## Sundaram, Shreyas

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Publication Topological conditions for in-network stabilization of dynamical systems(2013-04-01) Pajic, Miroslav; Sundaram, Shreyas; Mangharam, Rahul; Pappas, George; Pajic, Miroslav; Sundaram, Shreyas; Mangharam, Rahul; Pappas, GeorgeWe study the problem of stabilizing a linear system over a wireless network using a simple in-network computation method. Specifically, we study an architecture called the "Wireless Control Network'' (WCN), where each wireless node maintains a state, and periodically updates it as a linear combination of neighboring plant outputs and node states. This architecture has previously been shown to have low computational overhead and beneficial scheduling and compositionality properties. In this paper we characterize fundamental topological conditions to allow stabilization using such a scheme. To achieve this, we exploit the fact that the WCN scheme causes the network to act as a linear dynamical system, and analyze the coupling between the plant's dynamics and the dynamics of the network. We show that stabilizing control inputs can be computed in-network if the vertex connectivity of the network is larger than the geometric multiplicity of any unstable eigenvalue of the plant. This condition is analogous to the typical min-cut condition required in classical information dissemination problems. Furthermore, we specify equivalent topological conditions for stabilization over a wired (or point-to-point) network that employs network coding in a traditional way -- as a communication mechanism between the plant's sensors and decentralized controllers at the actuators.Publication The Wireless Control Network: Monitoring for Malicious Behavior(2010-12-15) Sundaram, Shreyas; Pajic, Miroslav; Hadjicostis, Christoforos N; Mangharam, Rahul; Pappas, George J; Sundaram, Shreyas; Pajic, Miroslav; Hadjicostis, Christoforos N; Mangharam, Rahul; Pappas, George JWe consider the problem of stabilizing a plant with a network of resource constrained wireless nodes. In a companion paper, we developed a protocol where each node repeatedly transmits a linear combination of the values in its neighborhood. For certain topologies, we showed that these linear combinations can be designed so that the closed loop system is stable (i.e., the wireless network itself acts as a controller for the plant). In this paper, we design a Intrusion Detection System (IDS) for this control scheme, which observes the transmissions of certain nodes in the network and uses that information to (a) recover the plant outputs (for data-logging and diagnostic purposes) and (b) identify malicious behavior by any of the wireless nodes in the network. We show that if the connectivity of the network is sufficiently high, the IDS only needs to observe a subset of the nodes in the network in order to achieve this objective. Our approach provides a characterization of the set of nodes that should be observed, a systematic procedure for the IDS to use to identify the malicious nodes and recover the outputs of the plant, and an upper bound on the delay required to obtain the necessary information.Publication Network Synthesis for Dynamical System Stabilization(2011-11-01) Pajic, Miroslav; Sundaram, Shreyas; Pappas, George; Mangharam, Rahul; Pajic, Miroslav; Sundaram, Shreyas; Pappas, George; Mangharam, RahulWe present our recent results in the area of distributed control over wireless networks. In our previous work, we introduced the concept of a Wireless Control Network (WCN), where the network acts as a decentralized structured controller. In this case, the network is not used only as a communication medium (as in traditional control paradigms), but instead as a fully distributed computational substrate. We show that the dynamics of the plant dictate the types of network topologies that can be used to stabilize the system. Finally, we describe how to obtain a stabilizing configuration for the WCN if the topological conditions are satisfied.Publication A Simple Distributed Method for Control over Wireless Networks(2011-04-01) Pajic, Miroslav; Sundaram, Shreyas; Pappas, George; Mangharam, Rahul; Pajic, Miroslav; Sundaram, Shreyas; Pappas, George; Mangharam, RahulWe present a distributed scheme used for control over wireless networks. In our previous work, we introduced the concept of a Wireless Control Network (WCN), where the network itself, with no centralized node, acts as the controller. In this work, we show how the WCN can be modified to include observer style updates which substantially improves robustness of the closed-loop system to link failures. In addition, we analyze how the WCN simplifies extraction of the communication and computation schedules and enables system compositionality and scalability.Publication Closing the Loop: A Simple Distributed Method for Control over Wireless Networks(2012-01-01) Pajic, Miroslav; Sundaram, Shreyas; LE NY, Jerome; Pappas, George J.; Mangharam, Rahul; Pajic, Miroslav; Sundaram, Shreyas; LE NY, Jerome; Pappas, George J.; Mangharam, RahulWe present a distributed scheme used for control over a network of wireless nodes. As opposed to traditional networked control schemes where the nodes simply route information to and from a dedicated controller (perhaps performing some encoding along the way), our approach, Wireless Control Network (WCN), treats the network itself as the controller. In other words, the computation of the control law is done in a fully distributed way inside the network. We extend the basic WCN strategy, where at each time-step, each node updates its internal state to be a linear combination of the states of the nodes in its neighborhood. This causes the entire network to behave as a linear dynamical system, with sparsity constraints imposed by the network topology. We demonstrate that with observer style updates, the WCN's robustness to link failures is substantially improved. Furthermore, we show how to design a WCN that can maintain stability even in cases of node failures. We also address the