Adaptive Tracking With Prescribed Performance for Generic Unmeasured-State-Dependent Systems: A Single-Gain and Compact Approach

This paper proposes a novel approach to global tracking with prescribed performance for unmeasured-state-dependent (USD) systems with a generic growth rate of arbitrary function-of-output type. Note that only constant growth rate was allowed in the existing approaches. This paper proves that one single dynamic high gain is adequate to compensate for the multiple nonlinearities and unknowns (instead of two or three gains as in the literature), which achieves, for the first time, the minimal number of dynamic high gains for such generic USD systems. To make the controller competent, crucial parameters, due to their extremely intricate coupling, have to be derived by an iterative algorithm, instead of being expressed explicitly. The derived parameters enable us to construct a composite Lyapunov function to be of dynamic-high-gain input-to-state practical stability (ISpS) and real ISpS in different senses. With this, we break the conventional two-stage analysis framework which had to be adopted by USD systems previously, and arrive at the compact approach which unifies control design and prescribed tracking performance analysis for the first time. The proposed approach avoids the massive and intractable rescaled Lyapunov analysis of the conventional two-stage framework, largely alleviating the complexity and length of the performance disclosure.