A constrained nonlinear stochastic optimal control for dynamic systems El-Khoury, Omar; Shafieezadeh, Abdollah
An ideal controller assumes that the system is unconstrained and the control force in unbounded. However, in reality, control devices are restricted by their force capacity. Traditionally, the clipping strategy has been used extensively, where an ideal actuator is assumed in the control design, and then the inequality constraints are enforced through saturation. This approach may not provide optimal solutions since constraints are not considered in the control optimization. To overcome this limitation, this paper presents a constrained nonlinear stochastic optimal control algorithm for dynamic systems subjected to Gaussian white noise excitations. In this control algorithm, stochasticity and nonlinearity of a Hamiltonian dynamic system is considered based on stochastic averaging of energy envelope using Markovian approximation. An Ito equation of energy envelope is derived and represented by diffusion and drift components. For the control design, a prescribed cost function, the diffusion and drift components together with the force constraints are considered in solving the Hamilton Jacobian Bellman (HJB) equation. This proposed control approach is called here Constrained Stochastic Control (CSC). The performance of the CSC algorithm is demonstrated for a hysteretic column and the results are compared to simulation results for Clipped Stochastic Control (Cl-SC) and uncontrolled cases. Noticeable improvements in peak and root mean square values of displacement in the CSC case are observed over the Cl-SC algorithm.
Item Citations and Data
Attribution-NonCommercial-NoDerivs 2.5 Canada