This paper reports a robust scheme for topology identification and control of networks running on linear dynamics. In the proposed method, the unknown network is enforced to asymptotically follow a reference dynamics using the combination of Lyapunov based adaptive feedback input and sliding mode control. The adaptive part controls the dynamics by learning the network structure, while the sliding mode part rejects the input uncertainty. Simulation studies are presented in several scenarios (detection of link failure, tracking time varying topology, achieving dynamic synchronization) to give support to theoretical findings.
Identification of linear time-invariant (LTI) systems plays an important role in control and reinforcement learning. Both asymptotic and finite-time offline system identification are well-studied in the literature. For online system identification, the idea of stochastic-gradient descent with reverse experience replay (SGD-RER) was recently proposed, where the data sequence is stored in several buffers and the stochastic-gradient descent (SGD) update performs backward in each buffer to break the time dependency between data points. Inspired by this work, we study distributed online system iden…
This paper considers the problem of linear time-invariant (LTI) system identification using input/output data. Recent work has provided non-asymptotic results on partially observed LTI system identification using a single trajectory but is only suitable for stable systems. We provide finite-time analysis for learning Markov parameters based on the ordinary least-squares (OLS) estimator using multiple trajectories, which covers both stable and unstable systems. For unstable systems, our results suggest that the Markov parameters are harder to estimate in the presence of process noise. Without p…
Non-asymptotic Identification of LTI Systems from a Single Trajectory
Department of Electrical and Computer Engineering, University of California, Riverside, CA（加州大学河滨分校电子工程与计算机科学系）；Electrical Engineering and Computer Science Department, University of Michigan, Ann Arbor, MI（密歇根大学安娜堡分校电气工程与计算机科学系）
In this paper, a necessary and sufficient condition for the controllability of networked systems with heterogeneous dynamics is established where the nodes are higher dimensional linear time invariant systems and the network topology is directed and weighted. The controllability of networked system over some specific topologies are also examined and some non-controllability results are obtained. The theoretical results are demonstrated with examples.
In many computational tasks and dynamical systems, asynchrony and randomization are naturally present and have been considered as ways to increase the speed and reduce the cost of computation while compromising the accuracy and convergence rate. In this work, we show the additional benefits of randomization and asynchrony on the stability of linear dynamical systems. We introduce a natural model for random asynchronous linear time-invariant (LTI) systems which generalizes the standard (synchronous) LTI systems. In this model, each state variable is updated randomly and asynchronously with some…
Efficient identification of linear, parameter-varying, and nonlinear systems with noise models
IMT School for Advanced Studies Lucca（IMT卢卡高等研究院）；Eindhoven University of Technology（埃因霍温理工大学）；HUN-REN Institute for Computer Science and Control（匈牙利科学院计算机科学与控制研究所（HUN-REN））
We consider the problem of estimating a linear time-invariant (LTI) dynamical system from a single trajectory via streaming algorithms, which is encountered in several applications including reinforcement learning (RL) and time-series analysis. While the LTI system estimation problem is well-studied in the {\em offline} setting, the practically important streaming/online setting has received little attention. Standard streaming methods like stochastic gradient descent (SGD) are unlikely to work since streaming points can be highly correlated. In this work, we propose a novel streaming algorith…
In this paper, the possibility of detecting topological variations by observing output trajectories from networked linear time-invariant systems is investigated, where the network topology can be general, but the nodes have identical higher-dimensional dynamics. A necessary and sufficient condition on the discernibility of topological variations is derived, in terms of the eigenspaces of the original and the modified network configuarations. By taking the specific network structures into consideration, some lower-dimensional conditions are derived, which reveal how the network topologies, sens…
We present a method for joint phase identification and topology recovery in unbalanced three phase radial networks using only voltage measurements. By recovering phases and topology jointly, we utilize all three phase voltage measurements and can handle networks where some buses have a subset of three phases. Our method is theoretically justified by a novel linearized formulation of unbalanced three phase power flow and makes precisely defined and reasonable assumptions on line impedances and load statistics. We validate our method on three IEEE test networks simulated under realistic conditio…
In this paper, the problem of choosing the best allocation of excitations and measurements for the identification of a dynamic network is formally stated and analyzed. The best choice will be one that achieves the most accurate identification with the least costly experiment. Accuracy is assessed by the trace of the asymptotic covariance matrix of the parameters estimates, whereas the cost criterion is the number of excitations and measurements. Analytical and numerical results are presented for two classes of dynamic networks in state space form: branches and cycles. From these results, a num…
We consider the problem of controlling a set of dynamically decoupled plants where the plants' subcontrollers communicate with each other according to a fixed and known network topology. We assume the communication to be instantaneous but there is a fixed processing delay associated with incoming transmissions. We provide explicit closed-form expressions for the optimal decentralized controller under these communication constraints and using standard LQG assumptions for the plants and cost function. Although this problem is convex, it is challenging due to the irrationality of continuous-time …
Accurate grid topology information is of paramount importance for routine power system operations, while the growing availability of synchrophasor data offers the opportunity to identify topology changes in real time. Identification of bus split events, where the substation becomes electrically disconnected, is becoming increasingly important for maintaining the security of power systems. This paper aims to provide an efficient modeling and monitoring framework for bus split events by using a concise bus-branch representation. The linear sensitivity analysis is first performed to quickly evalu…
We address the problem to estimate a dynamic network whose edges describe Granger causality relations and whose topology has a Kronecker structure. Such a structure arises in many real networks and allows to understand the organization of complex networks. We proposed a kernel-based PEM method to learn such networks. Numerical examples show the effectiveness of the proposed method.
