Control of nonlinear systems under dynamic constraints: A unified barrier function-based approach

Although there are fruitful results on adaptive control of constrained parametric/nonparametric strict-feedback nonlinear systems, most of them are contingent upon “feasibility conditions”, and/or are only applicable to constant and symmetric constraints. In this work, we present a robust adaptive control solution free from “feasibility conditions” and capable of accommodating much more general dynamic constraints. In our design, instead of employing the commonly used piecewise Barrier Lyapunov Function (BLF), we build a unified barrier function upon the constrained states, with which we convert the original constrained nonlinear system into an equivalent “non-constrained” one. Then by stabilizing the “unconstrained” system, the asymmetric state constraints imposed dynamically are handled gracefully. By blending a new coordinate transformation into the backstepping design, we develop a control strategy completely obviating the “feasibility conditions” for the system. It is worth noting that the requirement on the constraints to be obeyed herein is much less restrictive as compared to those imposed in most existing methods, rendering the resultant control less demanding in design and more user-friendly in implementation. Both theoretical analysis and numerical simulation verify the effectiveness and benefits of the proposed method.