Prescribed-time stabilization and inverse optimality for strict-feedback nonlinear systems

We consider the prescribed-time stabilization and inverse optimality for strict-feedback nonlinear systems with nonlinear growth condition. Different from the existing scaling designs for nonlinear systems, we propose new non-scaling designs characterized by new scaled quadratic Lyapunov functions. The advantage of our design is that it is simpler and easier for implementation. We first design a controller to ensure that the equilibrium at the origin of the plant is prescribed-time stable. Then we redesign the controller and solve the prescribed-time inverse optimal stabilization problem, with an infinite gain margin. Specifically, the designed controller is not only optimal with respect to a meaningful cost functional but also globally stabilizes the closed-loop system in the prescribed-time. Finally, a simulation example is given to illustrate the designs.