Optimization and Engineering

, Volume 15, Issue 1, pp 119-136

First online:

Dynamic programming approach to the numerical solution of optimal control with paradigm by a mathematical model for drug therapies of HIV/AIDS

  • Bao-Zhu GuoAffiliated withAcademy of Mathematics and Systems Science, Academia SinicaSchool of Computational and Applied Mathematics, University of the Witwatersrand
  • , Bing SunAffiliated withSchool of Mathematics, Beijing Institute of TechnologySchool of Computational and Applied Mathematics, University of the Witwatersrand Email author 

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In this paper, we present a new numerical algorithm to find the optimal control for the general nonlinear lumped systems without state constraints. The dynamic programming-viscosity solution (DPVS) approach is developed and the numerical solutions of both approximate optimal control and trajectory are produced. To show the effectiveness and efficiency of new algorithm, we apply it to an optimal control problem of two types of drug therapies for human immunodeficiency virus (HIV)/acquired immune deficiency syndrome (AIDS). The quality of the obtained optimal control and the trajectory pair is checked through comparison with the costs under the arbitrarily selected different controls. The results illustrate the effectiveness of the algorithm.


Optimal control Viscosity solution Dynamic programming Numerical solution