1. Bor-Sen Chen, Chia-Hung Chang, Yung-Jen Chuang
Robust model matching control of immune systems under environmental disturbances: Dynamic game approach
VC Lab, Dept. of Computer Science, NTHU, Taiwan
Bor-Sen Chen, Chia-Hung Chang, Yung-Jen Chuang

2. Outline Introduction Dynamic Systems Immune Systems
VC Lab, Dept. of Computer Science, NTHU, Taiwan

3. Introduction T cells B cells Antibodies Killer T-cells Helper T-cells
Cell death
Helper T-cells
Assist B-cells in maturing
B cells
Produce antibodies
Antibodies
Target pathogens by the antigens
VC Lab, Dept. of Computer Science, NTHU, Taiwan

4. Introduction
VC Lab, Dept. of Computer Science, NTHU, Taiwan

5. Introduction
VC Lab, Dept. of Computer Science, NTHU, Taiwan

6. Model of immune response
VC Lab, Dept. of Computer Science, NTHU, Taiwan

7. Model of immune response
VC Lab, Dept. of Computer Science, NTHU, Taiwan

8. Model of immune response
VC Lab, Dept. of Computer Science, NTHU, Taiwan

9. Model of immune response
VC Lab, Dept. of Computer Science, NTHU, Taiwan

10. Model of immune response
General disease dynamic model
VC Lab, Dept. of Computer Science, NTHU, Taiwan

11. Robust Therapeutic Control
Optima controlled cost function
Cost function did not include exogenous pathogens and environmental disturbances w(t)
Stengel, R.F., Ghigliazza, R., Kulkarni, N., Laplace, O., 2002a. Optimal control of innate immune response. Optim. Control Appl. Meth. 23, 91–104.
VC Lab, Dept. of Computer Science, NTHU, Taiwan

12. Robust Therapeutic Control
General disease dynamic model
↓↓↓compare
Tracking error must be as small as possible under environment disturbances w(t)
VC Lab, Dept. of Computer Science, NTHU, Taiwan

13. Robust Therapeutic Control
Worst-case effect on the tracking error can be minimized
Boyd, S.P., Linear Matrix Inequalities in System and Control Theory. Society for Industrial and Applied Mathematics, Philadelphia, PA.
POSITIVE!!
VC Lab, Dept. of Computer Science, NTHU, Taiwan

14. Robust Therapeutic Control
Minimax matching problem →minimax dynamic problem
VC Lab, Dept. of Computer Science, NTHU, Taiwan

15. Robust Therapeutic Control
Rewrite the minimax matching problem as
VC Lab, Dept. of Computer Science, NTHU, Taiwan

16. Robust Therapeutic Control
Solution
VC Lab, Dept. of Computer Science, NTHU, Taiwan
可喜可賀！

17. Computational simulation
Responses of Reference Model
VC Lab, Dept. of Computer Science, NTHU, Taiwan

18. Computational simulation
Consider stochastic disturbance
VC Lab, Dept. of Computer Science, NTHU, Taiwan

19. Computational simulation
Robust minimax matching control under continuous exogenous pathogens and environmental disturbances
VC Lab, Dept. of Computer Science, NTHU, Taiwan

20. Computational simulation
Minimax controls
VC Lab, Dept. of Computer Science, NTHU, Taiwan

21. Computational simulation
Side effects of durgs
VC Lab, Dept. of Computer Science, NTHU, Taiwan

22. Computational simulation
Self controls for drugs'’ side effects
VC Lab, Dept. of Computer Science, NTHU, Taiwan

23. Discussion Conventional optimal control
VC Lab, Dept. of Computer Science, NTHU, Taiwan

24. Discussion Conventional optimal control
VC Lab, Dept. of Computer Science, NTHU, Taiwan

25. Reference Uri Alon, An Introduction to Systems Biology, (2006)
R. Clark Robinson, An Introduction to Dynamical Systems, (2004)
VC Lab, Dept. of Computer Science, NTHU, Taiwan