Vector interpolation functions which approximate electromagnetic vector fields are constructed in this thesis. These vector functions are to be used when the solution of Maxwell's equations involves an irrotational or solenoidal vector field. In addition the functions are chosen so that they can easily be used in the implementation of a finite element method. / Four bases are constructed. The first two span the spaces of solenoidal or irrotational two component vector polynomials of order one in two variables whereas the other two span the spaces of solenoidal or irrotational three component vector polynomials of order one in three variables. The vector polynomials are then used within the finite element method to approximate the two component current density J and electric field E over a conducting plate and the three component current density in a three dimensional wire.

The Banach spaces L(X, Y), K(X, Y), Lw*(X*, Y), and Kw*(X*, Y) are studied to determine when they contain the classical Banach spaces co or l ∞. The complementation of the Banach space K(X, Y) in L(X, Y) is discussed as well as what impact this complementation has on the embedding of co or l∞ in K(X, Y) or L(X, Y). Results concerning the complementation of the Banach space Kw*(X*, Y) in Lw*(X*, Y) are also explored and how that complementation affects the embedding of co or l ∞ in Kw*(X*, Y) or Lw*(X*, Y). The l p spaces for 1 ≤ p < ∞ are studied to determine when the space of compact operators from one l p space to another contains co. The paper contains a new result which classifies these spaces of operators. Results of Kalton, Feder, and Emmanuele concerning the complementation of K(X, Y) in L(X, Y) are generalized. A new result using vector measures is given to provide more efficient proofs of theorems by Kalton, Feder, Emmanuele, Emmanuele and John, and Bator and Lewis as well as a new proof of the fact that l ∞ is prime.

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In this work torque vectoring methods are used to compensate for a low performance steer-by-wire system. Currently a number of vehicle manufacturers are considering introducing steer-by-wire into their range of vehicles. Some of the key concerns for the manufacturers are safety and cost. The safety can be subdivided in the integrity of the steering system and the effect on handling. The focus of this study is the use of low cost steering actuators on a vehicle and identify its effects on the vehicle's handling response. The test vehicle is dune buggy modified to accommodate the low performance steer-by-wire system without a direct mechanical link between the steering wheel and the wheels and equipped with various sensors to data recording. In order to investigate the influence of torque vectoring system on the steer-by-wire, an eight degrees of freedom vehicle model in Matlab/Simulink has been developed. The eight degrees of freedom are longitudinal and lateral translations, yaw and roll motion and rotation of each wheel. The Matlab/Simulink model also includes the dynamics of the actuators, which is validated against the experimental data. The actuator was shown to have a bandwidth of less than 0.3 Hz. The eight degrees of freedom model's response was validated against experimental data for both steady state and transient response up to 0.5 g. The tyre forces and moments are implemented by using the Dugoff tyre model, which has been validated against experimentally measured data. The torque vectoring system uses the cascade approach based on a reference model, which uses a two degrees of freedom (bicycle model) to generate the reference signal for control purposes. The upper level yaw controller is based on the optimal control theory and uses the LQR (Linear-quadratic regulator) approach. The lower level wheel slip controller is based on a slidingmode structure and prevents tyre force saturation. The simulation results show that the vehicle augmented with the torque vectoring system outperforms the low performance steer-by-wire vehicle and also the vehicle with conventional steering arrangement.

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