Formulation of a Market-based Approach for Structural Control

When designing a control system for structural control, the Linear Quadratic Regulation (LQR) approach is usually taken. While this centralized control approach optimally controls structural deflections during earthquakes, it is not well suited for systems employing a large number of sensors and actuators. As an alternative to LQR, a market-based control system is proposed. Market-based control is a decentralized solution that models the control system around a scarce commodity such as power. The laws of supply and demand are employed to determine the semi-optimal control solution. In both a one and multipledegree-of-freedom system, market-based control is shown to yield structural response reductions comparable to those obtained from the LQR solution. NOMENCLATURE {x} state-space response of the structure [F] state-space system matrix [G],[L] location matrix of actuators and loading {d},{v} displacement and velocity vectors J LQR cost function {y} regulated response vector [R] cost function weighting matrix [P] Riccati matrix [K], [KD] continuous and discrete control gain matrix P amount of power bought or sold p transaction price of power K, α market-base control weighting terms β inverse of the supply function slope ρ supplier profit Wi device wealth {u} control force vector T,Q,R,S market-based control weighting terms