Accès libre

Optimal Control Problems without Terminal Constraints: The Turnpike Property with Interior Decay

International Journal of Applied Mathematics and Computer Science's Cover Image
International Journal of Applied Mathematics and Computer Science
Mathematical Modeling in Medical Problems (Special section, pp. 349-428), Urszula Foryś, Katarzyna Rejniak, Barbara Pękala, Agnieszka Bartłomiejczyk (Eds.)
À propos de cet article

Citez

Dacorogna, B. (2008). Direct Methods in the Calculus of Variations, 2nd Edn, Springer, Berlin. Search in Google Scholar

Damm, T., Grüne, L., Stieler, M. and Worthmann, K. (2014). An exponential turnpike theorem for dissipative discrete time optimal control problems, SIAM Journal on Control Optimization 52(3): 1935–1957. Search in Google Scholar

Dorfman, R., Samuelson, P.A. and Solow, R.M. (1958). Linear Programming and Economic Analysis, McGraw-Hill, New York. Search in Google Scholar

Faulwasser, T., Flaßkamp, K., Ober-Blöbaum, S., Schaller, M. and Worthmann, K. (2022). Manifold turnpikes, trims, and symmetries, Mathematics of Control, Signals, and Systems 34: 759–788. Search in Google Scholar

Faulwasser, T., Korda, M., Jones, C.N. and Bonvin, D. (2017). On turnpike and dissipativity properties of continuous-time optimal control problems, Automatica 81: 297–304. Search in Google Scholar

Grüne, L. and Guglielmi, R. (2018). Turnpike properties and strict dissipativity for discrete time linear quadratic optimal control problems, SIAM Journal on Control Optimization 56(2): 1282–1302. Search in Google Scholar

Grüne, L. and Müller, M.A. (2016). On the relation between strict dissipativity and turnpike properties, Systems& Control Letters 90: 45–53. Search in Google Scholar

Grüne, L., Schaller, M. and Schiela, A. (2020). Exponential sensitivity and turnpike analysis for linear quadratic optimal control of general evolution equations, Journal of Differential Equations 268(12): 7311–7341. Search in Google Scholar

Gugat, M. (2021). On the turnpike property with interior decay for optimal control problems, Mathematics of Control Signals Systems 33: 237–258. Search in Google Scholar

Gugat, M. (2022). Optimal boundary control of the wave equation: The finite-time turnpike phenomenon, Mathematical Reports 24(74)(1–2): 179–186. Search in Google Scholar

Gugat, M. and Hante, F.M. (2019). On the turnpike phenomenon for optimal boundary control problems with hyperbolic systems, SIAM Journal on Control Optimization 57(1): 264–289. Search in Google Scholar

Gugat, M. and Lazar, M. (2023). Turnpike properties for partially uncontrollable systems, Automatica 149: 110844. Search in Google Scholar

Gugat, M. and Leugering, G. (2017). Time delay in optimal control loops for wave equations, ESAIM: Control Optimisation and Calculus of Variations 23(1): 13–37. Search in Google Scholar

Hernández-Santamaría, V., Lazar, M. and Zuazua, E. (2019). Greedy optimal control for elliptic problems and its application to turnpike problems, Numerische Mathematik 141(2): 455–493. Search in Google Scholar

Mammadov, M.A. (2014). Turnpike theorem for an infinite horizon optimal control problem with time delay, SIAM Journal on Control Optimization 52(1): 420–438. Search in Google Scholar

Porretta, A. and Zuazua, E. (2013). Long time versus steady state optimal control, SIAM Journal on Control Optimization 51(6): 4242–4273. Search in Google Scholar

Rabah, R., Sklyar, G. and Barkhayev, P. (2017). Exact null controllability, complete stabilizability and continuous final observability of neutral type systems, International Journal of Applied Mathematics and Computer Science 27(3): 489–499, DOI: 10.1515/amcs-2017-0034. Search in Google Scholar

Sakamoto, N. and Zuazua, E. (2021). The turnpike property in nonlinear optimal control—A geometric approach, Auto-matica 134: 109939. Search in Google Scholar

Sontag, E.D. (1991). Kalman’s controllability rank condition: From linear to nonlinear, in A.C. Antoulas (Ed.) Mathematical System Theory, Springer, Berlin, pp. 453–462. Search in Google Scholar

Trélat, E. and Zhang, C. (2018). Integral and measure-turnpike properties for infinite-dimensional optimal control systems, Mathematics of Control, Signals and Systems 30, Article no. 3. Search in Google Scholar

Trélat, E., Zhang, C. and Zuazua, E. (2018). Steady-state and periodic exponential turnpike property for optimal control problems in Hilbert spaces, SIAM Journal on Control Optimization 56(2): 1222–1252. Search in Google Scholar

Trélat, E. and Zuazua, E. (2015). The turnpike property in finite-dimensional nonlinear optimal control, Journal of Differential Equations 258(1): 81–114. Search in Google Scholar

Tucsnak, M. and Weiss, G. (2009). Observation and Control for Operator Semigroups, Birkhäuser, Basel. Search in Google Scholar

Zaslavski, A.J. (2006). Turnpike Properties in the Calculus of Variations and Optimal Control, Springer, New York. Search in Google Scholar

Zaslavski, A.J. (2014). Turnpike Phenomenon and Infinite Horizon Optimal Control, Springer, Cham. Search in Google Scholar

eISSN:
2083-8492
Langue:
Anglais
Périodicité:
4 fois par an
Sujets de la revue:
Mathematics, Applied Mathematics