On the shooting algorithm for partially-affine optimal control problems with control constraints

Resumo

where the state x is governed by an ODE determined by the functions f0 , fi : Rn → Rn that is partially-affine in the controls, this is, it has two types of controls: v that enters linearly and u, nonlinearly; the functions ηj : Rn ×Rn → R describe the constraints in the endpoints of x; the controls u and v are taken in the Lebesgue spaces U := L∞ ([0, T ]; Rl ) and V := L∞ ([0, T ]; Rm ), respectively; and φ : R2n → R is the cost function to be minimized. [...]