Cancer Therapy Optimization
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In this chapter, the method proposed to obtain suboptimal impulsive control strategies is applied to design tumor suppression therapies. First, it is assumed that the impulses are applied at a priori decided time instants. In a latter stage, the concept of minimum attention control is used to vary the time intervals between consecutive samples in order to increase therapeutic activity in periods during which cancer therapy is more intense, thereby reducing toxic effects in other periods. This strategy is obtained by modifying the functional being minimized to yield the control actions. Since the above control laws are open-loop, a closed-loop strategy is obtained by combining them with a receding horizon strategy. Accordingly, after obtaining a candidate optimal control impulsive sequence for a given time horizon, starting at the current time, only the first impulse of this sequence is applied, the whole optimization process being repeated at the time schedules to apply the next impulse, starting from the state at that time. As expected, this strategy improves the response in the face of disturbances.
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