EFFICIENT SEQUENTIAL QUADRATIC-PROGRAMMING IMPLEMENTATIONS FOR EQUALITY-CONSTRAINED DISCRETE-TIME OPTIMAL-CONTROL

Efficient sequential quadratic programming (SQP) implementations are p resented for equality-constrained, discrete-time, optimal control prob lems. The algorithm developed calculates the search direction for the equality-based variant of SQP and is applicable to problems with eithe r fixed or free final time. Problem solutions are obtained by solving iteratively a series of constrained quadratic programs. The number of mathematical operations required for each iteration is proportional to the number of discrete times N. This is contrasted by conventional me thods in which this number is proportional to N-3. The algorithm resul ts in quadratic convergence of the iterates under the same conditions as those for SQP and simplifies to an existing dynamic programming app roach when there are no constraints and the final time is fixed. A sim ple test problem and two application problems are presented. The appli cation examples include a satellite dynamics problem and a set of brac histochrone problems involving viscous friction.