Prescribed-time control of stochastic high-order nonlinear systems

Area of Science:

• Control Theory
• Nonlinear Systems
• Stochastic Systems

Background:

• Existing research on stochastic high-order nonlinear systems primarily focuses on asymptotic or finite-time stabilization.
• There is a need for control strategies that can achieve stabilization within a predetermined time.

Purpose of the Study:

• To develop a novel control design for achieving prescribed-time stabilization in stochastic high-order nonlinear systems.
• To ensure the closed-loop system possesses an almost surely unique strong solution.
• To guarantee that the system's equilibrium is mean-square stable within the prescribed time.

Main Methods:

• Design of a novel controller tailored for stochastic high-order nonlinear systems.
• Analysis of system properties including the existence of a unique strong solution.
• Mathematical formulation to prove prescribed-time mean-square stability.

Main Results:

• The proposed controller successfully achieves stabilization in a prescribed finite time.
• The closed-loop system is demonstrated to have an almost surely unique strong solution.
• The equilibrium of the closed-loop system is proven to be prescribed-time mean-square stable.

Conclusions:

• The developed control strategy effectively enables prescribed-time stabilization for stochastic high-order nonlinear systems.
• This approach extends beyond traditional asymptotic and finite-time stabilization methods.
• The controller's efficacy is validated through a practical example.