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Function minimization and constraints
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addition admissible assumed assumption asymptotically stable automated design Brownian motion canonical equations closed-loop system coefficient matrices computational methods conjugate gradient method conjugate points control system convergence convex functions convex set corresponding defined denoted depicted in Figure derived design problems deterministic differential equations direction vector eigenvalues equality constraints equivalent example exists feedback control feedback gains filter flow graph formulation hence hessian holds inequality constraints introduced iteration Lagrange multiplier Lagrangian Laplace transform Lemma linear optimal control method of successive min-max method minimization Moreover necessary condition Newton-Raphson method nonsingular nonzero open-loop optimal forcing functions optimal gain control parameter optimization performance functional performance integral polynomial positive definite positive semi-definite Proof quadratic function Repeat Problem respect result selected solving Specifically steepest-descent stochastic Subroutines successive approximations successive substitutions sufficient conditions Suppose Table tangent space Td(s Theorem transfer function twice continuously differentiable variables weak relative minimum yields