Abstract
We consider nonlinear systems with polynomial vector fields and pose two classes of system theoretic problems that may be solved by sum of squares programming. The first is disturbance analysis using three different norms to bound the reachable set. The second is the synthesis of a polynomial state feedback controller to enlarge the provable region of attraction. We also outline a variant of the state feedback synthesis for handling systems with input saturation. Both classes of problems are demonstrated using two-state nonlinear systems.
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Jarvis-Wloszek, Z., Feeley, R., Tan, W., Sun, K., Packard, A. Control Applications of Sum of Squares Programming. In: Henrion, D., Garulli, A. (eds) Positive Polynomials in Control. Lecture Notes in Control and Information Science, vol 312. Springer, Berlin, Heidelberg. https://doi.org/10.1007/10997703_1
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DOI: https://doi.org/10.1007/10997703_1
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-23948-2
Online ISBN: 978-3-540-31594-0
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