<p>The main contributions in this thesis are advances in parametric programming. The thesis is divided into three parts; theoretical advances, application areas and constrained control allocation. The first part deals with continuity properties and the structure of solutions to convex parametric quadratic and linear programs. The second part focuses on applications of parametric quadratic and linear programming in control theory. The third part deals with constrained control allocation and how parametric programming can be used to obtain explicit solutions to this problem.</p>

The main contributions in this thesis are advances in parametric programming. The thesis is divided into three parts; theoretical advances, application areas and constrained control allocation. The first part deals with continuity properties and the structure of solutions to convex parametric quadratic and linear programs. The second part focuses on applications of parametric quadratic and linear programming in control theory. The third part deals with constrained control allocation and how parametric programming can be used to obtain explicit solutions to this problem.

This thesis is focused on individual wheel actuators in road vehicles intended for vehicle motion control. Particular attention is paid to electro-mechanical actuators and how they can contribute to improving vehicle dynamics and safety. The employment of individual wheel actuators at the vehicle's four corner results in a large degree of over-actuation. Over-actuation has a potential of exploiting the vehicle's force constraints at a high level and of controlling the vehicle more freely. One important reason for using over-actuated vehicles is their capability to assist the driver to experience the vehicle as desired. This thesis demonstrates that critical situations close to the limits can be handled more efficiently by over-actuation. To maximise the vehicle performance, all the available actuators are systematically exploited within their force constraints.  Therefore, force constraints for the individually controlled wheel are formulated, along with important restrictions that follow as soon as a reduction in the degrees of freedom of the wheel occurs. Particular focus is directed at non-convex force constraints arising from combined tyre slip characteristics. To evaluate the differently actuated vehicles, constrained control allocation is employed to control the vehicle. The allocation problem is formulated as an optimisation problem, which is solved by non-linear programming. To emulate realistic safety critical scenarios, highly over-actuated vehicles are controlled and evaluated by the use of a driver model and a validated complex strongly non-linear vehicle model. it is shown that, owing to the actuator redundancy, over-actuated vehicles possess an inherent capacity to handle actuator faults, with less need for extra hardware or case-specific fault-handling strategies. / QC 20100722

In this thesis we study a number of nonlinear control problems motivated by their appearance in flight control. The results are presented in a general framework and can also be applied to other areas. The two main topics are backstepping and control allocation. Backstepping is a nonlinear control design method that provides an alternative to feedback linearization. Here, backstepping is used to derive robust linear control laws for two nonlinear systems, related to angle of attack control and flight path angle control, respectively. The resulting control laws require less modeling information than corresponding designs based on feedback linearization, and achieve global stability in cases where feedback linearization can only be performed locally. Further, a method for backstepping control of a rigid body is developed, based on a vector description of the dynamics. We also discuss how to augment an existing nonlinear controller to suppress constant input disturbances. Two methods, based on adaptive backstepping and nonlinear observer design, are proposed. Control allocation deals with actuator utilization for overactuated systems. In this thesis we pose the control allocation problem as a constrained least squares problem to account for actuator position and rate constraints. Efficient solvers based on active set methods are developed with similar complexity to existing, approximate, pseudoinverse methods. A method for dynamic control allocation is also proposed which enables a frequency dependent control distribution among the actuators to be designed. Further, the relationship between control allocation and linear quadratic control is investigated. It is shown that under certain circumstances, the two techniques give the same freedom in distributing the control effort among the actuators. An advantage of control allocation, however, is that since the actuator constraints are considered, the control capabilities of the actuator suite can be fully exploited.

In this thesis, attitude control of small satellites with dissimilar actuator is studied and the effects of control allocation methods on maneuvering are examined in detail. Magnetorquers and reaction wheels are considered as the actuators of a modeled remote sensing -nadir pointing- small satellite. Matlab&reg / Simulink simulation models are developed to model the satellite dynamics and the actuators on the satellite. The simulations are based on conceptual RASAT satellite, and, for verification, orbit data is taken from BILSAT satellite that is operated by TUBITAK Space Research Institute. Basic satellite control modes are developed and tested to obtain nominal control. Actuator failures are analyzed for different possible cases. A control allocation method called Blended Inverse that was originally proposed for steering CMGs is applied to select the actuators to avoid actuator saturation and singularity transition. The performance of traditional pseudo inverse method is compared with the blended inverse method and simulation results are given and discussed. The superiority of blended inverse over pseudo inverse is demonstrated.

