Institute for Software Integrated Systems Vanderbilt University A Model-based Framework for Compositional Design of Cyber-Physical Systems Xenofon Koutsoukos February 8, 2011

Overview  Model-based compositional design of networked control systems  Event-triggered networked control using passivity  Group coordination in multi- agent networks  Current and future work  Collaborators  Yuan Xue, Janos Sztipanovits  Nicholas Kottenstette, Derek Riley  Jia Bai, Emeka Eyisi, Heath LeBlanc, Joe Porter, Zhenkai Zheng 2

Networked Control Systems  CPS are monitored and controlled by networked controlled systems  Open systems  Dependable operation  Network uncertainties such as time-varying delays and packet loss cause significant challenges  Passive systems provide inherent safety that is fundamental in building systems that are insensitive to implementation uncertainties 3 Plant Dynamics Models Controller Models Physical design Software Architecture Models Software Component Code Software design System Architecture Models Resource Management Models System/Platform Design Passivity-based design of networked control systems: Decouple stability from network implementation side effects

Experimental Case Study 4 Objective: Demonstrate model-based design using passivity

Passivity-Based Architecture 5 Bilinear transform: power and wave vars. Bilinear transform (b) Power and Wave variables Passive down- and up-sampler (PUS, PDS) Delays Power junction Passive dynamical system

Robotic Control System  Dynamics 6

 Wave variables were introduced by Fettweis in order to circumvent the problem of delay-free loops and guarantee that the implementation of wave digital filters is realizable  Wave variables define a bilinear transformation under which a stable minimum phase continuous-time system is mapped to a stable minimum phase discrete-time system  Sensor output  Controller output  Passivity is preserved for fixed time delays and data dropouts  Tolerate typical time-varying delays Wave Variables 7

 Because of bandwidth constraints, the local digital controllers for each robot run at a faster rate than the network controller  Ensure that no energy is generated, and thus passivity is preserved  Passive down-sampling  Passive up-sampling where and Passive Up-sampling and Down-sampling 8

Power Junction  Compose a network in which multiple passive plants can be interconnected to multiple passive controllers  Interconnect wave variables from multiple controllers and plants such that the total power input is always greater than or equal to the total power output 9

Network Control Design 10  The multi-rate control network is  Passive if the plants and the controller are passive  - stable if the plants and the controller are strictly-output passive  Even in the presence of network delays and data loss Network Controller  Digital lag-compensator which minimizes the steady state error between the reference position and the actual position of every joint Robot Controller

PaNeCS: Model-Based Design Using Passivity Plant Controller Reference System Power Junction 11

Control Design Aspect 12 ControllerSystem PlantSystemReferenceSystem

Platform Design Aspect 13

Structural Semantics  Defined using  Meta-model notations  Object Constrained Language (OCL)  Implemented Constraints  Cardinality Constraints  Connection Constraints  Unique Name Constraints  OCL Example Description: There must be one connection between the DigitalController block and the BilinearTransformC block Equation: self.connectionParts("Controller_Bilinear").size()=1 14

Passivity Analysis  Passivity analysis of components  A C++ model interpreter within GME invokes a Matlab function  The CVX semidefinite programming tool is used to solve an LMI for each component (linear dynamics)  System-level analysis based on “correct-by-construction” approach  Individual components satisfy the passivity constraints  Passivity-preserving composition constraints encoded in the modeling language  Parallel interconnection  Negative feedback 15

PaNeCS Design Flow PaNeCS GME PaNeCS2tt Simulink TrueTime SL/tt model generatorBehavior simulation PaNeCS Code Generator Simulink models Bash scripts Executable code 16

Operational Semantics  Globally asynchronous locally synchronous execution model  Software components are executed periodically based on a local sampling period (executable Simulink models)  Asynchronous data communication  It is assumed that data messages do not arrive out of order  Zeros are supplied for missing data values  Preclude the possibility of blocking  Avoid introducing energy into the system (preserving passivity)  Buffer sizing  Data supply and consumption rates are known  As long as the PC clocks remain relatively close to each other, buffers will never grow without bound  No guarantee for non-ideal operation 17

Experimental Setup  Two CrustCrawler robotic arms  4 DOF with AX-12 smart servos at each joint  Novint haptic paddle  Five networked Windows PCs with Matlab/Simulink  Network infrastructure utilizes Netcat and SSH 18

Experiment 1: Nominal Case 19 x-y-z coordinates and angle of joint 2 of reference, robot 2, and robot 3

Experiment 2: Persistent Link Interruptions 20 Angle of joint 3 and y coordinate of reference, robot 2, and robot 3

Experiment 3: Intermittent Wireless Connection 21 Angle of joint 3 and y coordinate of reference, robot 2, and robot 3

Event-triggered NCS  Tracking using self-triggered control  Adaptive manipulator control (Slotine)  Self-triggered control (Tabuada)  Design preserves passivity  Triggering policy based on storage function  Event-driven passive sample and hold devices 22

Simulation Results 23 Event-triggered controlTime-triggered control

Group Coordination  Group coordination of networked agents  Surveillance and convoy tracking applications  Establish formation around a target  Distributed algorithms using local communication  Account for network delays and data loss  Discrete-time distributed design using passivity  Ensure - stability  In the presence of network delays and data loss  Regardless of the overlay network topology  Asymptotic formation establishment and output synchronization  Collision avoidance  Simulations using quadrotor UAVs  Simulink/TrueTime  NCSWT 24

NCS Model 25 Node Structure A 3-Node Network Non-passive UAV model Strictly-output passive UAV model

Passivity and Steady-State Analysis 26  The NCS is strictly output passive for any overlay network topology  Passivity-preserving inteconnection structure  The NCS is -stable for any overlay network topology  Asymmetric delays  Data loss  Steady-state analysis shows that the NCS can establish desired configurations  Steady-state output of agent i  Calculate reference inputs to asymptotically achieve a desired configuration

Simulation Results 27

Simulation Results 28

Current and Future Work  Passivity-based design  Safety  Performance  Event-triggered control based on passivity  Experimental evaluation  Anytime control algorithms  Networked multi-agent systems  Group coordination in networked multi-agent systems  Robust distributed algorithms  Effects of the network topology  Tools for system integration  NCSWT  System/Experimental studies  Fleet of quadrotor UAVs 29