OF IMMUNE SYSTEMS UNDER
ENVIRONMENTAL DISTURBANCES:
DYNAMIC GAME APPROACH
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Bor-Sen Chen, Chia-Hung Chang, Yung-Jen Chuang
VC Lab, Dept. of Computer Science, NTHU,
Taiwan
ROBUST MODEL MATCHING CONTROL
OUTLINE
Introduction
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VC Lab, Dept. of Computer Science, NTHU, Taiwan
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Immune Systems
Dynamic Systems
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INTRODUCTION
T cells
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Killer T-cells
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Assist B-cells in maturing
B cells
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Cell death
Helper T-cells
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VC Lab, Dept. of Computer Science, NTHU, Taiwan
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Produce antibodies
Antibodies
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Target pathogens by the antigens
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INTRODUCTION
VC Lab, Dept. of Computer Science, NTHU, Taiwan
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INTRODUCTION
VC Lab, Dept. of Computer Science, NTHU, Taiwan
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MODEL OF IMMUNE RESPONSE
VC Lab, Dept. of Computer Science, NTHU, Taiwan
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MODEL OF IMMUNE RESPONSE
VC Lab, Dept. of Computer Science, NTHU, Taiwan
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MODEL OF IMMUNE RESPONSE
VC Lab, Dept. of Computer Science, NTHU, Taiwan
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MODEL OF IMMUNE RESPONSE
VC Lab, Dept. of Computer Science, NTHU, Taiwan
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MODEL OF IMMUNE RESPONSE
General disease dynamic model
VC Lab, Dept. of Computer Science, NTHU, Taiwan
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ROBUST THERAPEUTIC CONTROL
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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
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ROBUST THERAPEUTIC CONTROL
General disease dynamic model
↓↓↓compare
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Tracking error must be as small as possible
under environment disturbances w(t)
VC Lab, Dept. of Computer Science, NTHU, Taiwan
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ROBUST THERAPEUTIC CONTROL
Worst-case effect on the tracking error can be
minimized
Boyd, S.P., 1994. Linear Matrix Inequalities in System and Control Theory.
Society for Industrial and Applied Mathematics, Philadelphia, PA.
VC Lab, Dept. of Computer Science, NTHU, Taiwan
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ROBUST THERAPEUTIC CONTROL
Minimax matching problem
→minimax dynamic problem
VC Lab, Dept. of Computer Science, NTHU, Taiwan
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ROBUST THERAPEUTIC CONTROL
Rewrite the minimax matching problem as
VC Lab, Dept. of Computer Science, NTHU, Taiwan
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ROBUST THERAPEUTIC CONTROL
VC Lab, Dept. of Computer Science, NTHU, Taiwan
Solution
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COMPUTATIONAL SIMULATION
Responses of Reference Model
VC Lab, Dept. of Computer Science, NTHU, Taiwan
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COMPUTATIONAL SIMULATION
Consider stochastic disturbance
VC Lab, Dept. of Computer Science, NTHU, Taiwan
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COMPUTATIONAL SIMULATION
Robust minimax matching control under
continuous exogenous pathogens and
environmental disturbances
VC Lab, Dept. of Computer Science, NTHU, Taiwan
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COMPUTATIONAL SIMULATION
VC Lab, Dept. of Computer Science, NTHU, Taiwan
Minimax controls
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COMPUTATIONAL SIMULATION
Side effects of durgs
VC Lab, Dept. of Computer Science, NTHU, Taiwan
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COMPUTATIONAL SIMULATION
Self controls for drugs'’ side effects
VC Lab, Dept. of Computer Science, NTHU, Taiwan
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DISCUSSION
VC Lab, Dept. of Computer Science, NTHU, Taiwan
Conventional optimal control
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DISCUSSION
VC Lab, Dept. of Computer Science, NTHU, Taiwan
Conventional optimal control
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REFERENCE
VC Lab, Dept. of Computer Science, NTHU, Taiwan
Uri Alon, An Introduction to Systems Biology,
(2006)
 R. Clark Robinson, An Introduction to Dynamical
Systems, (2004)
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