Locally Optimal Control of Complex Networks

Area of Science:

• Control Theory
• Nonlinear Dynamics
• System Optimization

Background:

• Linear system control problems can yield nonlocal trajectories.
• This poses challenges when the system dynamics are nonlinear and linearization is state-space dependent.
• Ensuring local control is crucial for practical applications.

Purpose of the Study:

• To solve the problem of optimally controlling a linearized system with nonlocal trajectory issues.
• To develop a method guaranteeing local control actions for linearized dynamics.
• To enable effective control over extended state-space regions.

Main Methods:

• Derivation of a time-varying set encompassing all possible control trajectories.
• Parametrization of trajectories by time and energy.
• Utilizing a series of local control actions for distant state control.

Main Results:

• A guaranteed method for achieving local control trajectories within a defined set.
• A strategy for controlling systems over large state-space distances by sequential relinearization.
• The derived set ensures control action terminus remains within a valid local region.

Conclusions:

• The proposed method ensures local control trajectories for linearized systems.
• Sequential local control actions provide a viable solution for long-distance state transitions.
• This approach enhances the applicability of optimal control in nonlinear systems.