Parametrization procedure solution of optimal control problems over spline spaces.
Thesis DisciplineElectrical Engineering
Degree GrantorUniversity of Canterbury
Degree NameDoctor of Philosophy
In this thesis we report on investigations into the numerical solution of deterministic, continuous-time optimal control problems via parametrization techniques. These methods involve the linear expansion of one or more problem variables (i.e. control, state, co-state) in terms of basis functions. In this way the original optimal control problem can be reduced to a finite-dimensional minimization problem which may be solved numerically using standard mathematical programming algorithms. Two specific techniques are considered here; we refer to them as the control parametrization (CP) and the state parametrization procedures (SP). As their names imply, the CP and SP procedures involve the expansion of the control and state, respectively, in terms of basis functions. The importance of splines in the interpolation and approximation of functions is well known. In this research the viability of employing splines in conjunction with the above mentioned parametrization procedures is examined. The rates of convergence of the CP and SP solutions are also analysed; under appropriate smoothness conditions, explicit error bounds are derived for the control, state and cost functional convergences. Numerical results supporting the validity of these error bounds are presented. All the numerical computations in this research have been done on the University of Canterbury Burroughs 6700 / 7700 machine using single-precision arithmetic.