Optimal switching control for drug therapy process in cancer chemotherapy. (English) Zbl 1403.92110
Summary: In this paper, the drug therapy problem in cancer chemotherapy is formulated as an optimal control problem of switched systems. In this problem, the modes switch under state-dependent. This is different from the existing optimal control problem of switched systems, in which the modes switch under time-dependent. Thus, the existing optimal control approaches of switched systems with time-dependent switching can not directly used to solve this Problem, and a new numerical computation method is required to develop for solving such problem. Firstly, based on introducing a binary function, relaxing the binary functions and including a penalty term on the relaxation, we obtain an equivalent optimal control problem of constrained nonlinear system. By using the time-scaling transformation, the smoothing technique, and the idea of \(l_1\) penalty function method, the equivalent optimal control problem is transformed into a nonlinear parameter optimization problem. Then, a gradient-based continuous filled function algorithm is developed for solving the nonlinear parameter optimization problem. Finally, a numerical example is used to illustrate our method is low time-consuming, has faster convergence speed, and yields a better objective function value than the existing algorithms.
MSC:
| 92C50 | Medical applications (general) |
| 93C30 | Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems) |
| 93C10 | Nonlinear systems in control theory |
| 93B17 | Transformations |
| 49N90 | Applications of optimal control and differential games |
| 90C20 | Quadratic programming |
| 93-04 | Software, source code, etc. for problems pertaining to systems and control theory |
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