Prescribed-performance tracking for high-power nonlinear dynamics with time-varying unknown control coefficients

Prescribed-performance control (PPC) for high-power dynamics with time-varying unknown control coefficients requires to address two open problems: (a) given a Nussbaum function, which properties hold for the power of the Nussbaum function? (b) to avoid high gains, how to design a switching gain that increases only when the tracking error is close to violate the performance bounds? To address the first problem, we show with a counterexample and a positive example that only some Nussbaum functions are suited to handle time-varying unknown control coefficients for high-power dynamics. To address the second problem, we propose a new switching conditional inequality.