Pappas, George J
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Publication Topological conditions for in-network stabilization of dynamical systems(2013-04-01) 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 Multi-Modal Control of Systems with Constraints(2001-12-04) Koo, T. John; Pappas, George J; Sastry, ShankarIn multi-modal control paradigm, a set of controllers of satisfactory performance have already been designed and must be used. Each controller may be designed for a different set of outputs in order to meet the given performance objectives and system constraints. When such a collection of control modes is available, an important problem is to be able to accomplish a variety of high level tasks by appropriately switching between the low-level control modes. In this paper, we propose a framework for determining the sequence of control modes that will satisfy reachability tasks. Our framework exploits the structure of output tracking controllers in order to extract a finite graph where the mode switching problem can be efficiently solved, and then implement it using the continuous controllers. Our approach is illustrated on a robot manipulator example, where we determine the mode switching logic that achieves the given reachability task.Publication Hybrid Controllers for Path Planning: A Temporal Logic Approach(2005-01-01) Fainekos, Geogios E; Kress-Gazit, Hadas; Pappas, George JRobot motion planning algorithms have focused on low-level reachability goals taking into account robot kinematics, or on high level task planning while ignoring low-level dynamics. In this paper, we present an integrated approach to the design of closed–loop hybrid controllers that guarantee by construction that the resulting continuous robot trajectories satisfy sophisticated specifications expressed in the so–called Linear Temporal Logic. In addition, our framework ensures that the temporal logic specification is satisfied even in the presence of an adversary that may instantaneously reposition the robot within the environment a finite number of times. This is achieved by obtaining a Büchi automaton realization of the temporal logic specification, which supervises a finite family of continuous feedback controllers, ensuring consistency between the discrete plan and the continuous execution.Publication Scalable Scheduling of Building Control Systems for Peak Demand Reduction(2012-06-15) Nghiem, Truong; Behl, Madhur; Mangharam, Rahul; Pappas, GeorgeIn large energy systems, peak demand might cause severe issues such as service disruption and high cost of energy production and distribution. Under the widely adopted peak-demand pricing policy, electricity customers are charged a very high price for their maximum demand to discourage their energy usage in peak load conditions. In buildings, peak demand is often the result of temporally correlated energy demand surges caused by uncoordinated operation of sub-systems such as heating, ventilating, air conditioning and refrigeration (HVAC&R) systems and lighting systems. We have previously presented green scheduling as an approach to schedule the building control systems within a constrained peak demand envelope while ensuring that custom climate conditions are facilitated. This paper provides a sufficient schedulability condition for the peak constraint to be realizable for a large and practical class of system dynamics that can capture certain nonlinear dynamics, inter-dependencies, and constrained disturbances. We also present a method for synthesizing periodic schedules for the system. The proposed method is demonstrated in a simulation example to be scalable and effective for a large-scale system.Publication Discrete synchronization of hybrid systems(2002-12-10) Tabuada, Paulo; Pappas, George JControl theory is currently faced with new paradigms and challenges that fall beyond traditional problems. Nowadays applications tend to be distributed, and require partial synchronization among their various subsystems. In this paper, we give initial steps towards discrete synchronization problems for systems which are compositions of several, possibly distributed, hybrid systems. Such problems arise frequently in the coordination of multi-agent systems, where each agent is modeled as a hybrid system. This results in control problems where the model is the composition of decoupled subsystems, but the specification is coupled across subsystems. A centralized solution to this problem requires computing the product hybrid systems resulting in state explosion. We alternatively consider decentralized solutions to such discrete synchronization problems. Partially decentralized synchronization is achieved if each subsystem is allowed to communicate with the subsystems it needs to partially synchronize with. The required communication between agents is provided by mobile abstractions of the remaining agents. These abstractions, which are property-dependent, are then used to derive local controllers using global, but minimal, observations.Publication Geometric Programming Relaxations for Linear System Reachability(2004-06-30) Yazarel, Hakan; Pappas, George JOne of the main obstacles in the safety analysis of continuous and hybrid systems has been the computation of the reachable set for continuous systems in high dimensions. In this paper, we present a novel method that exploits the structure of linear dynamical systems, and the monotonicity of the exponential function in order to obtain safety certificates of continuous linear systems. By over-approximating the sets of initial and final states, the safety verification problem is expressed as a series of geometric programs which can be further transformed into linear programs. This provides the ability to verify the safety properties of high dimensional linear systems with realistic computation times. In addition, our optimization based formulation computes time intervals over which the system is safe and unsafe.Publication Event-based Green Scheduling of Radiant Systems in Buildings(2013-03-01) Nghiem, Truong X; Pappas, George; Mangharam, RahulThis paper looks at the problem of peak power demand reduction for intermittent operation of radiant systems in buildings. Uncoordinated operation of the circulation pumps of a multi-zone hydronic radiant system can cause temporally correlated electricity demand surges when multiple pumps are activated simultaneously. Under a demand-based electricity pricing policy, this uncoordinated behavior can result in high electricity costs and expensive system operation. We have previously presented Green Scheduling with the periodic scheduling approach for reducing the peak power demand of electric radiant heating systems while maintaining indoor thermal comfort. This paper develops an event-based state feedback scheduling strategy that, unlike periodic scheduling, directly takes into account the disturbances and is thus more suitable for building systems. The effectiveness of the new strategy is demonstrated through simulation in MATLAB.Publication A Simple Distributed Method for Control over Wireless Networks(2011-04-01) 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 Finite state abstraction of a stochastic model of the lactose regulation system of Escherichia coli(2006-12-15) Julius, Agung; Kumar, R. Vijay; Halász, Ádám; Pappas, George JThis paper focuses on the lactose regulation system in Escherichia coli bacteria, one of the most extensively studied examples of positive feedback in a naturally occurring gene network. State-of-the-art nonlinear dynamical system models predict a bi-stability phenomenon that is confirmed in experiments. However, such deterministic models fail to explain experimental observations of spontaneous transition between the two stable states in the system and the simultaneous occurrence of both steady states in a population of cells. In this paper, we propose a stochastic model that explains this phenomenon. Furthermore, we also extract a coarser two-state continuous-time Markov chain as a higher level abstraction of this model, and show that macroscopic properties are retained in the abstraction.Publication Flying Hot Potatoes(2002-05-08) Mishra, Pradyumna; Pappas, George JOptical communication networks and air traffic management systems share the same fundamental routing problem as both optical packets and aircraft must continuously move within the network, while avoiding conflicts. In this paper, we explore the use of hot potato and deflection routing algorithms, which are established routing methods in optical communication networks, in the conflict-free routing of air traffic. Hot potato algorithms allow the incorporation of conflict resolution constraints into the routing problem, in contrast to most approaches that decouple the optimal routing problem from the conflict resolution problem.