Nonlinear Suboptimal Tracking Controller Design Using State-Dependent Riccati Equation Technique

Abstract

In this brief, a new technique for solving a suboptimal tracking problem for a class of nonlinear dynamical systems is presented. Toward this end, an optimal tracking problem using a discounted cost function is defined and a control law with a feedback-feedforward structure is designed. A state-dependent Riccati equation (SDRE) framework is used in order to find the gains of both the feedback and the feedforward parts, simultaneously. Due to the significant properties of the SDRE technique, the proposed method can handle the presence of input saturation and state constraint. It is also shown that the tracking error converges asymptotically to zero under mild conditions on the discount factor of the corresponding cost function and the desired trajectory. Two simulation and experimental case studies are also provided to illustrate and demonstrate the effectiveness of our proposed design methodology.