Damped Load Balancing in Multi-Agent Systems: A Reference-Based Error-Direct Control with Self-Reinforcing Guard Potential

This paper presents a load balancing controller for multi-agent systems based on three principles: (1) identify the target system's capacity (Ref) through empirical methods, (2) control by error-direct proportional response where remaining headroom equals bandwidth, and (3) guard against variance using signed D→I integration that accumulates Guard Potential during load increase and actively releases during decrease. The causal structure is D→I→P (PDI), not classical P+I+D (PID). We prove closed-loop asymptotic stability using a two-state Lyapunov function spanning both push-side and pull-side dynamics. Experimental results on five load scenarios — including reproduction of a real Single Point of Failure incident — confirm that error-direct control eliminates capacity exceedance and D→I guard provides additional safety margin.