problem of WCN synthesis with guaranteed optimal performance of the plant, with respect to standard cost functions. We extend the synthesis procedure to deal with continuous-time plants and demonstrate how the WCN can be used on a practical, industrial application, using a process-in-the-loop setup with real hardware.Publication The Wireless Control Network: Synthesis and Robustness(2010-12-15) Pajic, Miroslav; Sundaram, Shreyas; Ny, Jerome Le; Pappas, George J; Mangharam, Rahul; Pajic, Miroslav; Sundaram, Shreyas; Ny, Jerome Le; Pappas, George J; Mangharam, RahulWe consider the problem of stabilizing a plant with a network of resource constrained wireless nodes. Traditional networked control schemes are designed with one of the nodes in the network acting as a dedicated controller, while the other nodes simply route information to and from the controller and the plant. We introduce the concept of a Wireless Control Network (WCN) where the entire network itself acts as the controller. Specifically, at each time-step, each node updates its internal state to be a linear combination of the states of the nodes in its neighborhood. We show that this causes the entire network to behave as a linear dynamical system, with sparsity constraints imposed by the network topology. We then provide a numerical design procedure to determine the appropriate linear combinations to be applied by each node so that the transmissions of the nodes closest to the actuators will stabilize the plant. We also show how our design procedure can be modified to maintain mean square stability under packet drops in the network.Publication Reputation-Based Networked Control With Data-Corrupting Channels(2011-04-01) Sundaram, Shreyas; Chang, Jian; Venkatasubramanian, Krishna K.; Enyioha, Chinwendu; Lee, Insup; Pappas, George; Sundaram, Shreyas; Chang, Jian; Venkatasubramanian, Krishna K.; Enyioha, Chinwendu; Lee, Insup; Pappas, GeorgeWe examine the problem of reliable networked control when the communication channel between the controller and the actuator periodically drops packets and is faulty i.e., corrupts/alters data. We first examine the use of a standard triple modular redundancy scheme (where the control input is sent via three independent channels) with majority voting to achieve mean square stability. While such a scheme is able to tolerate a single faulty channel when there are no packet drops, we show that the presence of lossy channels prevents a simple majority-voting approach from stabilizing the system. Moreover, the number of redundant channels that are required in order to maintain stability under majority voting increases with the probability of packet drops. We then propose the use of a reputation management scheme to overcome this problem, where each channel is assigned a reputation score that predicts its potential accuracy based on its past behavior. The reputation system builds on the majority voting scheme and improves the overall probability of applying correct (stabilizing) inputs to the system. Finally, we provide analytical conditions on the probabilities of packet drops and corrupted control inputs under which mean square stability can be maintained, generalizing existing results on stabilization under packet drops.Publication Topological Conditions for Wireless Control Networks(2011-01-01) Pajic, Miroslav; Sundaram, Shreyas; Pappas, George J.; Mangharam, Rahul; Pajic, Miroslav; Sundaram, Shreyas; Pappas, George J.; Mangharam, RahulWe study the problem of stabilizing a linear system over a wireless control network. We propose a scheme where each wireless node maintains a scalar state, and periodically updates it as a linear combination of neighboring plant outputs and node states. We make connections to decentralized fixed modes and structured system theory to provide conditions on the network topology that allow the system to be stabilized. Our analysis provides the minimal number of feedback edges that have to be introduced to stabilize the system over a network, and shows that as long as the network connectivity is larger than the geometric multiplicity of any unstable eigenvalue, stabilizing controllers can be constructed at each actuator. A byproduct of our analysis is that by co-designing the network dynamics with the controllers, delays in the network are not a factor in stabilizing the system.Publication The Wireless Control Network: A New Approach for Control over Networks(2011-01-01) Pajic, Miroslav; Sundaram, Shreyas; Pappas, George; Mangharam, Rahul; Pajic, Miroslav; Sundaram, Shreyas; Pappas, George; Mangharam, RahulWe present a method to stabilize a plant with a network of resource constrained wireless nodes. As opposed to traditional networked control schemes where the nodes simply route information to and from a dedicated controller (perhaps performing some encoding along the way), our approach treats the network itself as the controller. Specifically, we formulate a strategy for each node in the network to follow, where at each time-step, each node updates its internal state to be a linear combination of the states of the nodes in its neighborhood. We show that this causes the entire network to behave as a linear dynamical system, with sparsity constraints imposed by the network topology.We provide a numerical design procedure to determine appropriate linear combinations to be applied by each node so that the transmissions of the nodes closest to the actuators will stabilize the plant. We also show how our design procedure can bemodified to maintain mean square stability under packet drops in the network, and present a distributed scheme that can handle node failures while preserving stability.We call this architecture aWireless Control Network, and show that it introduces very low computational and communication overhead to the nodes in the network, allows the use of simple transmission scheduling algorithms, and enables compositional design (where the existing wireless control infrastructure can be easily extended to handle new plants that are brought online in the vicinity of the network).