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Conjugate Gradient Descent
The Gradient of the Cost Functional for Some Common
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adjoint system assumed bang-bang control basic bilinear CG descent choose chosen compensator conjugate descent conjugate gradient descent conjugate w.r.t. continuous function continuous function input control system convergence cost contours cost criterion cost functional cycle DC motor defined descent directions descent method descent sequence desired differential equations element evaluated Example F(xi field voltage Figure find the gradient functional F gives gradient methods hence Hilbert space identity matrix initial condition initial guess interval let us consider linear operator magnitude minimizes minimum n x n norm obtained output shaft position plant positive definite precondition quadratic functional random number response result satisfies scalar product scaling matrix second derivative matrix shown in Fig simulation diagram solution steepest descent step stochastic inputs system differential equations Taylor series test signal Theorem tracking variable vector x(tf zero