Robust Output Regulation With Prescribed Performance for Second-Order Non-Polynomial Nonlinear Systems

This article focuses on the robust output regulation problem with prescribed performance for uncertain second-order nonlinear systems with non-polynomial nonlinearity. According to the existing framework for the robust output regulation problem of such nonlinear systems, we introduce some standard assumptions, and then construct two internal models of nonlinear forms to reproduce the steady-state information. Then, we convert the considered problem into the robust stabilization problem with prescribed performance of an augmented system containing the studied nonlinear system and the internal models. We incorporate a novel error transformation into the existing technique to design a stabilization controller, based on which we synthesize our control law to solve our original problem. Finally, we present two simulation examples to test our results. Note to Practitioners—This paper is motivated by a goal to ensure satisfaction of prescribed performance when achieving output regulation, rather than only considering steady-state performance traditionally. In addition to steady-state performance, transient performance also matters in the practical application. For example, regarding the microelectromechanical systems, guarantee of transient performance can reduce or prevent collisions between the movable plate and the fixed one, thus prolonging the device lifetime. We introduce the concept of prescribed performance to include transient and steady-state performance. Satisfaction of prescribed performance can protect both devices and humans in practice, effectively expanding the practical applicability of the output regulation theory. The theory of robust output regulation can avoid applying the solution of regulator equations related to the plant, which is quite practical since many parameters in the models of devices can be hardly obtained accurately. In addition, we consider second-order nonlinear systems with non-polynomial nonlinearity, including more physical systems compared with polynomial ones. For example, the models of single-link robotic manipulator systems contain the sine function, i.e., non-polynomial nonlinearity, for which our results are also suitable. All in all, the results in this paper have not only profound theoretical significance, but also important practical application value.