1. A Simple Distributed Method for Control over Wireless Networks Authors: Miroslav Pajic, Shereyas Sundaram, George J. Pappas and Rahul Mangharam Presented by: Raquel Guerreiro Machado

2. Wireless Networked Control Systems – Distributive – Wireless: dynamics can change operating point and physical dynamics of the closed loops system – Mean Square Stability Wireless Control Network (WCN) – Network as controller – Increases robustness to link failure – Enables system compositionality and scalability Important Concepts

3. Control Systems PLANT CONTROLLER Sensors Actuators

4. Networked Control Systems Sensors Actuators Routing Controllers

5. Wireless Control Networks

6. No centralized controller Each node maintain a state States stored in nodes are obtained through linear combination of its previous state and neighbors information –Sensors: Plant’s state information –Control nodes: Node’s state Plant’s inputs are computed from the Control node states that are neighbors of the actuators Wireless Control Networks

8. Plant’s update procedure: Node’s update procedure: Closed-loop system: Wireless Control Networks

9. Stable Configuration

10. More realistic system model Link quality modeled as probability of dropping packets Unreliable link modeled as memoryless, discrete, independent and identically distributed random process Robustness to link failures

11. State update procedure Robustness to link failures

12. State update procedure Robustness to link failures

13. The Wireless Control Network: Synthesis and Robustness A simple Distributed Method for Control over Wireless Networks Robustness to link failures

14. Extract the maximal probability if message drops (p m ) for which there exists a configuration that guarantees MSS Robustness to link failures

16. Precompute different stabilizing configurations that correspond to all possible choices of k or fewer nodes failing –Each node N k different sets of weights for all neighbors –Should maintain d*N k scalar weights, d = # of neighbors Design WCN so if some nodes fail it remains stable –Stability condition: –So far, can deal with a single node failure Robustness to node failures

17. Each node transmits exactly once per frame Possible to schedule more than one node per time slot Graph coloring techniques d i is the maximal degree of interference graph Minimum of d i time slots. Communication schedule is static Scheduling Communication

19. New control loops

20. Industrial Application

22. Firefly embedded wireless nodes. –Based on Atmel ATmega1281 8-bit microcontroller –Chipcon CC2420 IEEE 802.15.4 standard-compliant radio transciever Linear iterative procedure implemented as a simple task on top of the nano-RK RTOS Period of WCN task is 80ms The plant was implemented in Simulink For the interface between Simulink and real hardware: National Instruments PCI-6229 Experimental Platform

25. Experimental Results

26. WCN robustness to link failures analysis assume independent link failures. Scheme to handle node failures can be applied only if the network topology the requirements for which there exists a stabilizing configuration Assumes the topology of the WCM is specified a priori Limitations and Future Work