For over a century, physicians have prescribed x-ray radiation to destroy or impede the growth of cancerous tumours. Modern radiation therapy machines shape the radiation beam to balance the competing goals of maximizing irradiation of cancerous tissue and minimizing irradiation of healthy tissue, an objective complicated by tumour motion during the treatment and errors positioning the patient to align the tumour with the radiation beam. Recent medical imaging advances have motivated interest in using feedback during radiation therapy to track the tumour in real time and mitigate these complications. This thesis investigates how real-time feedback control can be used to track the tumour and focus the radiation beam tightly around the tumour. Improving on these results, a feedback control system is proposed for intensity modulated radiation therapy which allows a non-uniform radiation dose to be applied to the tumour. Motivated by the results of the proposed control systems, this thesis also examines two theoretical control problems: estimating the output of an unknown system when a sensor delay prevents its direct measurement, and designing a controller to provide an arbitrarily fast nonovershooting step response.

For over a century, physicians have prescribed x-ray radiation to destroy or impede the growth of cancerous tumours. Modern radiation therapy machines shape the radiation beam to balance the competing goals of maximizing irradiation of cancerous tissue and minimizing irradiation of healthy tissue, an objective complicated by tumour motion during the treatment and errors positioning the patient to align the tumour with the radiation beam. Recent medical imaging advances have motivated interest in using feedback during radiation therapy to track the tumour in real time and mitigate these complications. This thesis investigates how real-time feedback control can be used to track the tumour and focus the radiation beam tightly around the tumour. Improving on these results, a feedback control system is proposed for intensity modulated radiation therapy which allows a non-uniform radiation dose to be applied to the tumour. Motivated by the results of the proposed control systems, this thesis also examines two theoretical control problems: estimating the output of an unknown system when a sensor delay prevents its direct measurement, and designing a controller to provide an arbitrarily fast nonovershooting step response.