Computation of optimal inputs and trajectories in linear regulators with energy constraints by using Warner's a logorithm

Abstract

In solving a linear regulator problem subjected to the integral type of energy constraint, the classical method requires that the proper magnitude of Lagrangian multiplier should be determined by a trial-and-error procedure. In this work, the Lagrangian multiplier is introduced as a state variable and a method to solve the isoperimetric problem is formulated by using Warner's algorithm. The new method essentially leads to evaluation of a two-point boundary value problem, requiring a far smaller number of differential equations to be solved than the Newton-Raphson-Kan torovich method and ensuring a faster convergence rate by adopting Warner's algorithm It also features the simultaneous computation of optimal inputs and trajectories. The optimal inputs and trajectories subjected to integral constraint are illustrated using a first-order linear dynamic system as an example.