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Publication Verisig: verifying safety properties of hybrid systems with neural network controllers(2019-04-01) Ivanov, Radoslav; Weimer, James; Alur, Rajeev; Pappas, George J.; Lee, InsupThis paper presents Verisig, a hybrid system approach to verifying safety properties of closed-loop systems using neural networks as controllers. We focus on sigmoid-based networks and exploit the fact that the sigmoid is the solution to a quadratic differential equation, which allows us to transform the neural network into an equivalent hybrid system. By composing the network’s hybrid system with the plant’s, we transform the problem into a hybrid system verification problem which can be solved using state-of-theart reachability tools. We show that reachability is decidable for networks with one hidden layer and decidable for general networks if Schanuel’s conjecture is true. We evaluate the applicability and scalability of Verisig in two case studies, one from reinforcement learning and one in which the neural network is used to approximate a model predictive controller.Publication Verifying the Safety of Autonomous Systems with Neural Network Controllers(2020-12-01) Ivanov, Radoslav; Carpenter, Taylor J.; Weimer, James; Alur, Rajeev; Pappas, George; Lee, InsupThis paper addresses the problem of verifying the safety of autonomous systems with neural network (NN) controllers. We focus on NNs with sigmoid/tanh activations and use the fact that the sigmoid/tanh is the solution to a quadratic differential equation. This allows us to convert the NN into an equivalent hybrid system and cast the problem as a hybrid system verification problem, which can be solved by existing tools. Furthermore, we improve the scalability of the proposed method by approximating the sigmoid with a Taylor series with worst-case error bounds. Finally, we provide an evaluation over four benchmarks, including comparisons with alternative approaches based on mixed integer linear programming as well as on star sets.Publication Architecture for a Fully Distributed Wireless Control Network(2011-04-12) Pajic, Miroslav; Aneja, Mansimar; Vemuri, Srinivas; Pappas, George; Mangharam, Rahul; Sundaram, ShreyasWe demonstrate a distributed scheme 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 demonstration, we show how the WCN can be utilized for distillation column control, a well-known process control problem. To illustrate the use of a WCN, we have utilized a process-in-the-loop simulation, where the behavior of a distillation column was simulated in Simulink and interfaced with an actual, physical network (used as the control network), which consists of several wireless nodes, sensors and actuators. The goal of this demonstration is to show the benefits of a fully-distributed robust wireless control/actuator network, which include simple scheduling, scalability and compositionality.Publication R-Charon, a Modeling Language for Reconfigurable Hybrid Systems(2006-03-29) Sokolsky, Oleg; Pappas, George; Kratz, Fabian; Lee, InsupThis paper describes the modeling language as an extension for architectural reconfiguration to the existing distributed hybrid system modeling language Charon. The target application domain of R-Charon includes but is not limited to modular reconfigurable robots and large-scale transportation systems. While largely leaving the Charon syntax and semantics intact, R-Charon allows dynamic creation and destruction of components (agents) as well as of links (references) between the agents. As such, R-Charon is the first formal, hybrid automata based modeling language which also addresses dynamic reconfiguration. We develop and present the syntax and operational semantics for R-Charon on three levels: behavior (modes), structure (agents) and configuration (system).Publication Green Scheduling: Scheduling of Control Systems for Peak Power Reduction(2011-07-01) Nghiem, Truong; Behl, Madhur; Pappas, George; Mangharam, RahulHeating, cooling and air quality control systems within buildings and datacenters operate independently of each other and frequently result in temporally correlated energy demand surges. As peak power prices are 200-400 times that of the nominal rate, this uncoordinated activity is both expensive and operationally inefficient. While several approaches for load shifting and model predictive control have been proposed, we present an alternative approach to fine-grained coordination of energy demand by scheduling energy consuming control systems within a constrained peak power while ensuring custom climate environments are facilitated. Unlike traditional real-time scheduling theory, where the execution time and hence the schedule are a function of the system variables only, control system execution (i.e. when energy is supplied to the system) are a function of the environmental variables and the plant dynamics. To this effect, we propose a geometric interpretation of the system dynamics, where a scheduling policy is represented as a hybrid automaton and the scheduling problem is presented as designing a hybrid automaton. Tasks are constructed by extracting the temporal parameters of the system dynamics. We provide feasibility conditions and a lazy scheduling approach to reduce the peak power for a set of control systems. The proposed model is intuitive, scalable and effective for the large class of systems whose state-time profile can be linearly approximated.Publication On the Feasibility of Linear Discrete-Time Systems of the Green Scheduling Problem(2011-11-01) Nghiem, Truong; Li, Zheng; Behl, Madhur; Huang, Pei-Chi; Pappas, George; Mok, Aloysius K.; Mangharam, RahulPeak power consumption of buildings in large facilities like hospitals and universities becomes a big issue because peak prices are much higher than normal rates. During a power demand surge an automated power controller of a building may need to schedule ON and OFF different environment actuators such as heaters and air quality control while maintaining the state variables such as