Discrete-Time Distributed Potential-Based Coordination in Networked Multi-Agent Systems

Multi-agent systems are often employed in applications requiring coordinated behavior. Potential-based control, based on driving agents toward critical points of predefined potential functions, is a widely adopted approach for its simplicity, flexibility, and intrinsic stability. While well-studied in continuous-time, applying it in discrete-time systems, common in real-world applications, can introduce challenges related to stability and approximation accuracy. This paper proposes a novel framework for distributed discrete-time potential-based coordination control that, under the mild assumption of convexity of the potential functions, preserves key properties of the continuous-time formulation while accommodating heterogeneous systems with actuator saturation. Numerical results validate the theoretical findings.