Optimal Semiactive Control of Elevated Highway Bridges: An Upper Bound on Performance via a Dynamic Programming Approach

Controllable damping studies for seismic protection of elevated highway bridges found that a clipped LQR strategy achieves performance similar to that with a fully linear actuator when attempting to reduce the bridge deck response, but only comparable to that with a purely passive damper when seeking to reduce pier response (Erkus et al., 2002). This paper examines this more challenging pier response problem using a dynamic programming approach to obtain the optimal dissipative control force - assuming the excitation is deterministic and known a priori - through a numerical solution of the Euler-Lagrange equations. The resulting (non-causal) optimal performance, an upper bound on the performance of any controllable damping strategy, is still rather lower than active control performance (which is causal, requiring no future excitation information). This result suggests that even highly adaptive control laws to command controllable dampers may never approach fully active system performance for some control objectives.