Author(s)

Sie Long Kek¹, Jiao Li², Kok Lay Teo³

¹Center for Research on Computational Mathematics, Universiti Tun Hussein Onn Malaysia, Batu Pahat, Malaysia.
²School of Mathematics and Computing Science, Changsha University of Science and Technology, Changsha, China.
³Department of Mathematics and Statistics, Curtin University of Technology, Perth, Australia.

In this paper, an efficient computational approach is proposed to solve the discrete time nonlinear stochastic optimal control problem. For this purpose, a linear quadratic regulator model, which is a linear dynamical system with the quadratic criterion cost function, is employed. In our approach, the model-based optimal control problem is reformulated into the input-output equations. In this way, the Hankel matrix and the observability matrix are constructed. Further, the sum squares of output error is defined. In these point of views, the least squares optimization problem is introduced, so as the differences between the real output and the model output could be calculated. Applying the first-order derivative to the sum squares of output error, the necessary condition is then derived. After some algebraic manipulations, the optimal control law is produced. By substituting this control policy into the input-output equations, the model output is updated iteratively. For illustration, an example of the direct current and alternating current converter problem is studied. As a result, the model output trajectory of the least squares solution is close to the real output with the smallest sum squares of output error. In conclusion, the efficiency and the accuracy of the approach proposed are highly presented.

Least Squares Solution, Stochastic Optimal Control, Linear Quadratic Regulator, Sum Squares of Output Error, Input-Output Equations

Kek, S. , Li, J. and Teo, K. (2017) Least Squares Solution for Discrete Time Nonlinear Stochastic Optimal Control Problem with Model-Reality Differences. Applied Mathematics, 8, 1-14. doi: 10.4236/am.2017.81001.