Stochastic optimal control via Bellman's principle

Crespo, Luis G.; Sun, Jian‐Qiao

doi:10.1016/s0005-1098(03)00238-3

Cited by 71 publications

(32 citation statements)

References 17 publications

(25 reference statements)

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“…The saturated optimal control is determined by the minimization of the right hand side of the HJB equation (18) or (19) …”

Section: Dynamical Programming Equation and Saturated Optimal Comentioning

confidence: 99%

“…The strategy has been applied to minimize the response [12] , the feedback stabilization [13] and the feedback maximization of the reliability [14,15] of quasi Hamiltonian systems. At the same time, the cell mapping method is applied by Sun and Crespo [16][17][18] to solve the dynamical programming equation in the stochastic optimal control of nonlinear systems, while a hybrid solution method was proposed by Bratus and Dimentberg [19][20][21] to solve the dynamical programming equation for the bounded control of linear systems subject to external excitations of Gaussian white noise.…”

Section: Introductionmentioning

confidence: 99%

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Stochastic Optimal Control of Strongly Nonlinear Systems under Wide-Band Random Excitation with Actuator Saturation

Feng

Zhu

2008

Acta Mech. Solida Sin.

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A bounded optimal control strategy for strongly non-linear systems under non-white wide-band random excitation with actuator saturation is proposed. First, the stochastic averaging method is introduced for controlled strongly non-linear systems under wide-band random excitation using generalized harmonic functions. Then, the dynamical programming equation for the saturated control problem is formulated from the partially averaged Itô equation based on the dynamical programming principle. The optimal control consisting of the unbounded optimal control and the bounded bang-bang control is determined by solving the dynamical programming equation. Finally, the response of the optimally controlled system is predicted by solving the reduced Fokker-Planck-Kolmogorov (FPK) equation associated with the completed averaged Itô equation. An example is given to illustrate the proposed control strategy. Numerical results show that the proposed control strategy has high control effectiveness and efficiency and the chattering is reduced significantly comparing with the bang-bang control strategy.

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“…The saturated optimal control is determined by the minimization of the right hand side of the HJB equation (18) or (19) …”

Section: Dynamical Programming Equation and Saturated Optimal Comentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Stochastic Optimal Control of Strongly Nonlinear Systems under Wide-Band Random Excitation with Actuator Saturation

Feng

Zhu

2008

Acta Mech. Solida Sin.

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“…(15) or Eq. (22) and completing the averaging, the following fully averaged Itô equations are obtained:…”

Section: Response Of Optimally Controlled Systemsmentioning

confidence: 99%

“…Thus, this control strategy is very promising and deserves further development. At the same time, the cell mapping method is applied by Crespo and Sun [20][21][22] to solve the dynamical programming equation in the stochastic optimal control of nonlinear systems and a hybrid solution method was proposed by Bratus and Dimentberg, etc. [23][24][25] to solve the dynamic programming equation for the bounded control of linear systems subject to external excitations of Gaussion white noise.…”

Section: Introductionmentioning

confidence: 99%

Optimal control strategies for stochastically excited quasi partially integrable Hamiltonian systems

2007

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In this paper two different control strategies designed to alleviate the response of quasi partially integrable Hamiltonian systems subjected to stochastic excitation are proposed. First, by using the stochastic averaging method for quasi partially integrable Hamiltonian systems, an n-DOF controlled quasi partially integrable Hamiltonian system with stochastic excitation is converted into a set of partially averaged Itô stochastic differential equations. Then, the dynamical programming equation associated with the partially averaged Itô equations is formulated by applying the stochastic dynamical programming principle. In the first control strategy, the optimal control law is derived from the dynamical programming equation and the control constraints without solving the dynamical programming equation. In the second control strategy, the optimal control law is obtained by solving the dynamical programming equation. Finally, both the responses of controlled and uncontrolled systems are predicted through solving the Fokker-Plank-Kolmogorov equation associated with fully averaged Itô equations. An example is worked out to illustrate the application and effectiveness of the two proposed control strategies.

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“…29 The stochastic optimal controls for linear and nonlinear systems have been studied and many control strategies have been presented. [29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46] However, the stochastic optimal control for a nonlinear system with a noised observation was only considered in several studies. 43 Under a specified condition, the separation theorem was applied to convert the nonlinear stochastic system with a noised observation into a completely observable linear system for determining optimal control, but the application is strongly limited.…”

Section: Introductionmentioning

confidence: 99%

Optimal Vibration Control for Structural Quasi-Hamiltonian Systems with Noised Observations

Ying¹,

Hu²,

Huan³

2017

IJAV

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A structural control system with smart sensors and actuators is considered and its basic dynamic equations are given. The controlled, stochastically excited, and dissipative Hamiltonian system with a noised observation is obtained by discretizing the nonlinear stochastic smart structure system. The estimated nonlinear stochastic system with control is obtained, in which the optimally estimated state is determined by the observation based on the extended Kalman filter. Then the dynamical programming equation for the estimated system is obtained based on the stochastic dynamical programming principle. From this, the optimal control law dependent on the estimated state is determined. The proposed optimal control strategy is applied to two nonlinear stochastic systems with controls and noised observations. The control efficacy for stochastic vibration response reductions of the systems is illustrated with numerical results. The proposed optimal control strategy is applicable to general nonlinear stochastic structural systems with smart sensors, smart actuators and noised observations.

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Stochastic optimal control via Bellman's principle

Cited by 71 publications

References 17 publications

Stochastic Optimal Control of Strongly Nonlinear Systems under Wide-Band Random Excitation with Actuator Saturation

Stochastic Optimal Control of Strongly Nonlinear Systems under Wide-Band Random Excitation with Actuator Saturation

Optimal control strategies for stochastically excited quasi partially integrable Hamiltonian systems

Optimal Vibration Control for Structural Quasi-Hamiltonian Systems with Noised Observations

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