Gray, W. Steven; Ebrahimi-Fard, Kurusch; Schmeding, Alexander Decompositions of nonlinear input-output systems to zero the output. (English) Zbl 1545.93206 Syst. Control Lett. 187, Article ID 105783, 8 p. (2024). MSC: 93C10 × Cite Format Result Cite Review PDF Full Text: DOI
Venkatesh, G. S.; Gray, W. Steven Formal power series approach to nonlinear systems with additive static feedback. (English) Zbl 1519.93083 Int. J. Control 96, No. 6, 1619-1637 (2023). MSC: 93B52 93B24 93C10 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Gray, W. Steven; Palmstrøm, Mathias; Schmeding, Alexander Continuity of formal power series products in nonlinear control theory. (English) Zbl 1519.93102 Found. Comput. Math. 23, No. 3, 803-832 (2023). MSC: 93C10 46A04 46A13 47N70 22E65 46B45 16T30 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Gray, W. Steven Entropy of generating series for nonlinear input-output systems and their interconnections. (English) Zbl 07612166 SIGMA, Symmetry Integrability Geom. Methods Appl. 18, Paper 082, 15 p. (2022). MSC: 93C10 94A17 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Grushkovskaya, Victoria; Ebenbauer, Christian Extremum seeking control of nonlinear dynamic systems using Lie bracket approximations. (English) Zbl 1543.93110 Int. J. Adapt. Control Signal Process. 35, No. 7, 1233-1255 (2021). MSC: 93C10 93D20 93C40 93C15 × Cite Format Result Cite Review PDF Full Text: DOI
Benner, Peter; Seidel-Morgenstern, Andreas; Zuyev, Alexander Analysis of switching strategies for the optimization of periodic chemical reactions with controlled flow-rate. (English) Zbl 1480.49023 Awrejcewicz, Jan (ed.), Perspectives in dynamical systems III: control and stability. Selected papers based on the presentations at the 15th international conference on dynamical systems – theory and applications, DSTA, Łódź, Poland, December 2–5, 2019. Cham: Springer. Springer Proc. Math. Stat. 364, 59-69 (2021). MSC: 49K30 92E20 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Gray, W. Steven; Ebrahimi-Fard, Kurusch Generating series for networks of Chen-Fliess series. (English) Zbl 1454.93090 Syst. Control Lett. 147, Article ID 104827, 9 p. (2021). MSC: 93B70 93C10 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Gray, W. Steven; Venkatesh, G. S.; Duffaut Espinosa, Luis A. Nonlinear system identification for multivariable control via discrete-time Chen-Fliess series. (English) Zbl 1453.93061 Automatica 119, Article ID 109085, 8 p. (2020). Reviewer: Denis Sidorov (Irkutsk) MSC: 93B30 93C35 93C40 93C10 × Cite Format Result Cite Review PDF Full Text: DOI
Ebrahimi-Fard, Kurusch; Gray, W. Steven; Manchon, Dominique Evaluating generating functions for periodic multiple polylogarithms via rational Chen-Fliess series. (English) Zbl 1456.11161 Burgos Gil, José Ignacio (ed.) et al., Periods in quantum field theory and arithmetic. Based on the presentations at the research trimester on multiple zeta values, multiple polylogarithms, and quantum field theory, ICMAT 2014, Madrid, Spain, September 15–19, 2014. Cham: Springer. Springer Proc. Math. Stat. 314, 445-468 (2020). MSC: 11M32 11G55 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Gray, W. Steven; Venkatesh, G. S. Relative degree of interconnected SISO nonlinear control systems. (English) Zbl 1408.93044 Syst. Control Lett. 124, 99-105 (2019). MSC: 93B15 93C10 93B52 × Cite Format Result Cite Review PDF Full Text: DOI
