Composite-observer-based asynchronous control for hidden Markov nonlinear systems with disturbances

In this article, an asynchronous adaptive tracking control approach is presented for a type of hidden Markov jump nonlinear systems with external disturbances. In this joint jump process model, hidden Markov model signifies the dynamics of the actual system, whereas the signal emits from the detector symbolizes the transmitted information. This leads to the phenomenon of asynchronization between the modes of the system and that of the controller. Accordingly, an asynchronous observer is developed by using the mode information from the detector to develop an asynchronous control approach. The observer contains a disturbance estimation part, to compensate the unknown external inputs. Utilizing the backstepping scheme, a strict-feedback asynchronous tracking controller is formulated, guaranteeing that all signals within the closed-loop system are semi-globally uniformly ultimately bounded in probability. Finally, the validity of the presented methodology is illustrated by means of a simulation example.