Constant-ratio trajectories in optimal control systems

Abstract

For a plant consisting of pure integrators and for certain performance indices the optimal saturating control input can have an infinite number of switches. If the time-interval between the ith and (i + l)th switches is τ _i , for some state trajectories the ratio τ _i+1 / τ _i is independent of i; these are termed constant-ratio trajectories. In the present paper methods are described for computing with high precision the parameters of constant-ratio trajectories. Results are obtained for plants of up to 16th order. An analogy between constant-ratio trajectories and the oscillatory modes of linear optimal systems is supported by these results.