Designing Fuzzy Descriptor Observer with Unmeasured Premise Variables for Head-Two-Arms-Trunk System

Abstract

Abstract Using the technique of unknown input observer, this paper aims at estimating internal variables of people living with a complete spinal cord injury (SCI). The goal is to provide a better understanding on the sitting control strategy of SCI people. The observer design is based on a Head-Two-Arms-Trunk (H2AT) model, belonging to a class of nonlinear descriptor systems. For observer design, this model is represented in a specific Takagi-Sugeno (TS) fuzzy form with nonlinear consequents. In contrast to previous fuzzy estimation results based on conventional TS fuzzy modeling, the new TS formulation allows separating all unmeasured premise variables in the nonlinear consequent parts. This contributes to reduce the computational burden of the observer design and the structural complexity of the designed fuzzy observer. In particular, the new formulation enables a more effective way to deal with unmeasured premise variables. Using Lyapunov stability theorem, sufficient conditions to design the unknown input observer are derived in the form of linear matrix inequalities, conveniently solved by convex optimization techniques. Simulation results demonstrate the effectiveness of the proposed observer design.