Sim, Xian Wen (2023) Stochastic approximation approaches for discrete-time nonlinear stochastic optimal control problem in engineering applications. Masters thesis, Universiti Tun Hussein Onn Malaysia.

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Abstract

Decisions and control of stochastic dynamical systems are challenging tasks. This thesis explores the use of the stochastic approximation (SA) approach to solve discrete-time nonlinear stochastic optimal control problems in engineering. In the presence of Gaussian white noise, the state dynamics become fluctuate, uncertain and incomplete information. So, optimizing and controlling such dynamic systems will not provide a satisfactory solution. Therefore, the SA for state-control (SASC) algorithm is proposed to associate state estimation and control law design for solving the control problem. Then, the optimal solution of the extended Kalman filter (EKF) is compared as a benchmark solution. Moreover, the variants of the SA approach, namely SA with momentum (SAM), Nesterov accelerated gradient (NAG), and adaptive moment estimation (Adam), are applied in the SASC algorithm for better iterations. For illustration, engineering applications, which are inverted pendulum-cart system, four-tank system, and Duffing electrical oscillator, are studied. The simulation results showed that trajectories of state and output are estimated close to actual trajectories using the optimal control law designed. From these results, the tilt angle and the cart position were regulated around steady states through the optimal external force. In addition, the liquid levels in four tanks were optimally estimated upon the optimal voltages of pumps. Further, the flux and voltage of the nonlinear inductor were optimally calculated under the sinusoidal source voltage. The efficiency and accuracy of the SASC algorithm with Adam are highly recommended. In conclusion, the SASC algorithm is applicable for solving discrete-time nonlinear stochastic optimal control problems effectively

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