Robust market-based control method for nonlinear structure

For a nonlinear control system, there are many uncertainties, such as the structural model, controlled parameters and external loads. Although the significant progress has been achieved on the robust control of nonlinear systems through some researches on this issue, there are still some limitations, for instance, the complicated solving process, weak conservatism of system, involuted structures and high order of controllers. In this study, the computational structural mechanics and optimal control theory are adopted to address above problems. The induced norm is the eigenvalue problem in structural mechanics, i.e., the elastic stable Euler critical force or eigenfrequency of structural system. The segment mixed energy is introduced with a precise integration and an extended Wittrick-Williams (W-W) induced norm calculation method. This is then incorporated in the market-based control (MBC) theory and combined with the force analogy method (FAM) to solve the MBC robust strategy (R-MBC) of nonlinear systems. Finally, a singledegree- of-freedom (SDOF) system and a 9-stories steel frame structure are analyzed. The results are compared with those calculated by the H∞ -robust (R-H∞) algorithm, and show the induced norm leads to the infinite control output as soon as it reaches the critical value. The R-MBC strategy has a better control effect than the R-H∞ algorithm and has the advantage of strong strain capacity and short online computation time. Thus, it can be applied to large complex structures.