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Optimization of a Simple Servomechanism
State Representation of Systems
Calculus of Variations
5 other sections not shown
adjoint assume boundary conditions calculus of variations Chapter characteristic equation chart circle column components constraint Control Systems corresponding cost defined by Equation diagram differential equation discrete-time dynamic programming eigenvalues eigenvectors equal Euler-Lagrange equation evaluations expression Fibonacci final value find the value first-order given by Equation Hamiltonian illustrate initial value input vector instant integral squared error interval Lagrange multiplier Laplace transform let us consider linear system matrix exp maximization maximum principle maximum value method minimum norm obtain one-stage process optimal control input optimal control problem optimal input optimal trajectory origin orthogonal output phase plane possible quantity relationship result Riccati equation right-hand endpoint satisfied scalar second-order sequence servomechanism shown in Fig side of Equation solved specified Substituting Equation Suppose switching curve transfer the system transition matrix transversality condition unimodal function variable x0 vector space vector-matrix voltage written zero