Hybrid Systems and Networked Control Systems Michael S. Branicky EECS Dept. Case Western Reserve University NSF Planning Meeting on Cyber-Physical Systems 27 July 2006

Networked ControlHardware Diagnostics +Monitoring Software Engineering Security

Hybrid Dynamical System* A set of dynamical systems plus rules for jumping among them [Raibert’s Hopper] ___________________ * M.S. Branicky. Introduction to hybrid systems. In Handbook of Networked and Embedded Control Systems, Birkhauser, 2005.

Hybrid Dynamical System: Automata Viewpoint* [Thermostat] [Raibert’s Hopper] [Bouncing Ball] ___________________ * M.S. Branicky. Introduction to hybrid systems. In Handbook of Networked and Embedded Control Systems, Birkhauser, 2005.

Adding Control: CHDS* [Tiptronic Transmission] An HDS plus controlled switching and jumps ___________________ * M.S. Branicky. Introduction to hybrid systems. In Handbook of Networked and Embedded Control Systems, Birkhauser, 2005.

Networked Control Systems* (1) Numerous distributed agents Physical and informational dependencies ___________________ * M.S. Branicky, V. Liberatore, and S.M. Phillips. Networked control system co-simulation for co-design. Proc. ACC, 2003.

Networked Control Systems* (2) Control loops closed over heterogeneous networks ___________________ * M.S. Branicky, V. Liberatore, and S.M. Phillips. Networked control system co-simulation for co-design. Proc. ACC, 2003.

Mathematical Model: NCS Architecture* An NCS Architecture is a 3-tuple: Agent Dynamics: a set of stochastic hybrid systems dX i (t)/dt = f i (Q i (t), X i (t), Q I [t], Y I [t], R(t)) Y i (t) = g i (Q i (t), X i (t), Q I [t], Y I [t], R(t)) Network Information Flows: a directed graph G I = (V, E I ), V = {1, 2, …, N}; e.g., e = (i, j) Network Topology: a colored, directed multigraph G N = (V, C, E N ), V = {1, 2, …, N}; e.g., e = (c, i, j) ___________________ * M.S. Branicky, V. Liberatore, and S.M. Phillips. Networked control system co-simulation for co-design. Proc. ACC, 2003.

Fundamental Issues* Time-Varying Transmission Period Network Schedulability, Routing Protocols Network-Induced Delays Packet Loss Plant Controller h(t) Plant Controller h Delay Plant Controller r Plant Controller Network h 1 (t) h N (t) ___________________ * M.S. Branicky, S.M. Phillips, W. Zhang (various): Proc. ACC, 2000; IEEE Cont. Systs. Mag., 2001; Proc. CDC, 2002.

Previous Work Nilsson: Time-Stamp Packets, Gain Schedule on Delay Walsh et al.: no delay+Max. Allowable Transfer Interval Zhang, Branicky, Phillips: h suff Hassibi, Boyd: Asynchronous dynamics systems Elia, Mitter, others: Info theory: BW reqts. for CL stability Teel/Nesic: Small gain theorem, composability

Control and Scheduling Co-Design* Control-theoretic characterization of stability and performance (bounds on transmission rate) Transmission scheduling satisfying network bandwidth constraints Simultaneous optimization of both of these = Co-Design Plant Controller Network h 1 (t) h N (t) ___________________ * M.S. Branicky, S.M. Phillips and W. Zhang. Scheduling and feedback co-design for networked control systems. Proc. CDC, 2002.

Co-Simulation* Simulation languages Bandwidth monitoring VisualizationNetwork dynamicsPlant output dynamics Packet queueing and forwarding Co-simulation of systems and networks Plant agent (actuator, sensor, …) Router Controller agent (SBC, PLC, …) ___________________ * M.S. Branicky, V. Liberatore, and S.M. Phillips. Networked control system co-simulation for co-design. Proc. ACC, 2003.

Co-Simulation Methodology* Simultaneously simulate both the dynamics of the control system and the network activity Vary parameters: –Number of plants, controllers, sensors –Sample scheduling –Network topology, routing algorithms –Cross-traffic –Etc. ___________________ * M.S. Branicky, V. Liberatore, and S.M. Phillips. Networked control system co-simulation for co-design. Proc. ACC, 2003.

