsystem connections. It has also been made clear that under some situations, local static output feedbacks are not helpful in constructing a causal NDS.
Identifiability of a single module in a network of transfer functions is determined by the question whether a particular transfer function in the network can be uniquely distinguished within a network model set, on the basis of data. Whereas previous research has focused on the situations that all network signals are either excited or measured, we develop generalized analysis results for the situation of partial measurement and partial excitation. As identifiability conditions typically require a sufficient number of external excitation signals, this work introduces a novel network model structure such that excitation from unmeasured noise signals is included, which leads to less conservative identifiability conditions than relying on measured excitation signals only. More importantly, graphical conditions are developed to verify global and generic identifiability of a single module based on the topology of the dynamic network. Depending on whether the input or the output of the module can be measured, we present four identifiability conditions which cover all possible situations in single module identification. These conditions further lead to synthesis approaches for allocating excitation signals and selecting measured signals, to warrant single module identifiability. In addition, if the identifiability conditions are satisfied, indirect identification methods are developed to provide a consistent estimate of the module. All the obtained results are also extended to identifiability of multiple modules in the network.
The outbreak of coronavirus disease 2019 (COVID-19) has led to significant challenges for schools, workplaces and communities to return to operations during the pandemic, while policymakers need to balance between individuals safety and operational efficiency. In this paper, we present a mixed-integer programming model for redesigning routes and bus schedules for the University of Michigan (UM)s campus bus system, to prepare for students return in the 2020 Fall semester. To ensure less than 15-minute travel time for all routes and to enforce social distancing among passengers, we propose a hub-and-spoke design and utilize real data of student activities to identify hub locations and reduce the number of bus stops used in the new routes. The new bus routes, although using only 50% or even fewer seats in each bus, can still satisfy peak-hour demand in regular semesters at UM. We sample a variety of scenarios that cover variations of peak demand, social-distancing requirements, broken-down buses or no-shows of drivers, to demonstrate the system resiliency of the new routes and schedules via simulation. Our approach can be generalized to redesign public transit systems with social distancing requirement during the pandemic, to reduce passengers infection risk.
Dynamic user equilibrium (DUE) is a Nash-like solution concept describing an equilibrium in dynamic traffic systems over a fixed planning period. DUE is a challenging class of equilibrium problems, connecting network loading models and notions of system equilibrium in one concise mathematical framework. Recently, Friesz and Han introduced an integrated framework for DUE computation on large-scale networks, featuring a basic fixed-point algorithm for the effective computation of DUE. In the same work, they present an open-source MATLAB toolbox which allows researchers to test and validate new numerical solvers. This paper builds on this seminal contribution, and extends it in several important ways. At a conceptual level, we provide new strongly convergent algorithms designed to compute a DUE directly in the infinite-dimensional space of path flows. An important feature of our algorithms is that they give provable convergence guarantees without knowledge of global parameters. In fact, the algorithms we propose are adaptive, in the sense that they do not need a priori knowledge of global parameters of the delay operator, and which are provable convergent even for delay operators which are non-monotone. We implement our numerical schemes on standard test instances, and compare them with the numerical solution strategy employed by Friesz and Han.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
