Local stability analysis using simulations and sum-of-squares programming

Automatica - Tập 44 - Trang 2669-2675 - 2008
Ufuk Topcu1, Andrew Packard1, Peter Seiler2
1Department of Mechanical Engineering, University of California, Berkeley 94720-1740, USA
2Honeywell Technology Center, Minneapolis, MN, 55418, USA

Tài liệu tham khảo

Boyd, 2004 Chesi, 2005, LMI-based computation of optimal quadratic Lyapunov functions for odd polynomial systems, International Journal of Robust Nonlinear Control, 15, 35, 10.1002/rnc.967 Chiang, 1989, Stability regions of nonlinear dynamical systems: A constructive methodology, IEEE Transactions on Automatic Control, 34, 1229, 10.1109/9.40768 Davison, 1971, A computational method for determining quadratic Lyap. functions for nonlinear systems, Automatica, 7, 627, 10.1016/0005-1098(71)90027-6 Genesio, 1985, On the estimation of asymptotic stability regions: State of the art and new proposals, IEEE Transactions on Automatic Control, 30, 747, 10.1109/TAC.1985.1104057 Hachicho, O., & Tibken, B. (2002). Estimating domains of attraction of a class of nonlinear dynamical systems with LMI methods based on the theory of moments. In Proc. CDC (pp. 3150–3155) Hauser, J., & Lai, M. C. (1992). Estimating quadratic stability domains by nonsmooth optimization. In Proc. ACC (pp. 571–576) Koc˘vara, M., & Stingl, M. (2005). PENBMI user’s guide Papachristodoulou, A. (2005). Scalable analysis of nonlinear systems using convex optimization. Ph.D. dissertation. Caltech Parrilo, 2003, Semidefinite programming relaxations for semialgebraic problems, Mathematical Programming Series B, 96, 293, 10.1007/s10107-003-0387-5 Prokhorov, D. V., & Feldkamp, L. A. (1999). Application of SVM to Lyapunov function approximation. In Proc. int. joint conf. on neural networks Serpen, G. (2005). Search for a Lyapunov function through empirical approximation by artificial neural nets: Theoretical framework. In Proc. int. joint conf. on artificial neural networks. (pp. 735–740) Sturm, 1999, Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones, Optimization Methods and Software, 11, 625, 10.1080/10556789908805766 Tan, W. (2006). Nonlinear control analysis and synthesis using sum-of-squares programming. Ph.D. dissertation. UC, Berkeley Tan, W., & Packard, A. (2006). Stability region analysis using sum of squares programming. In Proc. ACC (pp. 2297–2302) Tempo, 2005 Tibken, B. (2000). Estimation of the domain of attraction for polynomial systems via LMIs. In Proc. CDC (pp. 3860–3864) Tibken, B., & Fan, Y. (2006). Computing the domain of attraction for polynomial systems via BMI optimization methods. In Proc. ACC (pp. 117–122) Toker, O., & Ozbay, H. (1995). On the NP-hardness of solving bilinear matrix inequalities and simultaneous stabilization with static output feedback. In Proc. ACC (pp. 2525–2526) Vannelli, 1985, Maximal Lyapunov functions and domains of attraction for autonomous nonlinear systems, Automatica, 21, 69, 10.1016/0005-1098(85)90099-8 Vidyasagar, 1993