Market-based control strategy for long-span structures considering the multi-time delay issue

To solve the different time delays that exist in the control device installed on spatial structures, in this study, discrete analysis using a 2N precise algorithm was selected to solve the multi-time-delay issue for long-span structures based on the market-based control （MBC） method. The concept of interval mixed energy was introduced from computational structural mechanics and optimal control research areas, and it translates the design of the MBC multi-time-delay controller into a solution for the segment matrix. This approach transforms the serial algorithm in time to parallel computing in space, greatly improving the solving efficiency and numerical stability. The designed controller is able to consider the issue of time delay with a linear controlling force combination and is especially effective for large time-delay conditions. A numerical example of a long-span structure was selected to demonstrate the effectiveness of the presented controller, and the time delay was found to have a significant impact on the results.