From Static Risk Registers to Dynamic Risk Circuits: A Control-System Model for Predictive Project Cost Governance

This paper establishes a unified dynamic control-system formulation for project cost and risk — formally showing that fixed cost, variable cost, and total budget collectively behave like an RLC control plant with distortion ε(t) as the controlled state and risk velocity 𝑖(𝑡)=𝑑𝜀𝑑𝑡 as the principal dynamic observable. Unlike static variance methods, the framework embeds risk appetite, systematic risk, overshoot, damping, and risk premium directly into the governing second-order equation. Capital cost is not assumed — it is inferred from two orthogonal drivers: the risk exposure ratio ρ and the performance efficiency potential 𝛺, including a project-level Alignment Efficiency Index 𝑐𝑜𝑠(𝛼). The result is a closed-form expression for capital capacity 𝑋 = 2𝜌𝛺 that becomes measurable from live financial behaviour. This allows budgets to be dynamically recalibrated as the project evolves — not after damage occurs — enabling predictive control, not post-mortem accounting. In effect, this work converts risk from an administrative spreadsheet concept into a measurable engineering dynamic state variable.