International Journal of Robust and Nonlinear Control

Volume 24, Issue 16 pp. 2365-2387

Research Article

A sum of squares approach to backstepping controller synthesis for piecewise affine and polynomial systems

B. Samadi,

B. Samadi

Department of Electrical Engineering, Amirkabir University of Technology, Tehran, Iran

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L. Rodrigues,

Corresponding Author

L. Rodrigues

Department of Electrical and Computer Engineering, Concordia University, 1515 St. Catherine W., Montréal, QC H3G 2W1 Canada

Correspondence to: L. Rodrigues, Department of Electrical and Computer Engineering, Concordia University, 1515 St. Catherine W., Montréal, QC H3G 2W1, Canada.

E-mail: [email protected]

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B. Samadi,

B. Samadi

Department of Electrical Engineering, Amirkabir University of Technology, Tehran, Iran

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L. Rodrigues,

Corresponding Author

L. Rodrigues

Department of Electrical and Computer Engineering, Concordia University, 1515 St. Catherine W., Montréal, QC H3G 2W1 Canada

Correspondence to: L. Rodrigues, Department of Electrical and Computer Engineering, Concordia University, 1515 St. Catherine W., Montréal, QC H3G 2W1, Canada.

E-mail: [email protected]

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First published: 10 April 2013

https://doi.org/10.1002/rnc.2994

Citations: 14

B. Samadi is currently with the Department of Research and Development, Maplesoft, 615 Kumph Drive, Waterloo, ON N2V 1K8, Canada.

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SUMMARY

This paper develops a backstepping controller synthesis methodology for piecewise polynomial (PWP) systems in strict form. The main contribution of the paper is to formulate sufficient conditions for controller design for PWP systems in strict form as a sum of squares feasibility problem under the assumption that an initial control Lyapunov function exists to start the iterative backstepping procedure. This problem can then be translated into a convex SDP problem and solved by available software packages. The controller synthesis problem for PWP systems in strict feedback form is divided into two cases. The first case consists of the construction of a sum of squares polynomial control Lyapunov function for PWP systems with discontinuous vector fields. The second case addresses the construction of a PWP control Lyapunov function for PWP systems with continuous vector fields. One major advantage of the proposed method is the fact that it can handle systems with discontinuous vector fields and sliding modes. The new synthesis method is applied to several numerical examples. One of these examples offers the first convex optimization solution to piecewise affine (PWA) control of a benchmark circuit system addressed before in the literature using non-convex PWA control solutions. Copyright © 2013 John Wiley & Sons, Ltd.

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Volume24, Issue16

10 November 2014

Pages 2365-2387

A sum of squares approach to backstepping controller synthesis for piecewise affine and polynomial systems

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A sum of squares approach to backstepping controller synthesis for piecewise affine and polynomial systems

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