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Stochastic non-minimal state space control with application to automated drug delivery

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This paper shows how a standard proportional-integral-plus controller, based on a non-minimal state space (NMSS) design, can be extended to reduce the effects of measurement noise and so yield smoother control inputs for automated drug delivery control applications. Use of a NMSS model for state variable feedback control design, in which all the states are based on the directly measured input and output variables, removes the need for state estimation. Nonetheless, a stochastic NMSS form, with a Kalman filter, can optionally be introduced to reduce the effect of measurement noise and so yield smoother control inputs. In this case, the Kalman filter attenuates measurement noise but does not address state disturbances. In this article, we propose a modification to the stochastic NMSS control system to enable the elimination of such state disturbances. This involves further extending the non-minimal state vector to include additional terms based on the innovations. We compare the deterministic, stochastic and extended stochastic NMSS controllers via a simulation of the control of anaesthesia using propofol.