Hybrid impulsive control for global stabilization of subfully actuated systems

Area of Science:

• Control Theory
• Hybrid Systems
• Nonlinear Dynamics

Background:

• Subfully actuated systems (sub-FAS) present challenges due to singular sets, limiting conventional control methods.
• Existing stabilization techniques for sub-FAS often require restrictive initial condition constraints.
• The high-order fully actuated (HOFA) system approach is a common but sometimes infeasible control strategy for sub-FAS.

Purpose of the Study:

• To develop a novel hybrid impulsive control method for the global stabilization of sub-FAS.
• To address the limitations of existing methods by removing constraints on initial states.
• To establish criteria for global stabilization of sub-FAS using the proposed hybrid controller.

Main Methods:

• Devised a hybrid controller combining the high-order fully actuated (HOFA) system approach with state-dependent impulsive control.
• Transformed sub-FAS into hybrid systems using the developed controller.
• Utilized both stabilizing and destabilizing impulses to manage singular sets within the sub-FAS.

Main Results:

• Achieved global stabilization of sub-FAS without constraints on initial conditions.
• Derived criteria for global stabilization applicable to the transformed hybrid systems.
• Demonstrated the effectiveness of the proposed approach through two illustrative examples.

Conclusions:

• The hybrid impulsive control method offers a feasible solution for global stabilization of sub-FAS, overcoming limitations of prior approaches.
• The use of state-dependent impulses, including both stabilizing and destabilizing types, is crucial for managing system singularities.
• This research provides a new theoretical framework and practical approach for controlling complex sub-FAS systems.