Second-order method for optimal control problems with state constraints and piecewise-constant controls

Discusses a second-order algorithm for optimal control problems with state constraints. The authors show that without discretization of control variables the second order-method would require enormous computational effort unless an accessory problem (optimal control problem with state constraints itself) is solved at every iteration. Then, the authors propose an SQP type algorithm which, in general, can demand direction finding subproblems with the increasing number of constraints. However, under some easily satisfied regularity assumptions, the number of constraints can be bounded. Some numerical results illustrating the authors´ approach are also provided