Robust-to-Dynamics Optimization

Published Online:https://doi.org/10.1287/moor.2023.0116

References

  • [1] Ahmadi AA, Günlük O (2015) Robust-to-dynamics linear programming. Proc. 54th IEEE Conf. Decision Control (IEEE, Piscataway, NJ), 5915–5919.Google Scholar
  • [2] Ahmadi AA, Jungers RM (2016) Lower bounds on complexity of Lyapunov functions for switched linear systems. Nonlinear Anal. Hybrid Systems 21:118–129.CrossrefGoogle Scholar
  • [3] Ahmadi AA, Chaudhry A, Sindhwani V, Tu S (2023) Safely learning dynamical systems. Working paper, Princeton University, Princeton, NJ.Google Scholar
  • [4] Ahmadi AA, Jungers RM, Parrilo PA, Roozbehani M (2014) Joint spectral radius and path-complete graph Lyapunov functions. SIAM J. Control Optim. 52:687–717.CrossrefGoogle Scholar
  • [5] Almagor S, Ouaknine J, Worrell J (2019) The semialgebraic orbit problem. Leibniz Internat. Proc. Informatics, vol. 136 (Schloss Dagstuhl, Wadern, Germany), 6:1–6:15.Google Scholar
  • [6] Ando T, Shih M-H (1998) Simultaneous contractibility. SIAM J. Matrix Anal. Appl. 19:487–498.CrossrefGoogle Scholar
  • [7] Andrade GP, Frongillo R, Piliouras G (2023) No-regret learning in games is Turing complete. Proc. 24th ACM Conf. Econom. Comput. (Association for Computing Machinery, New York), 111.Google Scholar
  • [8] Athanasopoulos N, Jungers RM (2016) Computing the domain of attraction of switching systems subject to non-convex constraints. Proc. 19th Internat. Conf. Hybrid Systems Comput. Control (ACM, New York), 41–50.Google Scholar
  • [9] Barvinok A (2002) A Course in Convexity, vol. 54 (American Mathematical Society, Providence, RI).CrossrefGoogle Scholar
  • [10] Ben-Tal A, Nemirovski A (2002) Robust optimization–methodology and applications. Math. Programming 92:453–480.CrossrefGoogle Scholar
  • [11] Ben-Tal A, El Ghaoui L, Nemirovski A (2009) Robust Optimization (Princeton University Press, Princeton, NJ).CrossrefGoogle Scholar
  • [12] Berger MA, Wang Y (1992) Bounded semigroups of matrices. Linear Algebra Appl. 166:21–27.CrossrefGoogle Scholar
  • [13] Bertsimas D, Brown DB, Caramanis C (2011) Theory and applications of robust optimization. SIAM Rev. 53:464–501.CrossrefGoogle Scholar
  • [14] Bertsimas D, Pachamanova D, Sim M (2004) Robust linear optimization under general norms. Oper. Res. Lett. 32:510–516.CrossrefGoogle Scholar
  • [15] Birkhoff G (1946) Tres observaciones sobre el algebra lineal. Universidad Nacional de Tucuman Ser. A 5:147–154.Google Scholar
  • [16] Bitsoris G (1988) Positively invariant polyhedral sets of discrete-time linear systems. Internat. J. Control 47:1713–1726.CrossrefGoogle Scholar
  • [17] Blanchini F (1999) Set invariance in control. Automatica J. IFAC 35:1747–1767.CrossrefGoogle Scholar
  • [18] Blondel VD, Nesterov Y (2005) Computationally efficient approximations of the joint spectral radius. SIAM J. Matrix Anal. Appl. 27:256–272.CrossrefGoogle Scholar
  • [19] Blondel VD, Portier N (2002) The presence of a zero in an integer linear recurrent sequence is NP-hard to decide. Linear Algebra Appl. 351:91–98.CrossrefGoogle Scholar
  • [20] Blondel VD, Tsitsiklis JN (2000) A survey of computational complexity results in systems and control. Automatica J. IFAC 36:1249–1274.CrossrefGoogle Scholar
  • [21] Boyd S, Vandenberghe L (2004) Convex Optimization (Cambridge University Press, Cambridge, UK).CrossrefGoogle Scholar
  • [22] Cornfeld I, Fomin S, Sinai Y (1982) Ergodic Theory (Springer-Verlag, New York).CrossrefGoogle Scholar
  • [23] Dahleh M, Dahleh MA, Verghese G (2004) Lectures on dynamic systems and control. Working paper, Munther Dahleh Research Group, Cambridge, MA.Google Scholar
  • [24] Djelassi H, Mitsos A, Stein O (2021) Recent advances in nonconvex semi-infinite programming: Applications and algorithms. EURO J. Comput. Optim. 9:100006.CrossrefGoogle Scholar
  • [25] Garcia CE, Prett DM, Morari M (1989) Model predictive control: Theory and practice—A survey. Automatica J. IFAC 25:335–348.CrossrefGoogle Scholar
  • [26] Gilbert EG, Tan KT (1991) Linear systems with state and control constraints: The theory and application of maximal output admissible sets. IEEE Trans. Automatic Control 36:1008–1020.CrossrefGoogle Scholar
