Premium
Application of numerical hill‐climbing in control of systems via Liapunov's direct method
Author(s) -
Bennett Howard A.,
Luus Rein
Publication year - 1971
Publication title -
the canadian journal of chemical engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.404
H-Index - 67
eISSN - 1939-019X
pISSN - 0008-4034
DOI - 10.1002/cjce.5450490523
Subject(s) - control theory (sociology) , hill climbing , nonlinear system , optimal control , climbing , mathematics , quadratic equation , state variable , state (computer science) , mathematical optimization , control (management) , computer science , engineering , physics , thermodynamics , algorithm , geometry , structural engineering , quantum mechanics , artificial intelligence
The procedure of determining the control effort which minimizes the forward difference of the quadratic function x(k) T Qx(k) combined with improving Q by numerical hill‐climbing is investigated to determine the feasibility of establishing time sub‐optimal control policies for both linear and nonlinear systems. For linear systems, Rosenbrock's hill‐climbing procedure is more efficient for improving Q than the method of Hooke and Jeeves; moreover it yields policies closer to the optimum when the number of state variables exceeds six. The “best” value of Q obtained by hill‐climbing depends on the initial choice of Q and the initial state of the system x (0). The evaluation, carried out with a linear gas absorber and a nonlinear continuous stirred tank reactor, shows that the combined sub‐optimal procedure yields results close to time‐optimal control with little computational effort.