LMI-Based Adaptive Tracking Control for Parametric Strict-Feedback Systems

This paper presents an effective linear matrix inequality (LMI)-based adaptive scheme to design the output tracking controller for parametric strict-feedback systems. In our previous paper, the concepts of virtual desired variables (VDVs) and, in turn, the so-called generalized kinematics are introduced to benefit the tracking design. All the VDVs can be determined without fail from the generalized kinematics via a newly defined recursive procedure if the systems are in strict-feedback form. The proposed adaptive tracking control is investigated for single-input and multi-input systems with unknown parameters. Different from the existent adaptive fuzzy control, our research is an exact approach, compared with the approach using universal approximation. Relative to the adaptive backstepping control, it makes the design procedure more straightforward. Moreover, we propose a new method called balance technique to deal with the infeasibility of LMIs for the specified structure of common positive definite matrix P, and adopt an overparameterization technique to make sure that the VDVs can be well-defined. From the numerical simulations, it is shown that the proposed scheme is very powerful with expected satisfactory performance.