LMIs for constrained polynomial interpolation with application in trajectory planning

Systems and Control Letters

Volumn 55, Issue 6, 2006, Pages 473-477

  Henrion, Didier ^a,b   Lasserre, Jean Bernard ^b,c  

^a LAAS CNRS   (France)

^b CZECH TECHNICAL UNIVERSITY IN PRAGUE   (Czech Republic)

^c INSTITUT DE MATHÉMATIQUES DE TOULOUSE   (France)

Author keywords

Algebraic polynomial approach; Computer aided control system design; Linear systems; LMI; Polynomial interpolation; Positive polynomials; Trajectory planning

Indexed keywords

ALGEBRA; CONSTRAINT THEORY; CONTROL SYSTEM ANALYSIS; LINEAR SYSTEMS; PLANNING; POLYNOMIALS; SATURATION (MATERIALS COMPOSITION); TRAJECTORIES;

ALGEBRAIC/POLYNOMIAL APPROACH; LINEAR MATRIX INEQUALITY (LMI); POSITIVE POLYNOMIALS; TRAJECTORY PLANNING;

INTERPOLATION;

EID: 33645943040     PISSN: 01676911     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.sysconle.2005.09.011     Document Type: Article

References (11)

1. Fliess M., and Marquez R. Continuous-time linear predictive control and flatness: a module-theoretic setting with examples. Internat. J. Control 73 7 (2000) 606-623
2. Henrion D., Tarbouriech S., and Kučera V. Control of linear systems subject to input constraints: a polynomial approach. Automatica 37 4 (2001) 597-604
3. Kailath T. Linear Systems (1980), Prentice-Hall, Englewood Cliffs, NJ
4. Kučera V. Discrete Linear Control: The Polynomial Approach (1979), Wiley, Chichester, UK
5. Lasserre J.B. Global optimization with polynomials and the problem of moments. SIAM J. Optim. 11 3 (2001) 796-817
6. Lévine J., and Nguyen D.V. Flat output characterization for linear systems using polynomial matrices. Systems Control Lett. 48 (2003) 69-75
7. Nesterov Yu. Squared functional systems and optimization problems. In: Frenk H., Roos K., Terlaky T., and Zhang S. (Eds). High Performance Optimization (2000), Kluwer Academic Publishers, Dordrecht, The Netherlands 405-440 (Chapter 17)
8. P.A. Parrilo, Structured semidefinite programs and semialgebraic geometry methods in robustness and optimization, Ph.D. Thesis, California Institute of Technology, Pasadena, CA, 2000.
9. PolyX, Ltd. The Polynomial Toolbox for Matlab. Prague, Czech Republic. Version 2.5 released in 2000.
10. Powers V., and Reznick R. Polynomials that are positive on an interval. Trans. Amer. Math. Soc. 352 10 (2000) 4677-4692
11. Sturm J.F. Using SeDuMi 1.02, a Matlab Toolbox for optimization over symmetric cones. Optim. Methods Software 11-12 (1999) 625-653