References
- Dacorogna, B. (2008). Direct Methods in the Calculus of Variations, 2nd Edn, Springer, Berlin.
- 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.
- Dorfman, R., Samuelson, P.A. and Solow, R.M. (1958). Linear Programming and Economic Analysis, McGraw-Hill, New York.
- 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.
- 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.
- 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.
- Grüne, L. and Müller, M.A. (2016). On the relation between strict dissipativity and turnpike properties, Systems& Control Letters 90: 45–53.
- 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.
- Gugat, M. (2021). On the turnpike property with interior decay for optimal control problems, Mathematics of Control Signals Systems 33: 237–258.
- Gugat, M. (2022). Optimal boundary control of the wave equation: The finite-time turnpike phenomenon, Mathematical Reports 24(74)(1–2): 179–186.
- 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.
- Gugat, M. and Lazar, M. (2023). Turnpike properties for partially uncontrollable systems, Automatica 149: 110844.
- 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.
- 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.
- 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.
- Porretta, A. and Zuazua, E. (2013). Long time versus steady state optimal control, SIAM Journal on Control Optimization 51(6): 4242–4273.
- 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.
- Sakamoto, N. and Zuazua, E. (2021). The turnpike property in nonlinear optimal control—A geometric approach, Auto-matica 134: 109939.
- 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.
- 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.
- 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.
- Trélat, E. and Zuazua, E. (2015). The turnpike property in finite-dimensional nonlinear optimal control, Journal of Differential Equations 258(1): 81–114.
- Tucsnak, M. and Weiss, G. (2009). Observation and Control for Operator Semigroups, Birkhäuser, Basel.
- Zaslavski, A.J. (2006). Turnpike Properties in the Calculus of Variations and Optimal Control, Springer, New York.
- Zaslavski, A.J. (2014). Turnpike Phenomenon and Infinite Horizon Optimal Control, Springer, Cham.