Abstract
A semi-analytical direct optimal control solution for strongly excited and dissipative Hamiltonian systems is proposed based on the extended Hamiltonian principle, the Hamilton-Jacobi-Bellman (HJB) equation and its variational integral equation, and the finite time element approximation. The differential extended Hamiltonian equations for structural vibration systems are replaced by the variational integral equation, which can preserve intrinsic system structure. The optimal control law dependent on the value function is determined by the HJB equation so as to satisfy the overall optimality principle. The partial differential equation for the value function is converted into the integral equation with variational weighting. Then the successive solution of optimal control with system state is designed. The two variational integral equations are applied to sequential time elements and transformed into the algebraic equations by using the finite time element approximation. The direct optimal control on each time element is obtained respectively by solving the algebraic equations, which is unconstrained by the system state observed. The proposed control algorithm is applicable to linear and nonlinear systems with the quadratic performance index, and takes into account the effects of external excitations measured on control. Numerical examples are given to illustrate the optimal control effectiveness.
| Original language | English |
|---|---|
| Pages (from-to) | 1956-1964 |
| Number of pages | 9 |
| Journal | Communications in Nonlinear Science and Numerical Simulation |
| Volume | 17 |
| Issue number | 4 |
| DOIs | |
| Publication status | Published - 1 Apr 2012 |
Keywords
- Dynamical programming
- Hamiltonian dynamics principle
- Semi-analytical optimal control solution
- Structural vibration system
ASJC Scopus subject areas
- Numerical Analysis
- Modelling and Simulation
- Applied Mathematics