Optimal Control

by Heinz Schättler (Author), Urszula Ledzewicz (Author)
Applies geometric optimal control to real life problems arising in cancer research, for the first time published in book form
Combines rigorous mathematical analysis with biomedical background and interpretations
Detailed complete solutions of optimal control problems for mathematically challenging, up-to-date biomedical models
Outcomes of elaborate constructions of solutions provide insights into design of optimal protocols and at the same time are great illustrations of the power of geometric methods

This monograph develops a framework for time-optimal control problems, focusing on minimal and maximal time-optimal controls for linear-controlled evolution equations. Its use in optimal control provides a welcome update to Fattorini’s work on time-optimal and norm-optimal control problems. By discussing the best way of representing various control problems and equivalence among them, this systematic study gives readers the tools they need to solve practical problems in control.

This monograph develops a framework for time-optimal control problems, focusing on minimal and maximal time-optimal controls for linear-controlled evolution equations. Its use in optimal control provides a welcome update to Fattorini’s work on time-optimal and norm-optimal control problems. By discussing the best way of representing various control problems and equivalence among them, this systematic study gives readers the tools they need to solve practical problems in control.

Optimal control deals with the problem of finding a control law for a given system such that a certain optimality criterion is achieved. An optimal control is a set of differential equations describing the paths of the control variables that minimize the cost functional.