Unified tracking control under full-state constraints imposed irregularly

It is nontrivial to address the control problem of nonlinear systems with irregular constraining conditions (where the constraints, possibly time-varying, asymmetric and alternating positively and negatively, would occur or disappear in the middle of system operation). In this work, we present a control design framework for uncertain pure-feedback systems under the aforementioned constraining conditions. By making use of auxiliary constraining boundaries, we analytically extend the originally imposed constraints over the entire time interval of system operation, with which we introduce a useful state transformation with unique features. It is such transformation that allows for the development of the control scheme capable of uniformly addressing a variety of constraints formed dynamically and imposed irregularly. It is shown that, for the scenarios where the constraints are partially or fully imposed or removed at any time instant during system operation, one only needs to reset the corresponding extended constraining boundaries in the control scheme instead of altering its structure. Both theoretical analysis and numerical simulation authenticate the effectiveness of the proposed method.