Performance limitations in feedback control systems with application to radiotherapy

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External radiotherapy is a cancer treatment process where external high-energy x-ray beams are used to eradicate tumor cells.  Recently, the applicant and other researchers have introduced feedback control into the radiotherapy process so that the x-ray beam tracks the position of the tumor as it moves; movement is caused by a number of processes, including breathing, heart beat, and changes in the gastrointestinal tract.  Advantages of the feedback scheme include a reduction in side effects, more accurate radiation dose delivery to the tumor, and a reduction in treatment time.  The radiotherapy research has revealed deficiencies in current control engineering knowledge, and has inspired research in several directions, including the direction of the proposed research.  The basic question that the proposed research seeks to answer is:  are there any limitations on what can be done using feedback control?  Understanding the existence and nature of such performance limitations is important because the knowledge helps engineers avoid trying to solve impossible problems, and aids engineers in modifying problems to overcome performance limitations that otherwise cannot be overcome.  The proposed research will focus on several aspects of controller performance.  First, the issue of "tracking" is addressed:  is there a limit to how well the x-ray beam can track the tumor?  Second, the issue of "disturbance rejection" is dealt with:  if the patient moves on the treatment table, is there any fundamental reason why the tumor tracking system should not be able to accommodate the movement?  Finally, the issue of "robustness" is studied:  how much knowledge about the patient's tumor dynamics must be known for treatment to be effective?   Several potential causes for the existence of performance limitations will be considered, including time delays, instabilities in the system, and controller structure.  Although motivated by and applied specifically to radiotherapy, the theoretical work in the proposed research is general; indeed, almost any system that uses feedback control (airplanes, automobiles, nuclear reactors, distillation columns, rockets, etc.) can potentially benefit from the work.