This article addresses the problem of designing therapies for the myeloma bone disease that optimize in a systematic way a compromise between drug toxicity and tumor repression. For that sake, the techniques of optimal control are applied to the dynamics of tumor growth, and the necessary conditions of Pontryagin's minimum principle are solved using a numerical relaxation algorithm. A therapy to accelerate bone mass recovery is applied in parallel, based on a PI control rule. Since the optimal controller provides an open-loop control, it is turned into a feedback law by following a receding horizon strategy. For that sake, an optimal manipulated variable profile is first computed over a time horizon, but only the initial part of this function is applied. The whole optimization procedure is then repeated starting at a time instant that corresponds to the end of the previously applied control. 
Optimal and receding horizon control of tumor growth in myeloma bone disease