Control of Nonlinear Systems with Asymmetric yet Time-varying Output Constraint: A Direct Transformational Approach

In this paper, an adaptive control for strict-feedback nonlinear systems with output constraint is investigated. Different from the Barrier Lyapunov Function (BLF) based constant constraint control methods, an nonlinear output-dependent transformation is introduced, which removes the commonly used conservative design of converting the output constraint into tracking error related constraint, relaxing the requirement on the initial condition of system output; Then by constructing a new coordinate transformation, together with the backstepping and tuning function techniques, the developed adaptive control ensures that all signals in the closed-loop systems are bounded and the symmetric output constraint is not violated. Furthermore, to deal with the asymmetric yet time-varying output constraint and to reduce the difficulty of stability analysis in the asymmetric BLF (ABLF) control schemes, another nonlinear output-dependent transformation is developed such that the output constraint can be handled directly and the extra effort to ensure the continuity and differentiability of virtual controllers is not needed. The effectiveness and superiority of the proposed method has also be validated via numerical simulation.