A novel adaptive control framework for second-order nonlinear systems with parametric uncertainty subject to state constraints

Designing controllers for unknown nonlinear systems that simultaneously satisfy state constraints and achieve asymptotic tracking poses significant challenges. This paper presents a novel adaptive control framework for strict-feedback systems with state constraints, consisting of two key components. The first component employs conventional control techniques for systems without state constraints, utilizing existing controllers to ensure system stability. The second component introduces specific terms designed to enforce state constraint satisfaction, incorporating barrier function-based terms to achieve this objective. The advantage of this control framework lies in its ability to directly incorporate a wide range of existing controllers, which are designed for systems without constraints, as the first component to ensure system stability. In this way, the only requirement is to design the barrier function-related terms to guarantee constraint satisfaction, thereby simplifying the complexity of constraint control design.