American Institute of Mathematical Sciences

Advanced
August  2008, 21(3): 687-701. doi: 10.3934/dcds.2008.21.687

Nearly optimal patchy feedbacks

Alberto Bressan 1, and  Fabio S. Priuli 2,

1. 

Department of Mathematics, Penn State University, University Park, Pa.16802
2. 

Department of Mathematical Sciences, NTNU, Trondheim, NO-7491, Norway

Received  August 2007 Revised  January 2008 Published  April 2008

The paper is concerned with a general optimization problem for a nonlinear control system, in the presence of a running cost and a terminal cost, with free terminal time. We prove the existence of a patchy feedback whose trajectories are all nearly optimal solutions, with pre-assigned accuracy.
Keywords: Robustness., Optimization, Discontinuous Feedback Control.
Mathematics Subject Classification: Primary: 34A36, 49J15; Secondary: 49J30, 93D0.
Citation: Alberto Bressan, Fabio S. Priuli. Nearly optimal patchy feedbacks. Discrete & Continuous Dynamical Systems, 2008, 21 (3) : 687-701. doi: 10.3934/dcds.2008.21.687
[1]

Cristopher Hermosilla. Stratified discontinuous differential equations and sufficient conditions for robustness. Discrete & Continuous Dynamical Systems, 2015, 35 (9) : 4415-4437. doi: 10.3934/dcds.2015.35.4415
[2]

Heinz Schättler, Urszula Ledzewicz. Perturbation feedback control: A geometric interpretation. Numerical Algebra, Control & Optimization, 2012, 2 (3) : 631-654. doi: 10.3934/naco.2012.2.631
[3]

Rohit Gupta, Farhad Jafari, Robert J. Kipka, Boris S. Mordukhovich. Linear openness and feedback stabilization of nonlinear control systems. Discrete & Continuous Dynamical Systems - S, 2018, 11 (6) : 1103-1119. doi: 10.3934/dcdss.2018063
[4]

Fatihcan M. Atay. Delayed feedback control near Hopf bifurcation. Discrete & Continuous Dynamical Systems - S, 2008, 1 (2) : 197-205. doi: 10.3934/dcdss.2008.1.197
[5]

Elena Braverman, Alexandra Rodkina. Stabilization of difference equations with noisy proportional feedback control. Discrete & Continuous Dynamical Systems - B, 2017, 22 (6) : 2067-2088. doi: 10.3934/dcdsb.2017085
[6]

Sanling Yuan, Yongli Song, Junhui Li. Oscillations in a plasmid turbidostat model with delayed feedback control. Discrete & Continuous Dynamical Systems - B, 2011, 15 (3) : 893-914. doi: 10.3934/dcdsb.2011.15.893
[7]

Daniel Franco, Chris Guiver, Phoebe Smith, Stuart Townley. A switching feedback control approach for persistence of managed resources. Discrete & Continuous Dynamical Systems - B, 2021  doi: 10.3934/dcdsb.2021109
[8]

Ruxandra Stavre. Optimization of the blood pressure with the control in coefficients. Evolution Equations & Control Theory, 2020, 9 (1) : 131-151. doi: 10.3934/eect.2020019
[9]

Dan Tiba. Implicit parametrizations and applications in optimization and control. Mathematical Control & Related Fields, 2020, 10 (3) : 455-470. doi: 10.3934/mcrf.2020006
[10]

Shu Zhang, Jian Xu. Time-varying delayed feedback control for an internet congestion control model. Discrete & Continuous Dynamical Systems - B, 2011, 16 (2) : 653-668. doi: 10.3934/dcdsb.2011.16.653
[11]

Guirong Jiang, Qishao Lu. The dynamics of a Prey-Predator model with impulsive state feedback control. Discrete & Continuous Dynamical Systems - B, 2006, 6 (6) : 1301-1320. doi: 10.3934/dcdsb.2006.6.1301
[12]

Changzhi Wu, Kok Lay Teo, Volker Rehbock. Optimal control of piecewise affine systems with piecewise affine state feedback. Journal of Industrial & Management Optimization, 2009, 5 (4) : 737-747. doi: 10.3934/jimo.2009.5.737
[13]

Zhenyu Lu, Junhao Hu, Xuerong Mao. Stabilisation by delay feedback control for highly nonlinear hybrid stochastic differential equations. Discrete & Continuous Dynamical Systems - B, 2019, 24 (8) : 4099-4116. doi: 10.3934/dcdsb.2019052
[14]

Edward Hooton, Pavel Kravetc, Dmitrii Rachinskii. Restrictions to the use of time-delayed feedback control in symmetric settings. Discrete & Continuous Dynamical Systems - B, 2018, 23 (2) : 543-556. doi: 10.3934/dcdsb.2017207
[15]

Baltazar D. Aguda, Ricardo C.H. del Rosario, Michael W.Y. Chan. Oncogene-tumor suppressor gene feedback interactions and their control. Mathematical Biosciences & Engineering, 2015, 12 (6) : 1277-1288. doi: 10.3934/mbe.2015.12.1277
[16]

Haiying Jing, Zhaoyu Yang. The impact of state feedback control on a predator-prey model with functional response. Discrete & Continuous Dynamical Systems - B, 2004, 4 (3) : 607-614. doi: 10.3934/dcdsb.2004.4.607
[17]

B. A. Wagner, Andrea L. Bertozzi, L. E. Howle. Positive feedback control of Rayleigh-Bénard convection. Discrete & Continuous Dynamical Systems - B, 2003, 3 (4) : 619-642. doi: 10.3934/dcdsb.2003.3.619
[18]

Bernold Fiedler, Isabelle Schneider. Stabilized rapid oscillations in a delay equation: Feedback control by a small resonant delay. Discrete & Continuous Dynamical Systems - S, 2020, 13 (4) : 1145-1185. doi: 10.3934/dcdss.2020068
[19]

V. Rehbock, K.L. Teo, L.S. Jennings. Suboptimal feedback control for a class of nonlinear systems using spline interpolation. Discrete & Continuous Dynamical Systems, 1995, 1 (2) : 223-236. doi: 10.3934/dcds.1995.1.223
[20]

Cătălin-George Lefter, Elena-Alexandra Melnig. Feedback stabilization with one simultaneous control for systems of parabolic equations. Mathematical Control & Related Fields, 2018, 8 (3&4) : 777-787. doi: 10.3934/mcrf.2018034

2020 Impact Factor: 1.392

Tools

Metrics

  • PDF downloads (54)
  • HTML views (0)
  • Cited by (4)

Other articles
by authors

[Back to Top]

Copyright © 2021 American Institute of Mathematical Sciences