Infinite horizon robustly stable seismic protection of cable-stayed bridges using cost cumulants

• Published in: 2004 American Control Conference Proceedings; Volume 1 of 6 Vol. 1; pp. 691 - 696 vol.1
• Main Authors: Pham, K.D., Sain, M.K., Liberty, S.R.
• Format: Conference Proceeding Journal Article
• Language: English
• Published: Piscataway NJ IEEE 01.01.2004; Evanston IL American Automatic Control Council
• Subjects: Applied sciences; Bridges; Computer science; control theory; systems; Control system synthesis; Control systems; Control theory. Systems; Costs; Exact sciences and technology; Infinite horizon; Integral equations; Linear feedback control systems; Matrices; Protection; Robustness; State feedback; Stability margin; State feedback; Feedback regulation; Dynamical system; Infinite system; Linear control; Modeling; Stochastic system; Lagrange multiplier; Uncertain system; Linear combination; Stayed girder bridge; Earthquakes; Quadratic cost; Infinite horizon; Matrix equation; Mathematical programming; Robust stability; Operator equation; Terminal; Cost control; Constrained optimization; Robust control; Optimal control; Optimal solution; Equality constraint; Algebraic equation; Cumulant
• ISBN: 9780780383357; 0780383354
• ISSN: 0743-1619; 2378-5861
• DOI: 10.23919/ACC.2004.1383684

The basic idea behind infinite horizon state feedback k-cost-cumulant (kCC) control is to seek a constant state feedback law which minimizes the value of a finite linear combination of the first k cost cumulants of a traditional integral quadratic cost associated with a linear stochastic system, when there is no specification of a large terminal time. The paper begins with the development of matrix algebraic equations for the cost cumulants. These equations permit the incorporation of classes of linear feedback controllers for linear dynamical systems defined on infinite horizon. The infinite horizon control problem with the optimization goal of a finite linear combination of the first k cost cumulants is then stated. Because the control optimization problem at hand involves matrix equality constraints, the optimal feedback solution is investigated by utilizing a Lagrange multipliers technique. The efficacy and applicability of this control paradigm, based upon the first three cost cumulants, are demonstrated on the second earthquake generation benchmark for response control of cable-stayed bridges (Caicedo, J.M., et al., 2003). The simulation results indicate that the cost cumulants in the infinite horizon case offer significant improvements in robust stability margin while keeping comparable levels of structural performance when comparing to those of the baseline LQG in the benchmark.