2. Observer-Based Robust Bang-Bang Funnel Controller and Its Stability in Closed-Loop Systems

Time optimal control is preferable in many industrial scenarios, such as landing control of spacecrafts, emergency braking of high-speed rails, emergency braking of electric vehicles, and emergency control of electric power systems suffering severe grid faults. Tradition bang-bang control is normally used in linear systems, and recent works have proposed a bang-bang funnel control method for nonlinear systems. Nevertheless, the bang-bang funnel control requires to calculate high-order derivatives of the objective variables. This can magnify the measurement noise as well as external disturbances, and result in instability of the control system. In order to solve this problem, this chapter presents a RBC based on the high-gain observer for a nonlinear system suffering intermittent disturbances. The intermittent disturbance represents the system faults and sudden changes of operating conditions. A BCFC is employed, and the largest control capabilities of the control system is explored to stabilize the nonlinear system against the disturbances. The BCFC functions with the estimates of the tracking error of control target and its derivatives estimated with a high-gain state observer. This eliminates the use of the derivative calculations with respect to the tracking error of system output. Convergence of the estimation error of the observer is verified. The closed-loop stability of the RBC is proved in the sense of bounded-input bounded-state.