Structured models of cell migration incorporating molecular binding processes

The dynamic interplay between collective cell movement and the various molecules involved in the accompanying cell signalling mechanisms plays a crucial role in many biological processes including normal tissue development and pathological scenarios such as wound healing and cancer. Information about the various structures embedded within these processes allows a detailed exploration of the binding of molecular species to cell-surface receptors within the evolving cell population. In this paper we establish a general spatio-temporal-structural framework that enables the description of molecular binding to cell membranes coupled with the cell population dynamics. We first provide a general theoretical description for this approach and then illustrate it with two examples arising from cancer invasion

Adaptive estimation and control algorithms for certain classes of large-scale sensor and actuator uncertainties

textThis dissertation considers the general problem of controlling dynamic systems subject to large-scale sensor and actuator uncertainties. The assumption is made that the uncertainty is limited to either pure rotation (i.e. special orthogonal matrix) or that each axis is rotated independently. Although uncertainty can appear in more general forms, this representation describes a ``net-effect'' when the ideal axes have become misaligned that is of fundamental importance to the control of numerous systems. Adaptive observers and controllers are introduced that guarantee perfect reference trajectory tracking even with the appearance of these large-scale uncertainties. The specific contributions of this dissertation are as follows: (I) the problem of rigid-body attitude tracking with vector measurements, unknown gyro bias, and unknown body inertia matrix is addressed for the first time. In this problem, the body attitude acts as unknown special orthogonal matrix (i.e. sensor uncertainty). A set of adaptive observers and an adaptive controller is presented that guarantees perfect tracking as well as convergence of the attitude and bias estimates through a Lyapunov stability analysis. (II) An adaptive observer is developed for the scenario where the control is pre-multiplied by an unknown constant scaling and rotation matrix which gives a non-affine representation of the uncertainty. The observer is shown to be convergent given a certain persistence of excitation condition on the input signal and using a smooth projection scheme on the estimate of the unknown scaling. In addition, the observer is combined with a stabilizing control to guarantee perfect tracking which establishes a separation like property. (III) The class of uncertainties where each axis of the control is independently misaligned is examined. The problem is split into studies of in-plane and out-of-plane misalignment angles given that they exhibit fundamental technical differences in establishing convergence. Where possible, rigorous stability proofs are given for a series of adaptive observers. The structure of the observers assure that the estimates do not introduce any singularities into the control problem other than those inherent from the misalignment geometry. The inherent singularities are avoided through the use of projection schemes which allow for extension to the control problem. This work represents the first significant effort to develop adaptive observers and controllers for this class of misalignments.Aerospace Engineerin