Output Tracking Control of a Nonlinear System Based on Takagi-Sugeno Fuzzy Model: Generalized Partial Eigenstructure Assignment Approach

This paper introduces an innovative optimal control approach to achieve output tracking while incorporating
$H_{2}$
-performance specifications in a specific class of nonlinear dynamics modeled by the Takagi-Sugeno fuzzy model (TSFM). The primary innovation lies in extending partial eigenstructure assignment to TSFM-based nonlinear systems within the framework of sliding mode control (SMC). We propose a two-step methodology for designing optimal sliding surface gains. Initially, optimal state feedback gains are computed for each rule consequence containing a linear subsystem, adhering to predetermined eigenvalues and satisfying
$H_{2}$
-performance criteria. Subsequently, using a convex combination, the overall state feedback gain is calculated and utilized to design sliding matrix gains. The sliding matrix gains are then determined by strategically combining previously calculated state-feedback gains in a convex optimization problem. We reframe the output tracking strategy as a stabilization problem using a virtual control input and reformulate the optimization task concerning tracking state errors. This process yields state feedback gains, sliding gains, and the formulation of the virtual control input. The effectiveness of our approach is verified through comprehensive simulations, emphasizing its capability in addressing output tracking challenges within nonlinear systems.