Singular and non-singular control trajectories of agricultural and (bio) chemical processes may need to be recalculated from time to time for use in closed-loop optimal control, because of unforeseen changes in state values and noise. This is time consuming. As an alternative, in this paper, numerical, nonlinear, static state feedback laws are developed for optimal control on the singular arc t...

We describe the structure of optimal trajectories for a mathematical model for minimizing the tumor volume under anti-angiogenic treatment. The model under consideration was developed by Hahnfeldt, Panigrahy, Folkman and Hlatky in [6] and has an optimal singular arc that determines the form of optimal protocols. The most typical scenario of optimal controls is given by first giving full dose tr...

A new form of the equations of motion for a spacecraft with single gimbal control-moment gyros (CMG) is developed using a momentum approach. This set of four vector equations describing the rotational motion of the system is of order 2N + 7, where N is the number of CMGs. The control input is an N £ 1 column vector of torques applied to the gimbal axes. A modiŽ cation to a singularity robust Ly...

Mathematical models for cancer treatment that include immunological activity are considered as an optimal control problem with an objective that is motivated by a separatrix of the uncontrolled system. For various growth models on the cancer cells the existence and optimality of singular controls is investigated. For a Gompertzian growth function the optimal synthesis is described.

We present a framework for the direct discretization of the input/output map of dynamical systems governed by linear partial differential equations with distributed inputs and outputs. The approximation consists of two steps. First, the input and output signals are discretized in space and time, resulting in finite dimensional spaces for the input and output signals. These are then used to appr...