1. Wireless Network Design for Distributed Control Liu and Goldsmith - Appeared at CDC 2004 Presented by Vinod Namboodiri

2. Networked Control is Universal  Information among distributed sensors controllers actuators  needs to be exchanged to achieve a certain control objective

3. Automated Highway System Wireless networks become important

4. Wireless Network for Distributed Control  Multiple control systems co-exist  Performance tradeoffs Control wants accurate, timely, lossless data Random delay, losses acceptable in network design – esp. wireless  Optimize tradeoffs to achieve best end-to-end control performance

5. Joint Design is Important  Tradeoff exists between communication and controller performance  More the controller knows about system, better the performance More sensors Transmit sensor measurements more frequently  However, this increases communication burden Congestion can result in longer delays or packet losses – degrades control performance

6. Goals of Joint Design  Controller design robust and adaptive to communication faults like random delays and packet losses  Communication design optimized for control performance

7. Cross-Layer Design  Each layer of network stack optimized relative to end-to-end controller performance

8. Cross Layer Design Parameters  Packet Delay  Packet Loss  Data Resolution Affects network traffic, which in turn affects delay and losses Network, MAC and Link Layer Application Layer Linear Quadratic Cost Function (H2 norm), f(delay, loss, data resolution) Control Performance Measure

9. Strategy  Difficult to simultaneously optimize all the layers  Use sub-optimal iterative method over physical, MAC and application layers Fix data resolution and MAC protocol, and choose best physical/link layer For this link design and data resolution, choose the best MAC protocol Optimize data resolution for chosen link and MAC protocol Repeat till convergence

10. Layer Parameters  Physical Layer QPSK, BPSK Modulation  MAC Layer TDMA Random Access (RA) w/ and w/o ACK CSMA/ CA  Control Layer Sample Period

11. Physical Layer  Design choice of modulation BPSKQPSK Data Rate x 2x Larger probability of error y c.y, c>1 Error Coding can help reduce probability of error - (15,7) code means 15 coded bits for 7 bits of information - Code rate = information bits/coded bits

12. Choice of MAC  TDMA Collision free protocol based on time slots Time slot can be wasted if pre-assigned transmitter has no packet to send  Random Access (RA) Grab channel for transmission independently with a probability p Variations include with or without ACK  CSMA/CA Sense channel before transmitting Exponential backoff after a collision Loss free, can add significant delay Loss possible, delay depends on contention

13. Control Parameter – Sample Period  Greater sample period Lower data resolution Lesser traffic, possibly lesser delay and loss High data rate not required; impacts choice of physical layer design

14. Iteration 1, Step 1 – Link Design RA with ACK, p = 0.166 Sample Period = 5 ms Select QPSK, (15,11) code

15. Iteration 1, Step 2 – MAC Design QPSK, (15,11) code Sample Period = 5 ms Select p = 0.28

16. Iteration 1, Step 3 – Sample Period QPSK, (15,11) code RA with ACK, p = 0.28 Select sample period = 6ms

17. Iteration 2, Step 1: Link Design RA with ACK, p = 0.166 Sample Period = 6 ms Select QPSK, (15,11) code

18. Next Steps  p = 0.28 is again optimal  Thus, algorithm converges

19. Apparent Advantages of Cross- Layer Design  We chose QPSK even though it is more unreliable  Without joint design, we could have chosen BPSK and may have lead to system instability

20. Things to ponder about  Are all network faults considered in control design? Currently only random packet drops, random delay, data rate limits considered Bursty packet losses instead of independent packet losses Time varying channels instead of static channels

21.  Thank You

22. Link Layer Design with TDMA MAC

23. Example control system