Gray, W. Steven; Ebrahimi-Fard, Kurusch SISO output affine feedback transformation group and its Faà di Bruno Hopf algebra. (English) Zbl 1361.93016 SIAM J. Control Optim. 55, No. 2, 885-912 (2017). MSC: 93B52 93B25 93C10 93B18 16T30 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Duffaut Espinosa, Luis A.; Gray, W. Steven Functional series expansions for continuous-time switched systems. (English) Zbl 1317.93143 J. Dyn. Control Syst. 21, No. 2, 211-237 (2015). MSC: 93C30 93E03 93C10 03C15 34A34 47H30 60G51 × Cite Format Result Cite Review PDF Full Text: DOI
Litterer, Christian; Oberhauser, Harald On a Chen-Fliess approximation for diffusion functionals. (English) Zbl 1329.60185 Monatsh. Math. 175, No. 4, 577-593 (2014). MSC: 60H10 60J60 60F17 47A60 34H99 46T20 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Gray, W. Steven; Duffaut Espinosa, Luis A.; Thitsa, Makhin Left inversion of analytic nonlinear SISO systems via formal power series methods. (English) Zbl 1297.93091 Automatica 50, No. 9, 2381-2388 (2014). MSC: 93C10 93B18 93B52 × Cite Format Result Cite Review PDF Full Text: DOI
Thitsa, Makhin; Gray, W. Steven On the radius of convergence of interconnected analytic nonlinear input-output systems. (English) Zbl 1257.93050 SIAM J. Control Optim. 50, No. 5, 2786-2813 (2012). MSC: 93C10 93B28 47H30 × Cite Format Result Cite Review PDF Full Text: DOI Link
Gray, W. S.; Thitsa, M. A unified approach to generating series for mixed cascades of analytic nonlinear input-output systems. (English) Zbl 1253.93025 Int. J. Control 85, No. 11, 1737-1754 (2012). MSC: 93B15 × Cite Format Result Cite Review PDF Full Text: DOI
Chartier, Philippe; Murua, Ander; Sanz-Serna, Jesús María A formal series approach to averaging: exponentially small error estimates. (English) Zbl 1246.34043 Discrete Contin. Dyn. Syst. 32, No. 9, 3009-3027 (2012). MSC: 34C29 70K65 65L06 34A25 × Cite Format Result Cite Review PDF Full Text: DOI
Gray, W. Steven; Li, Yaqin Generating series for interconnected analytic nonlinear systems. (English) Zbl 1094.93012 SIAM J. Control Optimization 44, No. 2, 646-672 (2005). Reviewer: Bahman Yousefi (Shiraz) MSC: 93C10 93B28 47H30 47N70 × Cite Format Result Cite Review PDF Full Text: DOI
Gray, W. Steven; Wang, Yuan Fliess operators on \(L_{p}\) spaces: convergence and continuity. (English) Zbl 0994.93006 Syst. Control Lett. 46, No. 2, 67-74 (2002). MSC: 93B28 93B15 93C10 43A15 × Cite Format Result Cite Review PDF Full Text: DOI
Liu, Wensheng An approximation algorithm for nonholonomic systems. (English) Zbl 0887.34063 SIAM J. Control Optimization 35, No. 4, 1328-1365 (1997). MSC: 34H05 93C15 93B27 34E10 93B05 34A26 × Cite Format Result Cite Review PDF Full Text: DOI
Kawski, Matthias; Sussmann, Héctor J. Noncommutative power series and formal Lie-algebraic techniques in nonlinear control theory. (English) Zbl 0919.93035 Helmke, Uwe (ed.) et al., Operators, systems, and linear algebra. Three decades of algebraic systems theory. Dedicated to Paul A. Fuhrmann on the occasion of his 60th birthday. Stuttgart: B. G. Teubner. Eur. Consortium Math. Ind. 111-128 (1997). Reviewer: M.G.Nerurkar (Camden) MSC: 93C10 93B25 17B01 49K15 × Cite Format Result Cite Review PDF