Physics

Nonlinear system

Mathematics

Agronomy

Backstepping

Biology

Adaptive control

Mathematical optimization

Artificial intelligence

Controller (irrigation)

Control (management)

Inverse

Geometry

Computer science

Quantum mechanics

Control theory (sociology)

Optimal control

IEEE Transactions on Automatic Control

We solve the prescribed-time mean-square stabilization and inverse optimality control problems for stochastic strict-feedback nonlinear systems by developing a new nonscaling backstepping design scheme. A key novel design ingredient is that the time-varying function is not used to scale the coordinate transformations and is only suitably introduced into the virtual controllers. The advantage of this approach is that a simpler controller results and the control effort is reduced. By using this method, we design a new controller to guarantee that the equilibrium at the origin of the closed-loop system is prescribed-time mean-square stable. Then, we redesign the controller and solve the prescribed-time inverse optimal mean-square 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, two simulation examples are given to illustrate the stochastic nonlinear prescribed-time control design.

Stochastic Nonlinear Prescribed-Time Stabilization and Inverse Optimality