Online regulations of low order systems under bounded control

Abstract

Time-optimal solutions provide us with the fastest means to regulate a system in presence of input constraints. This advantage of time-optimal control solutions is offset by the fact that their real-time implementation involves computationally intensive iterative techniques. Moreover, time-optimal controls depend on the initial state and have to be recalculated for even the slightest perturbation. Clearly time-optimal controls are not good candidates for online regulation. Consequently, the search for alternatives to time-optimal solutions is a very active area of research. The work described here is inspired by the simplicity of optimal-aim concept. The "optimal-aim strategies" provide online regulation in presence of bounded inputs with minimal computational effort. These are based purely on state-space geometry of the plant and are inherently adaptive in nature. Optimal-aim techniques involve aiming of trajectory derivative (or the state velocity vector) so as to approach the equilibrium state in the best possible manner. This thesis documents the efforts to develop an online regulation algorithm for systems with input constraints. Through a number of hypotheses focussed on trying to reproduce the exact time-optimal solution, the diffculty associated with this task is demonstrated. A modification of optimal-aim concept is employed to develop a novel regulation algorithm. In this algorithm, aim directions are chosen in a special manner to generate the time-optimal control approximately. The control scheme thus developed is shown to be globally stabilizing for systems having eigenvalues in the CLHP (closed left half-plane). It is expected that this method or its modifications can be extended to higher dimensional systems as a part of future research. An alternative control algorithm involving a simple state-space aiming concept is also developed and discussed.