@MISC{Kaya_computationsand, author = {C Yalcin Kaya and J. Lyle Noakes}, title = {Computations And Time-Optimal Controls}, year = {} }

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Abstract

Introduction In control systems, one of the most common types of input function is the piecewise-constant function, where a sequence of constant inputs is used to control a given system, with appropriate switchings. For instance, in the aerodynamic control of some rocket vehicles, the tail fins are suitably deflected to several angular positions to achieve the necessary control action. This type of input results in a concatenation of a sequence of constant-input trajectories, or arcs. In the case when the input is bounded, a most frequently encountered type of piecewise-constant input is bang--bang, which switches between the upper and lower bounds of the control input. It is a well-known fact that the nonsingular time-optimal control solution of linear-analytic systems with bounded control inputs is the bang--bang control. The bang--bang solution is also encountered in other optimal control problems 2 . This situation arises especially when the hamiltonian is