temperature or air quality of any room within comfortable ranges. The green scheduling problem asks whether a scheduling policy is possible for a system and what is the necessary and sufficient condition for systems to be feasible. In this paper we study the feasibility of the green scheduling problem for HVAC(Heating, Ventilating, and Air Conditioning) systems which are approximated by a discrete-time model with constant increasing and decreasing rates of the state variables. We first investigate the systems consisting of two tasks and find the analytical form of the necessary and sufficient conditions for such systems to be feasible under certain assumptions. Then we present our algorithmic solution for general systems of more than 2 tasks. Given the increasing and decreasing rates of the tasks, our algorithm returns a subset of the state space such that the system is feasible if and only if the initial state is in this subset. With the knowledge of that subset, a scheduling policy can be computed on the fly as the system runs, with the flexibility to add power-saving, priority-based or fair sub-policies.Publication Case Study: Verifying the Safety of an Autonomous Racing Car with a Neural Network Controller(2020-04-01) Ivanov, Radoslav; Carpenter, Taylor J.; Weimer, James; Alur, Rajeev; Pappas, George; Lee, InsupThis paper describes a verification case study on an autonomous racing car with a neural network (NN) controller. Although several verification approaches have been recently proposed, they have only been evaluated on low-dimensional systems or systems with constrained environments. To explore the limits of existing approaches, we present a challenging benchmark in which the NN takes raw LiDAR measurements as input and outputs steering for the car. We train a dozen NNs using reinforcement learning (RL) and show that the state of the art in verification can handle systems with around 40 LiDAR rays. Furthermore, we perform real experiments to investigate the benefits and limitations of verification with respect to the sim2real gap, i.e., the difference between a system’s modeled and real performance. We identify cases, similar to the modeled environment, in which verification is strongly correlated with safe behavior. Finally, we illustrate LiDAR fault patterns that can be used to develop robust and safe RL algorithms.Publication Design and Implementation of Attack-Resilient Cyber-Physical Systems(2017-04-01) Weimer, James; Sokolsky, Oleg; Pajic, Miroslav; Pappas, George; Lee, Insup; Bezzo, NicolaRecent years have witnessed a significant increase in the number of security-related incidents in control systems. These include high-profile attacks in a wide range of application domains, from attacks on critical infrastructure, as in the case of the Maroochy Water breach [1], and industrial systems (such as the StuxNet virus attack on an industrial supervisory control and data acquisition system [2], [3] and the German Steel Mill cyberattack [4], [5]), to attacks on modern vehicles [6]-[8]. Even high-assurance military systems were shown to be vulnerable to attacks, as illustrated in the highly publicized downing of the RQ-170 Sentinel U.S. drone [9]-[11]. These incidents have greatly raised awareness of the need for security in cyberphysical systems (CPSs), which feature tight coupling of computation and communication substrates with sensing and actuation components. However, the complexity and heterogeneity of this next generation of safety-critical, networked, and embedded control systems have challenged the existing design methods in which security is usually consider as an afterthought.Publication Unit & Dynamic Typing in Hybrid Systems Modeling with CHARON(2006-10-04) Anand, Madhukar; Lee, Insup; Pappas, George; Sokolsky, OlegIn scientific applications, dimensional analysis forms a basis for catching errors as it introduces a type-discipline into the equations and formulae. Dimensions in physical quantities are measured via their standard units. However, many programming and modeling tools provide limited support for incorporating these units into the variables. Thus, it is quite difficult for a programmer to ensure dimensional consistency in the code. Different existing standards for units further complicates this problem and an incautious use could cause inconsistencies, often with catastrophic results. In this paper, we propose an extension of the basic type system in CHARON, a language for modeling of hybrid systems, to include Unit and Dynamic data types. Through a combination of indirect user-guided annotations and typeinference, we address the problem of ensuring both dimensional consistency, and consistency with respect to different unitsystems. Further, we also introduce dynamic data typing, that allows programmers to specify entities that bind at runtime. Such abstractions are particularly useful to program controllers for dynamic environments. We illustrate these benefits with an example on mobile robots.Publication Robust Test Generation and Coverage for Hybrid Systems(2007-04-01) Julius, Agung; Fainekos, Georgios E; Anand, Madhukar; Lee, Insup; Pappas, GeorgeTesting is an important tool for validation of the system design and its implementation. Model-based test generation allows to systematically ascertain whether the system meets its design requirements, particularly the safety and correctness requirements of the system. In this paper, we develop a framework for generating tests from hybrid systems’ models. The core idea of the framework is to develop a notion of robust test, where one nominal test can be guaranteed to yield the same qualitative behavior with any other test that is close to it. Our approach offers three distinct advantages: 1) It allows for computing and formally quantifying the robustness of some properties; 2) it establishes a method to quantify the test coverage for every test case; and 3) the procedure is parallelizable and therefore, very scalable. We demonstrate our framework by generating tests for a navigation benchmark application.