Abstract :
In this paper, an efficient computation method is developed for solving a general class
of minmax optimal control problems, where the minimum deviation from the violation
of the continuous state inequality constraints is maximized. The constraint transcription
method is used to construct a smooth approximate function for each of the continuous
state inequality constraints. We then obtain an approximate optimal control problem
with the integral of the summation of these smooth approximate functions as its cost
function. A necessary condition and a sufficient condition are derived showing the
relationship between the original problem and the smooth approximate problem. We
then construct a violation function from the solution of the smooth approximate optimal
control problem and the original continuous state inequality constraints in such a way
that the optimal control of the minmax problem is equivalent to the largest root of
the violation function, and hence can be solved by the bisection search method. The
control parametrization and a time scaling transform are applied to these optimal control
problems. We then consider two practical problems: the obstacle avoidance optimal
control problem and the abort landing of an aircraft in a windshear downburst.
Keywords :
continuous state inequality constraints , constraint transcription , Control parametrization , time scaling , aircraft abort landing , windshear downburst , obstacle avoidance , minmax optimal control , computation method
