Optimal Control for Navier-Stokes Takagi-Sugeno Fuzzy Equations Using Simulink

Abstract

In this paper, the unsteady Navier-Stokes Takagi-Sugeno (T-S) fuzzy equations (UNSTSFEs) are represented as a differential algebraic system of strangeness index one by applying any spatial discretization. Since such differential algebraic systems have a difficulty to solve in their original form, most approaches use some kind of index reduction. While processing this index reduction, it is important to take care of the manifolds contained in the differential algebraic equation (DAE) /singular system (SS) for each fuzzy rule. The Navier-Stokes equations are investigated along the lines of the theoretically best index reduction by using several discretization schemes. Applying this technique, the UNSTSFEs can be reduced into DAE. Optimal control for Navier-Stokes T-S fuzzy system with quadratic performance is obtained by finding the optimal control of singular T-S fuzzy system using Simulink. To obtain the optimal control, the solution of matrix Riccati differential equation (MRDE) is found by solving differential algebraic equation (DAE) using Simulink approach. The solution of Simulink approach is equivalent or very close to the exact solution of the problem. An illustrative numerical example is presented for the proposed method.