Tracking control of nonlinear stochastic systems with actuator nonlinearity

Actuator nonlinearity exists in many physical systems and devices such as electromagnetism, piezoelectric actuators, electronic relay circuits, smart materials, etc. In this paper, we consider tracking control of stochastic system with actuator nonlinearity. We use existing adaptive controller including parameter update law and control law, which can achieve exponential tracking of a class of nonlinear deterministic system. However, the controller cannot be practically applied since the presence of observation noise leads to divergence of parameter update law. Furthermore, the sensitivity of the control law signal induces bursting behavior which may, in practice, damage actuators. We modify both the parameter update law and the control law to avoid divergence and reduce the sensitivity. In addition, we consider two type of filtering techniques, i.e. classical Kalman filter to estimate joint state and parameter of a simplified linear time varying model, and continuous-discrete unscented Kalman filter to estimate state and all unknown parameters of the system. The effectiveness of our proposed control method is clarified by a numerical example of a second order dynamical system with dead-zone nonlinearity. Then, tracking performances obtained from both filtering methods are compared.