Partial State Constraints-Based Control for Nonlinear Systems With Backlash-Like Hysteresis

This paper focuses on the adaptive control problem for a class of nonlinear single-input single-output lower triangular systems with partial state constraints and unknown backlash-like hysteresis. To prevent the partial states from transgressing the predefined constrained region, a barrier Lyapunov function is presented, whose values will increase to infinity when any of its parameters grows to a given boundary value. To counteract the effect caused by the backlash-like hysteresis, an auxiliary variable with its adaptive mechanism is introduced in the backstepping technique. At the same time, the output of the considered systems can track the reference signal, and all the variables in the design procedure are uniformly ultimate boundedness. In the end, a numerical example is employed to validate the efficiency of the developed theoretical method.