  • [27] Hainry E (2009) Decidability and undecidability in dynamical systems. Research Report No. inria-00429965, Nancy Universite, LORIA, Universite Henri Poincare, Nancy, France.Google Scholar
  • [28] Halava V, Hirvensalo M (2007) Improved matrix pair undecidability results. Acta Inform. 44:191–205.CrossrefGoogle Scholar
  • [29] Jungers RM (2009) The joint spectral radius: Theory and applications. Lecture Notes Control Inform. Sci., vol. 385 (Springer, Berlin, Heidelberg).Google Scholar
  • [30] Karimov T, Kelmendi E, Ouaknine J, Worrell J (2022) What’s Decidable About Discrete Linear Dynamical Systems? (Springer Nature Switzerland, Cham, Switzerland), 21–38.Google Scholar
  • [31] Karimov T, Kelmendi E, Nieuwveld J, Ouaknine J, Worrell J (2023) The power of positivity. 2023 38th Annual ACM/IEEE Sympos. Logic Comput. Sci. (LICS) (IEEE, Piscataway, NJ), 1–11.Google Scholar
  • [32] Kerrigan EC, Maciejowski JM (2000) Invariant sets for constrained nonlinear discrete-time systems with application to feasibility in model predictive control. Proc. 39th IEEE Conf. Decision Control, vol. 5 (IEEE, Piscataway, NJ), 4951–4956.Google Scholar
  • [33] Khalil H (2002) Nonlinear Systems, 3rd ed. (Prentice Hall, Hoboken, NJ).Google Scholar
  • [34] Korda M, Henrion D, Jones CN (2014) Convex computation of the maximum controlled invariant set for polynomial control systems. SIAM J. Control Optim. 52:2944–2969.CrossrefGoogle Scholar
  • [35] Kozlov MK, Tarasov SP, Khachiyan LG (1980) The polynomial solvability of convex quadratic programming. USSR Comput. Math. Math. Phys. 20:223–228.CrossrefGoogle Scholar
  • [36] Legat B, Tabuada P, Jungers RM (2018) Computing controlled invariant sets for hybrid systems with applications to model-predictive control. Preprint, submitted February 17, https://arxiv.org/abs/1802.04522.Google Scholar
  • [37] López M, Still G (2007) Semi-infinite programming. Eur. J. Oper. Res. 180:491–518.CrossrefGoogle Scholar
  • [38] Majumdar A, Ahmadi AA, Tedrake R (2014) Control and verification of high-dimensional systems with DSOS and SDSOS programming. 53rd IEEE Conf. Decision Control (IEEE, Piscataway, NJ), 394–401.Google Scholar
  • [39] Mezić I, Wiggins S (1999) A method for visualization of invariant sets of dynamical systems based on the ergodic partition. Chaos 9:213–218.CrossrefGoogle Scholar
  • [40] Mulvey JM, Vanderbei RJ, Zenios SA (1995) Robust optimization of large-scale systems. Oper. Res. 43:264–281.LinkGoogle Scholar
  • [41] Niven I (1956) Irrational Numbers, The Carus Mathematical Monographs (Mathematical Association of America, Washington, DC).CrossrefGoogle Scholar
  • [42] Parrilo PA, Jadbabaie A (2008) Approximation of the joint spectral radius using sum of squares. Linear Algebra Appl. 428:2385–2402.CrossrefGoogle Scholar
  • [43] Paz A (1971) Introduction to Probabilistic Automata (Academic Press, New York).Google Scholar
  • [44] Reemtsen R, Rückmann J (1998) Semi-Infinite Programming (Springer-Science, New York).CrossrefGoogle Scholar
  • [45] Rostalski P, Sturmfels B (2010) Dualities in convex algebraic geometry. Preprint, submitted June 25, https://arxiv.org/abs/1006.4894.Google Scholar
  • [46] Rota GC, Strang WG (1960) A note on the joint spectral radius. Indagationes Mathematicae 22:379–381.CrossrefGoogle Scholar
  • [47] Rote G (2023) Probabilistic finite automaton emptiness is undecidable. Technical report, Institute of Computer Science, FU Berlin, Berlin.Google Scholar
  • [48] Royset JO (2020) Set-convergence and its application: A tutorial. Set-Valued Variational Anal. 28:707–732.CrossrefGoogle Scholar
  • [49] Schrijver A (1998) Theory of Linear and Integer Programming (John Wiley & Sons, Hoboken, NJ).Google Scholar
  • [50] Shorten R, Wirth F, Mason O, Wulff K, King C (2007) Stability criteria for switched and hybrid systems. SIAM Rev. 49:545–592.CrossrefGoogle Scholar
  • [51] Sipser M (2006) Introduction to the Theory of Computation, vol. 2 (Thomson Course Technology, Cambridge, MA).Google Scholar
INFORMS site uses cookies to store information on your computer. Some are essential to make our site work; Others help us improve the user experience. By using this site, you consent to the placement of these cookies. Please read our Privacy Statement to learn more.