Iterative LMI Approach to Robust State-feedback Control of Polynomial Systems with Bounded Actuators
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This paper presents a novel approach to state-feedback stabilization of polynomial systems with bounded actuators. To overcome limitation of the existing approaches, we introduce additional variables that separate the system matrices and the Lyapunov matrices. Therefore, parameterization of the state-feedback controllers is independent of the Lyapunov matrices. The proposed design condition is bilinear in the decision variables, and hence we provide an iterative algorithm to solve the design problem. At each iteration, the design condition is cast as convex optimization using the sum-of-squares technique and can be efficiently solved. In addition, the novel parameter-dependent Lyapunov functions are readily applied to robust state-feedback stabilization of polynomial systems subject to parametric uncertainty. Effectiveness of the proposed approach is demonstrated by numerical examples.
KeywordsBounded actuators convex optimization parameter-dependent LMI polynomial systems robust state-feedback stabilization sum-of-squares technique
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- C. W. Scherer and C. W. J. Hol, “Matrix sum-of-squares relaxations for robust semi-definite programs, Mathematical Programming Series B, vol. 107, Nos. 1–2, pp. 189–211, 2006.Google Scholar
- C. Ebenbauer and F. Allgower, “Analysis and design of polynomial control systems using dissipation inequalities and sum of squares,” Journal of Computers and Chemical Engineering, vol. 30, no. 11, pp. 1601–1614, 2006.Google Scholar
- H. Ichihara, “A Convex approach to state feedback synthesis for polynomial nonlinear systems with input saturation,” SICE Journal of Control, Measurement, and System Integration, vol. 6, no.3, pp. 186–193, 2013.Google Scholar
- S. Prajna, A. Papachristodoulou, and F. Wu, “Nonlinear control synthesis by sum of squares optimization: a Lyapunov-based approach,” Proc. of the Asian Control Conference, Melbourne, Australia, 2004. pp. 157–165.Google Scholar
- T. Jennawasin, M. Kawanishi, and T. Narikiyo, “Stabilization of nonlinear systems with bounded actuators using convex optimization,” Proc. of the 18th IFAC World Congress, Milano, Italy, pp. 6745–6750, August 2011.Google Scholar
- T. Jennawasin, M. Kawanishi, T. Narikiyo, and C. L. Lin, “An improved stabilizing condition for polynomial systems with bounded actuators: an SOS-based approach,” Proc. of the IEEE Multi-Conference on Systems and Control, Dubrovnik, Croatia, pp. 258–263, October 2012.Google Scholar
- S. Sajjadi-Kia and F. Jabbari, “Dilated-matrix inequalities for control design in systems with actuator constraint,” Proc. of 46th IEEE Conference on Decision and Control, New Orleans, USA, pp. 5678–5683, December 2007.Google Scholar