Abstract
The paper considers a problem of stochastic control and dynamics of a single-degree-of-freedom system with piecewise linear stiffness subjected to combined periodic and white noise external excitations. To minimize the system response energy a bounded in magnitude control force is applied to the systems. The stochastic optimal control problem is handled through the dynamic programming approach. Based on the solution to the Hamilton-Jacobi-Bellman equation it is proposed to use the dry friction control law in the non-resonant case. In the resonant case the stochastic averaging procedure has been used to derive stochastic differential equations for system response amplitude and phase. The joint PDF of response amplitude and phase is derived analytically and numerically using the Path Integration approach.
| Original language | English |
|---|---|
| Pages (from-to) | 118-124 |
| Number of pages | 7 |
| Journal | Probabilistic Engineering Mechanics |
| Volume | 35 |
| Early online date | 10 Oct 2013 |
| DOIs | |
| Publication status | Published - 1 Jan 2014 |
Keywords
- Fokker-Plank-Kolmogorov equation
- Hamilton-Jacobi-Bellman equation
- Path integration method
- Piecewise linear
- Stochastic averaging
- Stochastic optimal control
ASJC Scopus subject areas
- Nuclear Energy and Engineering
- Ocean Engineering
- Aerospace Engineering
- Civil and Structural Engineering
- Mechanical Engineering
- Statistical and Nonlinear Physics
- Condensed Matter Physics