Rong-hua Huan

Stochastic Optimal Control of Quasi Integrable Hamiltonian Systems Subject to Actuator Saturation

A modified bounded optimal control strategy for quasi integrable Hamiltonian systems subject to actuator saturation is proposed. First, an n degree-of-freedom (DOF) weakly controlled quasi Hamiltonian system subject to Gaussian white noise excitation is formulated and converted into Itô equations by adding Wong-Zakai correction terms. Then, the averaged Itô stochastic differential equations and dynamical programming equation are derived by using stochastic averaging method and the stochastic dynamical programming principle, respectively. The optimal control law consisting of unbounded optimal control and bounded bang-bang control is obtained from solving the dynamical programming equation. Finally, an example of a two DOF controlled quasi integrable Hamiltonian system is worked out in detail. Numerical results show that the proposed control strategy has high control effectiveness and efficiency and the chattering is reduced significantly comparing with bang-bang control strategy.

Optimal Bounded Semi-Active Control of Hysteretic Systems with MR Damper

A bounded stochastic optimal semi-active control strategy for random excited hysteretic systems by using MR damper is proposed and illustrated by an example of a single degree-of-freedom hysteretic system. First, the dynamics of MR damper and the hysteretic force are expressed by using the Bouc-Wen model. Then, the system is converted into an equivalent nonlinear non-hysteretic stochastic system, from which the optimal bounded semi-active control law consisting of optimal unbounded control and bang-bang control is derived by using stochastic averaging method and stochastic dynamical programming principle. Finally, the response of optimally controlled system is predicted from solving the Fokker-Planck-Kolmogorov (FPK) equation associated with the fully averaged Itô equation. Numerical results show that the proposed control strategy has high control effectiveness and efficiency.

Stochastic optimal vibration control of partially observable nonlinear quasi hamiltonian systems with actuator saturation

An optimal vibration control strategy for partially observable nonlinear quasi Hamiltonian systems with actuator saturation is proposed. First, a controlled partially observable nonlinear system is converted into a completely observable linear control system of finite dimension based on the theorem due to Charalambous and Elliott. Then the partially averaged Itô stochastic differential equations and dynamical programming equation associated with the completely observable linear system are derived by using the stochastic averaging method and stochastic dynamical programming principle, respectively. The optimal control law is obtained from solving the final dynamical programming equation. The results show that the proposed control strategy has high control effectiveness and control efficiency.

Optimal Vibration Control of a Class of Nonlinear Stochastic Systems with Markovian Jump

The semi-infinite time optimal control for a class of stochastically excited Markovian jump nonlinear system is investigated. Using stochastic averaging, each form of the system is reduced to a one-dimensional partially averaged Ito equation of total energy. A finite set of coupled dynamical programming equations is then set up based on the stochastic dynamical programming principle and Markovian jump rules, from which the optimal control force is obtained. The stationary response of the optimally controlled system is predicted by solving the Fokker-Planck-Kolmogorov (FPK) equation associated with the fully averaged Ito equation. Two examples are worked out in detail to illustrate the application and effectiveness of the proposed control strategy.

Probability-Weighted Optimal Control for Nonlinear Stochastic Vibrating Systems with Random Time Delay

A probability-weighted optimal control strategy for nonlinear stochastic vibrating systems with random time delay is proposed. First, by modeling the random delay as a finite state Markov process, the optimal control problem is converted into the one of Markov jump systems with finite mode. Then, upon limiting averaging principle, the optimal control force is approximately expressed as probability-weighted summation of the control force associated with different modes of the system. Then, by using the stochastic averaging method and the dynamical programming principle, the control force for each mode can be readily obtained. To illustrate the effectiveness of the proposed control, the stochastic optimal control of a two degree-of-freedom nonlinear stochastic system with random time delay is worked out as an example.