Non-linear stochastic optimal control of acceleration parametrically excited systems

Abstract

Acceleration parametrical excitations have not been taken into account due to the lack of physical significance in macroscopic structures. The explosive development of microtechnology and nanotechnology, however, motivates the investigation of the acceleration parametrically excited systems. The adsorption and desorption effects dramatically change the mass of nano-sized structures, which significantly reduces the precision of nanoscale sensors or can be reasonably utilised to detect molecular mass. This manuscript proposes a non-linear stochastic optimal control strategy for stochastic systems with acceleration parametric excitation based on stochastic averaging of energy envelope and stochastic dynamic programming principle. System acceleration is approximately expressed as a function of system displacement in a short time range under the conditions of light damping and weak excitations, and the acceleration parametrically excited system is shown to be equivalent to a constructed system with an additional displacement parametric excitation term. Then, the controlled system is converted into a partially averaged Itô equation with respect to the total system energy through stochastic averaging of energy envelope, and the optimal control strategy for the averaged system is derived from solving the associated dynamic programming equation. Numerical results for a controlled Duffing oscillator indicate the efficacy of the proposed control strategy.

Keywords:

• non-linear stochastic optimal control
• acceleration parametrically excited systems
• stochastic averaging of energy envelope
• stochastic dynamic programming principle

Additional information

Funding

This study was supported by the National Natural Science Foundation of China [grant number 11025211], [grant number 11302064], [grant number 11202181] and the special fund for the Doctoral Program of Higher Education of China [grant number 20110101110050], [grant number 20120101120171].

Notes on contributors

Yong Wang

Yong Wang received his PhD degree in solid mechanics from Zhejiang University for his work on robust control of uncertain quasi-Hamiltonian systems. He spent about two years at Tsinghua University and Arizona State University to work on vibration energy harvesting technique. He is now an associate professor at Zhejiang University in applied mechanics. His research interests include probabilistic structural dynamics, vibration control and modal testing.

Xiaoling Jin

Xiaoling Jin received her PhD degree in solid mechanics from Zhejiang University. She was a postdoctoral researcher in the Department of Electronic Engineering, City University of Hong Kong, and was a visiting fellow in the School of Mechanical and Manufacturing Engineering, The University of New South Wales, from June 2009 to August 2011. Now, she is an associate professor at Zhejiang University. Her research interests lie in the areas of non-linear stochastic dynamics and control, complex networks and tribology.

Zhilong Huang

Zhilong Huang received his MSc degree in solid mechanics from Peking University and the PhD degree in solid mechanics from Zhejiang University. Currently, he is a professor and vice-president of the School of Aeronautics and Astronautics at Zhejiang University. He was a winner of national outstanding youth fund and one of the 100 winners of outstanding doctoral dissertation. His research interests include non-linear stochastic dynamics and mechanical analysis of complex structures.