Optimal Control of Opinion Dynamics on Complex Networks via Discounted LQR: Theory and Computation

This paper investigates the optimal control problem of opinion dynamics within complex networks. By introducing a state transformation, the original problem is reformulated within a discounted Linear Quadratic Regulator (LQR) framework, establishing a connection between opinion control and classical control theory. Within this unified framework, the optimal control law can be obtained by solving the discrete-time algebraic Riccati equation, thereby circumventing the complexity of dealing with linear terms inherent in traditional dynamic programming approaches. Numerical experiments validate the effectiveness of the algorithm in a benchmark case, a 20-node complete network, and complex topologies. They also reveal the influence mechanisms of network heterogeneity on convergence speed and control energy consumption, providing a theoretical basis for public opinion guidance strategies under different network structures.