Controllability of complex networks with unilateral inputs.

Area of Science:

• Control Theory
• Network Science
• Systems Engineering

Background:

• Complex networks are ubiquitous in science and engineering.
• Controlling these networks often requires understanding their structure and dynamics.
• Traditional control methods may not be suitable for systems with restricted input types.

Purpose of the Study:

• To develop an algorithm for controlling complex networks using unilateral control inputs.
• To minimize the number of required unilateral control inputs.
• To identify network properties influencing unilateral controllability.

Main Methods:

• Reformulating classical controllability conditions into optimization problems.
• Developing an algorithm to construct an input matrix B for a given adjacency matrix A.
• Analyzing network topology to establish theoretical bounds on control inputs.

Main Results:

• An algorithm is developed that constructs an input matrix B for controllable systems.
• The method achieves near-minimal unilateral control inputs.
• Theoretical bounds on minimal controls are established based on network topology.
• Heuristics achieve these lower bounds for random and real-world networks.

Conclusions:

• Unilateral control of complex networks is feasible with a systematic algorithmic approach.
• Network topology plays a crucial role in determining the ease of achieving unilateral controllability.
• The developed method offers an efficient way to select minimal unilateral control inputs.