Optimal Nonlinear Stochastic Control of Hysteretic Systems

• Published in: Journal of engineering mechanics Vol. 126; no. 10; pp. 1027 - 1032
• Main Authors: Zhu, W. Q, Ying, Z. G, Ni, Y. Q, Ko, J. M
• Format: Journal Article
• Language: English
• Published: Reston, VA American Society of Civil Engineers 01.10.2000
• Subjects: Applied sciences; Computer science; control theory; systems; Control theory. Systems; Exact sciences and technology; Optimal control; TECHNICAL PAPERS; Averaging method; Total energy; Itô equation; Random excitation; Non linear control; Stochastic method; Non linear system; Stochastic system; Stochastic programming; Hysteresis loop; Hamilton Jacobi equation; Optimal control; Diffusion process; Stochastic control; System with one degree of freedom
• ISSN: 0733-9399; 1943-7889
• DOI: 10.1061/(ASCE)0733-9399(2000)126:10(1027)

A strategy for optimal nonlinear stochastic control of hysteretic systems with parametrically and or externally random excitations is proposed and illustrated with an example of a single-degree-of-freedom system. A hysteretic system subject to random excitation is first replaced by a nonlinear nonhysteretic stochastic system, from which an Itô equation for the averaged total energy of the system as a 1D controlled diffusion process is derived by using the stochastic averaging method of energy envelope. For a given performance index, a Hamilton-Jacobi-Bellman equation is then established based on the stochastic dynamical programming principle and solved to yield the optimal control force. Finally, the statistics of the responses of uncontrolled and controlled systems and those of the optimal control force are predicted analytically. Comparison with the modified optimal polynomial controller indicates that the proposed strategy is more effective and efficient.