The covector mapping principle is a special case of Riesz' representation theorem, which is a fundamental theorem in functional analysis. The name was...

basic pseudospectral method for optimal control is based on the covector mapping principle. Other pseudospectral optimal control techniques, such as the...

solution. The output dual is computed by an application of the covector mapping principle. DIDO implements a spectral algorithm based on pseudospectral...

beginning. For more details see Pontryagin's maximum principle. Adjoint equation Covector mapping principle Lagrange multiplier Kamien, Morton I.; Schwartz...

The operations can be made commutative by an application of the covector mapping principle. A continuous-time optimal control problem is information rich...

pseudospectral optimal control. In 2001, Ross and Fahroo announced the covector mapping principle, first, as a special result in pseudospectral optimal control...

Bang–bang control — control that switches abruptly between two states Covector mapping principle Differential dynamic programming — uses locally-quadratic models...

smooth, or real-analytic according as g. The mapping Sg, which associates to every vector field on M a covector field on M gives an abstract formulation of...

pseudospectral method Ross–Fahroo pseudospectral methods Ross–Fahroo lemma Covector mapping principle Ross, I. M.; Karpenko, M. (2012). "A Review of Pseudospectral...

V^{*}\times V\to F} given by evaluating a covector on a vector; the order of the domain vector spaces here reflects the covector/vector distinction. The inner product...

inverse of the change of basis. In contrast, the components, wi, of a covector (or row vector), w, transform with the matrix R itself, w ^ i = w j R i...

in a more informative form by introducing the following concepts: The covector α ξ = α i ( x , ξ ) d x i | x ∈ T x ∗ M {\displaystyle \alpha _{\xi }=\alpha...

structure of a symplectic manifold. Cotangent vectors are sometimes called covectors. One can also define the cotangent bundle as the bundle of 1-jets of functions...

To compute the curvature tensor, we take the exterior derivative of the covector fields making up our coframe: d σ 1 = p y exp ⁡ ( p ) d y ∧ d x = − ( p...