In the thesis, automatic flight control system is designed for Tilt Duct Unmanned Aerial Vehicle (UAV). The vehicle is a Vertical Take-Off Landing (VTOL) type with two symmetric rotors on the wings, one aft rotor on the aft body. It behaves like a helicopter but with higher speeds in forward flight. Transition flight of the aircraft from hover to cruise or take-off to forward flight is the primary concern of the thesis study with the nonlinearities and instabilities encountered, together with the over-actuated controls in this mode. A nonlinear simulation code is developed including nonlinear equations of motion together with the nonlinear aerodynamics, environmental eects, and rotor dynamics. Trim and linearization codes are also developed. Trim conditions for the transition flight phase are calculated for two different transition scenarios. Linear controllers are developed and nonlinear controller is designed for the transition mode. Nonlinear controller uses the state dependent Ricatti equation SDRE approach by using extended linearization. Two loop approach is used in order to increase controllability. In the inner loop, attitude rates are fed back and SDRE approach is used to calculate the feedback gain matrix online. In the outer loop, vehicle attitude is controlled using the eigenvalue assignment. Blended inverse algorithm based control allocation method is used in control of the over-actuated transition phase. This algorithm is shown to be quite effective among different methods in not only generating necessary forces needed for the control, but also allocating with more control authority on the desired actuator.

This dissertation introduces novel methods for solving highly challenging model- ing and control problems, motivated by advanced aerospace systems. Adaptable, ro- bust and computationally effcient, multi-resolution approximation algorithms based on Radial Basis Function Network and Global-Local Orthogonal Mapping approaches are developed to address various problems associated with the design of large scale dynamical systems. The main feature of the Radial Basis Function Network approach is the unique direction dependent scaling and rotation of the radial basis function via a novel Directed Connectivity Graph approach. The learning of shaping and rota- tion parameters for the Radial Basis Functions led to a broadly useful approximation approach that leads to global approximations capable of good local approximation for many moderate dimensioned applications. However, even with these refinements, many applications with many high frequency local input/output variations and a high dimensional input space remain a challenge and motivate us to investigate an entirely new approach. The Global-Local Orthogonal Mapping method is based upon a novel averaging process that allows construction of a piecewise continuous global family of local least-squares approximations, while retaining the freedom to vary in a general way the resolution (e.g., degrees of freedom) of the local approximations. These approximation methodologies are compatible with a wide variety of disciplines such as continuous function approximation, dynamic system modeling, nonlinear sig-nal processing and time series prediction. Further, related methods are developed for the modeling of dynamical systems nominally described by nonlinear differential equations and to solve for static and dynamic response of Distributed Parameter Sys- tems in an effcient manner. Finally, a hierarchical control allocation algorithm is presented to solve the control allocation problem for highly over-actuated systems that might arise with the development of embedded systems. The control allocation algorithm makes use of the concept of distribution functions to keep in check the "curse of dimensionality". The studies in the dissertation focus on demonstrating, through analysis, simulation, and design, the applicability and feasibility of these ap- proximation algorithms to a variety of examples. The results from these studies are of direct utility in addressing the "curse of dimensionality" and frequent redundancy of neural network approximation.

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The effective management of forces within heavy vehicles is essential for achieving desired performance outcomes. In this study, an auto-generated Model Predictive Control Allocation (MPCA) algorithm is presented. The controller is designed to distribute forces among individual actuators in a vehicle, focusing primarily on longitudinal forces while exploring lateral force dynamics. The approach integrates models of the actuators with vehicle dynamics, encompassing both point mass and dynamic vehicle models, within the controller framework. Through simulation, proof of the MPC's superior performance in reference tracking could be demonstrated, especially in comparison with baseline simulations employing force ratio split (FRS) and equal split (ES) distribution methods. Furthermore, findings show that it was possible to achieve a more energy efficient force distribution using the MPCs.

A comparison of two methods to deal with allocating controls for unattainable moments in an aircraft was performed using a testbed airframe that resembled an F/A-18 with a large control effector suite. The method of preserving the desired moment direction to deal with unattainable moments is currently used in a specific control allocator. A new method of prioritizing the pitch axis is compared to the moment-direction preservation. Realtime piloted simulations are completed to evaluate the characteristics and performance of these methods. A direct comparison between the method of preserving the moment direction by scaling the control solution vector and prioritizing the pitching moment axis is performed for a specific case. Representative maneuvers are flown with a highly unstable airframe to evaluate the ability to achieve the specific task. Flight performance and pilot interpretation are used to evaluate the two methods. Pilot comments and performance results favored the method of pitch-axis prioritization. This method provided favorable flight characteristics compared to the alternative method of preserving the moment direction for the specific tasks detailed in this paper. NOTE: An updated copy of this ETD was added on 09/28/2010. / Master of Science