M. Nagahara, D. E. Quevedo Sparse Representations for Packetized Predictive Networked Control, IFAC 18th World Congress, pp. 84-89, Aug., 2011.

1. Sparse Representations for Packetized
Predictive Networked Control
Masaaki Nagahara (Kyoto Univ.)
Daniel E. Quevedo (The Univ. of Newcastle)

2. Networked Control in Sparse Land
• In networked control, one has to transmit
control signals through unreliable networks.
• Packetized Predictive Control (PPC) can make
the system robust against packet dropouts.
• Sparse Representation can effectively
compress signals without much distortion.
• This work is
PPC + Sparse Representation

3. Table of Contents

4. Table of Contents

5. Packetized Predictive Control
• Compute a tentative control sequence for a
finite horizon of future time instants.
• Transmit the sequence as a packet to a buffer.
• If a packet is dropped out, use the control
stored in the buffer
[Bemporad(1998), Casavola et al.(2006), Tang-Silva(2009), Quevedo(2007,2011)]
Controller Buffer Plant

6. Controller Buffer Plant

7. Assumption: The first packet is successfully transmitted to the buffer.
Controller Buffer Plant

8. Assumption: The first packet is successfully transmitted to the buffer.
 the 4 values are stored in the buffer.
Controller Buffer Plant

9. Assumption: The first packet is successfully transmitted to the buffer.
 the 4 values are stored in the buffer.
Controller Buffer Plant

10. Controller Buffer Plant

11. Controller Buffer Plant

12. Packet-dropout occurs!
Controller Buffer Plant

13. Controller Buffer Plant

14. Design of control packets

15. Table of Contents

16. Sparsity-Promoting Optimization

17. Sparsity-Promoting Optimization

18. Feasible set

19. Feasible set
Sparse!

20. Feasible set
Not sparse

21. Iterative-Shrinkage Algorithm
• The solution of
can be effectively obtained via a fast algorithm.
[Beck-Teboulle, SIAM J. Imag. Sci., 2009]
[Zibulevsky-Elad, IEEE SP Mag., 2010]

22. Iterative-Shrinkage Algorithm
• The solution of
can be effectively obtained via a fast algorithm.
[Beck-Teboulle, SIAM J. Imag. Sci., 2009]
[Zibulevsky-Elad, IEEE SP Mag., 2010]

23. Table of Contents

24. Stability Analysis

25. Practical Stability
Terminal condition

26. Table of Contents

27. Examples

28. Transmitted Control Packets

29. Histogram of Quantized
Transmitted Values
Proposed
Conventional

30. Sparsity-promoting (proposed)
Energy-limiting (Conventional)

31. Sparsity-promoting (proposed)
Energy-limiting (Conventional)
Proposed method leads to more effective
compression than the conventional method
without much distortion.

33. Conclusion

34. Conclusion
Grazie!