Co-Simulation Components (1): Network Topology, Parameters* Capability like ns-2 to simulate network at packet level: state-of-art, open-source software follows packets over links queuing and de-queuing at router buffers GUI depicts packet flows can capture delays, drop rates, inter-arrival times ___________________ * M.S. Branicky, V. Liberatore, and S.M. Phillips. Networked control system co-simulation for co-design. Proc. ACC, 2003.

Extensions of ns-2 release*: plant “agents”: sample/send output at specific intervals control “agents”: generate/send control back to plant dynamics solved numerically using Ode utility, “in-line” (e.g., Euler), or through calls to Matlab Co-Simulation Components (2): Plant and Controller Dynamics Also: TrueTime [Lund] (Simulink plus network modules) Ptolemy, SHIFT [UCB] (+ other HS simu. langs.) Need: comprehensive tools (ns-2 +SL/LV/Omola +Corba) various HIL integrations (HW, µprocs, emulators) ___________________ * M.S. Branicky, V. Liberatore, and S.M. Phillips. Networked control system co-simulation for co-design. Proc. ACC, 2003.

Analysis and Design Tools Stability Regions* and Traffic Loci** Both for an inverted pendulum on a cart (4-d), with feedback matrix designed for nominal delay of 50ms. Queue size = 25 (left), 120 (right) ___________________ * W. Zhang, M.S. Branicky, and S.M. Phillips. Stability of networked control systems. IEEE Cont. Systs. Mag., Feb ** J.R. Hartman, M.S. Branicky, and V. Liberatore. Time-dependent dynamics in networked sensing and control. Proc. ACC, 2005.

Information Flow Flow –Sensor data –Remote controller –Control packets Timely delivery –Stability –Safety –Performance

Bandwidth Allocation for Control* Objectives: –Stability of control systems –Efficiency & fairness –Fully distributed, asynchronous, & scalable –Dynamic & self reconfigurable ___________________ * A.T. Al-Hammouri, M.S. Branicky, V. Liberatore, and S.M. Phillips. Decentralized and dynamic bandwidth allocation in networked control systems. Proc. WPDRTS, 2006.

Queue Control: Results* PI ¤ P¤P¤ ___________________ * A.T. Al-Hammouri, M.S. Branicky, V. Liberatore, and S.M. Phillips. Decentralized and dynamic bandwidth allocation in networked control systems. Proc. WPDRTS, 2006.

Synchronization: Ideas* Predictable application time –If control applied early, plant is not in the state for which the control was meant –If control applied for too long, plant no longer in desired state Keep plant simple –Low space requirements Integrate Playback, Sampling, and Control ___________________ * V. Liberatore. Integrated play-back, sensing, and networked control. Proc. INFOCOM, 2006.

Synchronization: Mechanics* Send regular control –Playback time Late playback okay –Expiration Piggyback contingency control ___________________ * V. Liberatore. Integrated play-back, sensing, and networked control. Proc. INFOCOM, 2006.

Plant Output* Open LoopPlay-Back ___________________ * V. Liberatore. Integrated play-back, sensing, and networked control. Proc. INFOCOM, 2006.

Cyber-Physical Systems Research –Control theory: (stoch.) HS, non-uniform/stochastic samp., event- vs. time-based hierarachical, composable (cf. Omola), multi-timescale (months to ms) –Delays, Jitter, Loss Rates, BW Characterization of networks (e.g., time-varying RTT, OWD delays) Application and end-point adaptability to unpredictable delays –Buffers –Control gains –Time synchronization –Bandwidth allocation, queuing strategies, network partitioning Control theoretical, blank-slate designs, Jack Stankovic’s *SP protocols –Co-simulation, co-design –Application-oriented, end-to-end QoS (beyond stability to performance) –Distributed, real-time embedded middleware: Resource constraints vs. inter-operability and protocols Sensors/transducers (cf. IEEE 1451, LXI Consortium), distributed timing services (IEEE 1588, NTP; John Eidson: Time is a first-class object), data gathering (Lui Sha’s observability), resource management (discovery, “start up”), “certificates”

Thanks NSF CCR on Networked Control Colleague: Vincenzo Liberatore, CWRU