Solution of the Bang-Bang Boundary Value Problem for Nth-Order Systems with Complex Eigenvalues

An algorithm for solving the bang-bang problem for an nth-order single-input system of complex eigenvalues is given. The method assumes a bang-bang control profile with given limits and a given number of switches. The solution, if it exists, is found by making an initial guess at the control profile from a knowledge of the system and determining what changes to it must be made to attain the desired final condition. A first-order method, which works for fairly accurate initial guesses, is given, supplemented by higher-order approaches that are useful when an accurate initial guess is impossible. Also, a simple third-order example is solved.