Optimal Preview Control of Markovian Jump Linear Systems

In this paper, we investigate the design of controllers, for discrete-time Markovian jump linear systems, that achieve optimal reference tracking in the presence of preview (reference look-ahead). For a quadratic cost and given a reference sequence, we obtain the optimal solution for the full information case. The optimal control policy consists of the additive contribution of two terms: a feedforward term and a feedback term. We show that the feedback term is identical to the standard optimal linear quadratic regulator for Markovian jump linear systems. We provide explicit formulas for computing the feedforward term, including an analysis of convergence

Design of optimal servomechanisms for Markovian jump linear systems (First Draft)

In this paper we investigate the design of controllers, for discrete-time Markovian jump linear systems, that achieve optimal reference tracking in the presence of preview. In particular, given a reference sequence, we obtain the optimal control law for the fully observed case, while the output feedback case is also briefly discussed. We provide the optimal control law for the infinite and finite optimization-horizon cases. The optimal control policy consists of the additive contribution of two terms: a feedforward term and a feedback term which is identical to the standard LQR solution. We provide explicit formulas for computing the feedforward term, while establishing a comparison with the internal model principle

Radiotherapy Cancer Treatment: Investigating Real-Time Position and Dose Control, the Sensor-Delayed Plant Output Estimation Problem, and the Nonovershooting Step Response Problem

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

Limitations on maximal tracking accuracy

This paper studies optimal tracking performance issues pertaining to finite-dimensional, linear, time-invariant feedback control systems. The problem under consideration amounts to determining the minimal tracking error between the output slid reference signals of a feedback system, attainable by all possible stabilizing compensators. An integral square error criterion is used as a measure for the tracking error, and explicit expressions are derived for this minimal trucking error with respect to step reference signals. It is shown that plant nonminimum phase zeros have a negative effect on a feedback system's ability to reduce the tracking error, and that in a multivariable system this effect results in a way depending on not only the zero locations, but also the zero directions. It is also shown that if unity feedback structure is used for tracking purposes, plant nonminimum phase zeros and unstable poles can together play a particularly detrimental role in the achievable tracking performance, especially when the zeros and poles are nearby and their directions are closely aligned. On the other hand, if a two-parameter controller structure is used, the achievable tracking performance depends only on the plant nonminimum phase zeros