Nonlinear control synthesis of ship roll by convex optimization

For nonlinear control of the ship roll, this paper presents a novel nonlinear controller design method using the sum of squares (SOS) technique combined with the dual of Lyapunov's stability theorem based on density function. With this method, under fixed load condition and ship speed, nonlinear controller is designed for ship roll. The simulations are performed by taking ship roll model as an example.

[1]  D. Mayne Nonlinear and Adaptive Control Design [Book Review] , 1996, IEEE Transactions on Automatic Control.

[2]  Weehong Tan,et al.  Nonlinear Control Analysis and Synthesis using Sum-of-Squares Programming , 2006 .

[3]  Charles N. Delzell,et al.  Positive Polynomials: From Hilbert’s 17th Problem to Real Algebra , 2001 .

[4]  A. Papachristodoulou,et al.  Robust Stability and Performance Analysis of a Longitudinal Aircraft Model Using Sum of Squares Techniques , 2005, Proceedings of the 2005 IEEE International Symposium on, Mediterrean Conference on Control and Automation Intelligent Control, 2005..

[5]  Qian Wang,et al.  Nonlinear Control Design of a Hypersonic Aircraft Using Sum-of-Squares Method , 2007, 2007 American Control Conference.

[6]  A. H. Nayfeh,et al.  STABILITY AND COMPLICATED ROLLING RESPONSES OF SHIPS IN REGULAR BEAM SEAS , 1990 .

[7]  A. Rantzer A dual to Lyapunov's stability theorem , 2001 .

[8]  Pablo A. Parrilo,et al.  Introducing SOSTOOLS: a general purpose sum of squares programming solver , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[9]  Wang Kunfei Chaos of Ships Rolling Motions and Its Nonlinear Simple and Direct Control , 2010 .

[10]  A. Isidori Nonlinear Control Systems , 1985 .

[11]  Z. Jarvis-Wloszek,et al.  Lyapunov Based Analysis and Controller Synthesis for Polynomial Systems using Sum-of-Squares Optimization , 2003 .

[12]  Francesc Pozo,et al.  Robust stabilisation of polynomial systems with uncertain parameters , 2010, Int. J. Syst. Sci..

[13]  P. Parrilo Structured semidefinite programs and semialgebraic geometry methods in robustness and optimization , 2000 .

[14]  Pablo A. Parrilo,et al.  Nonlinear control synthesis by convex optimization , 2004, IEEE Transactions on Automatic Control.