Communication and Control Co-design in Non-cooperative Games

2025-03-01

AI Summary

This paper addresses the joint communication–control design problem for a two-player stochastic differential game over an infinite horizon: each player comprises a scheduler and a remote controller, collaboratively optimizing a global objective yet competing noncooperatively, under intermittent communication constraints inducing state estimation delays and communication costs. Innovatively, we formulate the problem within a noncooperative game framework for communication-constrained control, deriving Nash equilibrium control policies based on conditional state estimates. The scheduler design is recast as computing the steady-state solution of a generalized Sylvester equation. Leveraging parametric randomized scheduling, truncated polynomial approximation, and projected gradient descent, we obtain closed-form Nash control laws and computationally tractable scheduling policies. Numerical simulations demonstrate that the proposed method achieves a significantly improved trade-off between communication cost and control performance compared to benchmark approaches.

Technology Category

• Planning, Routing, and Scheduling: Scheduling under Uncertainty
• Reasoning under Uncertainty: Stochastic Optimization
• Multiagent Systems: Agent Communication

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Security and Privacy: Large-scale security measurements
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems

Abstract

In this article, we revisit a communication-control co-design problem for a class of two-player stochastic differential games on an infinite horizon. Each 'player' represents two active decision makers, namely a scheduler and a remote controller, which cooperate to optimize over a global objective while competing with the other player. Each player's scheduler can only intermittently relay state information to its respective controller due to associated cost/constraint to communication. The scheduler's policy determines the information structure at the controller, thereby affecting the quality of the control inputs. Consequently, it leads to the classical communication-control trade-off problem. A high communication frequency improves the control performance of the player on account of a higher communication cost, and vice versa. Under suitable information structures of the players, we first compute the Nash controller policies for both players in terms of the conditional estimate of the state. Consequently, we reformulate the problem of computing Nash scheduler policies (within a class of parametrized randomized policies) into solving for the steady-state solution of a generalized Sylvester equation. Since the above-mentioned reformulation involves infinite sum of powers of the policy parameters, we provide a projected gradient descent-based algorithm to numerically compute a Nash equilibrium using a truncated polynomial approximation. Finally, we demonstrate the performance of the Nash control and scheduler policies using extensive numerical simulations.

Problem

• Optimize communication-control trade-off in two-player stochastic games.
• Compute Nash controller policies using state conditional estimates.
• Solve Nash scheduler policies via generalized Sylvester equation.

Innovation

• Co-design of communication and control strategies
• Nash equilibrium via generalized Sylvester equation
• Projected gradient descent for numerical computation