We studied the feedback maximization of reliability of multi-degree-of-freedom (MDOF) quasi integrable-Hamiltonian systems under combined harmonic and white noise excitations. First, the partially averaged It equations are derived by using the stochastic averaging method for quasi integrable-Hamiltonian systems under combined harmonic and white noise excitations. Then, the dynamical programming equation and its boundary and final time conditions for the control problems of maximizing the reliability is established from the partially averaged equations by using the dynamical programming principle. The nonlinear stochastic optimal control for maximizing the reliability is determined from the dynamical programming equation and control constrains. The reliability function of optimally controlled systems is obtained by solving the final dynamical programming equation. Finally, the application of the proposed procedure and effectiveness of the control strategy are illustrated by using an example.
An optimization method for time-delayed feedback control of partially observable linear building structures subjected to seismic excitation is proposed. A time-delayed control problem of partially observable linear building structure under horizontal ground acceleration excitation is formulated and converted into that of completely observable linear structure by using separation principle. The time-delayed control forces are approximately expressed in terms of control forces without time delay. The control system is then governed by It? stochastic differential equations for the conditional means of system states and then transformed into those for the conditional means of modal energies by using the stochastic averaging method for quasi-Hamiltonian systems. The control law is assumed to be modal velocity feedback control with time delay and the unknown control gains are determined by the modal performance indices. A three-storey building structure is taken as example to illustrate the proposal method and the numerical results are confirmed by using Monte Carlo simulation.
A strategy for time-delayed feedback controloptimization of quasi linear systems with random excitationis proposed. First, the stochastic averaging method isused to reduce the dimension of the state space and to derivethe stationary response of the system. Secondly, the controllaw is assumed to be velocity feedback control with timedelay and the unknown control gains are determined by theperformance indices. The response of the controlled systemis predicted through solving the Fokker-Plank-Kolmogorovequation associated with the averaged It equation. Finally,numerical examples are used to illustrate the proposed controlmethod, and the numerical results are confirmed byMonte Carlo simulation.
Xueping Li Demin Wei Weiqiu Zhu School of Civil Engineering and Transportation, South China University of Technology, 510640 Guangzhou, China Department of Mechanics, State Key Laboratory of Fluid Power Transmission and Control, Zhejiang University, 310027 Hangzhou, China
The stochastic averaging method for quasi-integrable Hamiltonian systems with time-delayed feedback bang-bang control is first introduced. Then, two time delay compensation methods, namely the method of changing control force amplitude (CFA) and the method of changing control delay time (CDT), are proposed. The conditions applicable to each compensation method are discussed. Finally, an example is worked out in detail to illustrate the application and effectiveness of the proposed methods and the two compensation methods in combination.
LIU ZhongHua1 & ZHU WeiQiu2 1 Department of Civil Engineering, Xiamen University, Xiamen 361005, China
The stochastic optimal control of partially observable nonlinear quasi-integrable Hamiltonian systems is investigated. First, the stochastic optimal control problem of a partially observable nonlinear quasi-integrable Hamiltonian system is converted into that of a completely observable linear system based on a theorem due to Charalambous and Elliot. Then, the converted stochastic optimal control problem is solved by applying the stochastic averaging method and the stochastic dynamical programming principle. The response of the controlled quasi Hamiltonian system is predicted by solving the averaged Fokker-Planck-Kolmogorov equation and the Riccati equation for the estimated error of system states. As an example to illustrate the procedure and effectiveness of the proposed method, the stochastic optimal control problem of a partially observable two-degree-of-freedom quasi-integrable Hamiltonian system is worked out in detail.
FENG Ju, ZHU WeiQiu & YING ZuGuang Department of Mechanics, State Key Laboratory of Fluid Power Transmission and Control, Zhejiang University, Hangzhou 310027, China
A modified nonlinear stochastic optimal bounded control strategy for random excited hysteretic systems with actuator saturation is proposed. First, a controlled hysteretic system is converted into an equivalent nonlinear nonhysteretic stochastic system. Then, the partially averaged It? stochastic differential equation and dynamical programming equation are established, respectively, by using the stochastic averaging method for quasi non-integrable Hamiltonian systems and stochastic dynamical programming principle, from which the optimal control law consisting of optimal unbounded control and bang-bang control is derived. Finally, the response of optimally controlled system is predicted by solving the Fokker-Planck-Kolmogorov (FPK) equation associated with the fully averaged It? equation. Numerical results show that the proposed control strategy has high control effectiveness and efficiency.
