control barrier function

This paper proposes a controller capable of satisfying the output constraints while providing a near-optimal performance. The method is designed for square nonlinear systems with stable internal dynamics. To this end, using a primary performance index and Taylor approximation, the problem is approximated by a constrained programming, whose constraints are written with the aid of Control Barrier Function (CBF) to ensure the output restrictions. As a result, a constrained near-optimal performance without encountering difficulties in Hamilton-Jacobi-Bellman (HJB) equations is obtained. In order to overcome the model uncertainties, which appear in the optimization problem, an adaptive structure is formulated. The online solution of the constrained optimization is obtained using a Projection Recurrent Neural Network (PRNN). As a result, a closed-form solution is provided that can be simply implemented without requiring additional solvers or toolboxes. Stability of the proposed method and constraints satisfaction are addressed thoroughly. Finally, effectiveness of the proposed method in realizing the aforementioned aims are illustrated through simulations on trajectory control of a surface vessel system and a comparative study on the constrained stabilization of a pendulum. The first simulation example shows the effectiveness of the method in constrained tracking, while the second example confirms the proper performance of the controller in stabilization and regulation applications.