This thesis is concerned with large-scale systems of Ordinary Differential Equations that model Biomolecular Reaction Networks (BRNs) in Systems and Synthetic Biology. It addresses the strategies of model reduction and decomposition used to overcome the challenges posed by the high dimension and stiffness typical of these models. A number of developments of these strategies are identified, and their implementation on various BRN models is demonstrated. The goal of model reduction is to construct a simplified ODE system to closely approximate a large-scale system. The error estimation problem seeks to quantify the approximation error; this is an example of the trajectory comparison problem. The first part of this thesis applies semi-definite programming (SDP) and dissipativity theory to this problem, producing a single a priori upper bound on the difference between two models in the presence of parameter uncertainty and for a range of initial conditions, for which exhaustive simulation is impractical. The second part of this thesis is concerned with the BRN decomposition problem of expressing a network as an interconnection of subnetworks. A novel framework, called layered decomposition, is introduced and compared with established modular techniques. Fundamental properties of layered decompositions are investigated, providing basic criteria for choosing an appropriate layered decomposition. Further aspects of the layering framework are considered: we illustrate the relationship between decomposition and scale separation by constructing singularly perturbed BRN models using layered decomposition; and we reveal the inter-layer signal propagation structure by decomposing the steady state response to parametric perturbations. Finally, we consider the large-scale SDP problem, where large scale SDP techniques fail to certify a system’s dissipativity. We describe the framework of Structured Storage Functions (SSF), defined where systems admit a cascaded decomposition, and demonstrate a significant resulting speed-up of large-scale dissipativity problems, with applications to the trajectory comparison technique discussed above.

Inertial Measurement Unit (IMU) and Global Positioning System (GPS) receivers are sensors that are widely used for land vehicle navigation. GPS receivers provide position and/or velocity data to any user on the Earth&rsquo / s surface independent of his position. Yet, there are some conditions that the receiver encounters difficulties, such as weather conditions and some blockage problems due to buildings, trees etc. Due to these difficulties, GPS receivers&rsquo / errors increase. On the other hand, IMU works with respect to Newton&rsquo / s laws. Thus, in stark contrast with other navigation sensors (i.e. radar, ultrasonic sensors etc.), it is not corrupted by external signals. Owing to this feature, IMU is used in almost all navigation applications. However, it has some disadvantages such as possible alignment errors, computational errors and instrumentation errors (e.g., bias, scale factor, random noise, nonlinearity etc.). Therefore, a fusion or integration of GPS and IMU provides a more accurate navigation data compared to only GPS or only IMU navigation data. v In this thesis, loosely coupled GPS/IMU integration systems are implemented using feed forward and feedback configurations. The mechanization equations, which convert the IMU navigation data (i.e. acceleration and angular velocity components) with respect to an inertial reference frame to position, velocity and orientation data with respect to any desired frame, are derived for the geographical frame. In other words, the mechanization equations convert the IMU data to the Inertial Navigation System (INS) data. Concerning this conversion, error model of INS is developed using the perturbation of the mechanization equations and adding the IMU&rsquo / s sensor&rsquo / s error model to the perturbed mechanization equation. Based on this error model, a Kalman filter is constructed. Finally, current navigation data is calculated using IMU data with the help of the mechanization equations. GPS receiver supplies external measurement data to Kalman filter. Kalman filter estimates the error of INS using the error mathematical model and current navigation data is updated using Kalman filter error estimates. Within the scope of this study, some real experimental tests are carried out using the software developed as a part of this study. The test results verify that feedback GPS/INS integration is more accurate and reliable than feed forward GPS/INS. In addition, some tests are carried out to observe the results when the GPS receiver&rsquo / s data lost. In these tests also, the feedback GPS/INS integration is observed to have better performance than the feed forward GPS/INS integration.

In this study, a parametric model for a main battle tank electric gun turret drive system stabilization controller has been developed. Main scope was the study of the muzzle deviation due to barrel flexibility. Traverse and elevation dynamics has been modeled to include the drive-line and barrel flexibilities. Order of the models has been kept large enough to cover the frequencies dominant in the interest scope but at the same time low enough to create a parametric model which can be used in real-time fire control computers. Therefore a 5-dof elevation and a 7-dof traverse models have been implemented. These models have been used to design a classical feedback and feedforward controllers which performed good enough to meet 0.5mrad stabilization accuracies. After satisfactory results have been obtained from the stabilization controller, a special coincidence algorithm has been implemented by time-series analysis of the disturbance signal which is constantly being measured by the feedforward gyro. Necessity of predicting the future muzzle angular orientation due to the latency in fire is discussed and by using autoregressive modeling of the disturbance signal, future values of the disturbance signal has been entered into the observer model. The prediction horizon has been set to the time delay value between the trigger is pulled by the gunner and the ammunition exit from the muzzle. By checking the future coincidence within a very narrow windowing (0.05mrad) a 100% first round hit probability in theory has been achieved. This is assured since the coincidence inhibited the fire signals which were to miss the aiming point with a large error.

This doctoral study aims to develop a methodology for use in determining aerodynamic models and parameters from actual flight test data for different types of autonomous flight vehicles. The stepwise regression method and equation error method are utilized for the aerodynamic model identification and parameter estimation. A closed loop aerodynamic parameter estimation approach is also applied in this study which can be used to fine tune the model parameters. Genetic algorithm is used as the optimization kernel for this purpose. In the optimization scheme, an input error cost function is used together with a final position penalty as opposed to widely utilized output error cost function. Available methods in the literature are developed for and mostly applied to the aerodynamic system identification problem of piloted aircraft / a very limited number of studies on autonomous vehicles are available in the open literature. This doctoral study shows the applicability of the existing methods to aerodynamic model identification and parameter estimation problem of autonomous vehicles. Also practical considerations for the application of model structure determination methods to autonomous vehicles are not well defined in the literature and this study serves as a guide to these considerations.