A variant of an (combined) adaptive controller design introducing sliding regime in Lyapunov derivative

In this note on a nonlinear example of a process model representing a methane gas yielding is applied Lyapunov approach. The design is realized with introducing sliding regime in Lyapunov derivative. However, the ensured sliding regime is different from the classical one with variable structure, because in this case, it affects directly the adaptive laws, not the control variable. The result is that high frequency oscillations of the control variable, typical for such regime are omitted. This design also guarantees good performance and a possibility for a slight adjustment of the controller, in the sense from no periodical to transient response with overshooting. Future developments may show that such approach in a design could have some advantages in comparison with the classical Lyapunov design approach.