Table 1 Dimensions of the resulting non-linear programming problems

Differential state variables p _x

4·(n _time−1)·(m _ext+1)

Algebraic state variables p _z

4·(n _time−1)·n _irr

Spline parameters p _u

n _g+d·(k+1)

Internal knot locations t _knot

n _g

Initial values x ₀

m _ext+1

K matrix values

n·d

Equality constraints

Differential state collocation constraints

3·(n _time−1)·(m _ext+1)

Differential state continuity constraints

(n _time−2)·(m _ext+1)

Algebraic state collocation constraints

(3·(n _time−1)+1)·n _irr

Algebraic state continuity constraints

(n _time−2)·(n _irr)

Initial value constraints

m _ext+1

K null space constraints

m _int·d

K orthogonality constraints

$\frac{d·(d+1)}{2}$