Nonlinear control and estimation techniques with applications to vision-based and biomedical systems

This dissertation is divided into four self-contained chapters. In Chapter 1, a new estimator using a single calibrated camera mounted on a moving platform is developed to asymptotically recover the range and the three-dimensional (3D) Euclidean position of a static object feature. The estimator also recovers the constant 3D Euclidean coordinates of the feature relative to the world frame as a byproduct. The position and orientation of the camera is assumed to be measurable unlike existing observers where velocity measurements are assumed to be known. To estimate the unknown range variable, an adaptive least squares estimation strategy is employed based on a novel prediction error formulation. A Lyapunov stability analysis is used to prove the convergence properties of the estimator. The developed estimator has a simple mathematical structure and can be used to identify range and 3D Euclidean coordinates of multiple features. These properties of the estimator make it suitable for use with robot navigation algorithms where position measurements are readily available. Numerical simulation results along with experimental results are presented to illustrate the effectiveness of the proposed algorithm. In Chapter 2, a novel Euclidean position estimation technique using a single uncalibrated camera mounted on a moving platform is developed to asymptotically recover the three-dimensional (3D) Euclidean position of static object features. The position of the moving platform is assumed to be measurable, and a second object with known 3D Euclidean coordinates relative to the world frame is considered to be available a priori. To account for the unknown camera calibration parameters and to estimate the unknown 3D Euclidean coordinates, an adaptive least squares estimation strategy is employed based on prediction error formulations and a Lyapunov-type stability analysis. The developed estimator is shown to recover the 3D Euclidean position of the unknown object features despite the lack of knowledge of the camera calibration parameters. Numerical simulation results along with experimental results are presented to illustrate the effectiveness of the proposed algorithm. In Chapter 3, a new range identification technique for a calibrated paracatadioptric system mounted on a moving platform is developed to recover the range information and the three-dimensional (3D) Euclidean coordinates of a static object feature. The position of the moving platform is assumed to be measurable. To identify the unknown range, first, a function of the projected pixel coordinates is related to the unknown 3D Euclidean coordinates of an object feature. This function is nonlinearly parameterized (i.e., the unknown parameters appear nonlinearly in the parameterized model). An adaptive estimator based on a min-max algorithm is then designed to estimate the unknown 3D Euclidean coordinates of an object feature relative to a fixed reference frame which facilitates the identification of range. A Lyapunov-type stability analysis is used to show that the developed estimator provides an estimation of the unknown parameters within a desired precision. Numerical simulation results are presented to illustrate the effectiveness of the proposed range estimation technique. In Chapter 4, optimization of antiangiogenic therapy for tumor management is considered as a nonlinear control problem. A new technique is developed to optimize antiangiogenic therapy which minimizes the volume of a tumor and prevents it from growing using an optimum drug dose. To this end, an optimum desired trajectory is designed to minimize a performance index. Two controllers are then presented that drive the tumor volume to its optimum value. The first controller is proven to yield exponential results given exact model knowledge. The second controller is developed under the assumption of parametric uncertainties in the system model. A least-squares estimation strategy based on a prediction error formulation and a Lyapunov-type stability analysis is developed to estimate the unknown parameters of the performance index. An adaptive controller is then designed to track the desired optimum trajectory. The proposed tumor minimization scheme is shown to minimize the tumor volume with an optimum drug dose despite the lack of knowledge of system parameters. Numerical simulation results are presented to illustrate the effectiveness of the proposed technique. An extension of the developed technique for a mathematical model which accounts for pharmacodynamics and pharmacokinetics is also presented. Futhermore, a technique for the estimation of the carrying capacity of endothelial cells is also presented.