Constraint aggregation based numerical optimal control

A numerical optimal control problem containing state and control constraints is discussed based on the constraint aggregation and Pontryagin maximal principle. First, a Control Vector Parameterization (CVP) method is used to convert the original optimal control problem into a nonlinear programming problem. Then, a Kreisselmeier-Steinhauser(KS) function is applied to lump all state constraints into a final time constraint, the gradients of object function and constraint are obtained by solving the adjoint equations. Finally, the numerical solution is obtained through Sequential Quadratic Programming (SQP) method. The smoothness of the constraint decreases after KS function aggregation, to this problem, a self-adaptive constraint aggregation method is presented. The method can effectively decrease numerical computation without reducing the optimization precision. Simulation examples demonstrate the effectiveness of this method.