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Control of Uncertain Systems

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Springer Handbook of Automation

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Abstract

Dynamical systems typically have uncertainties due to modeling errors, measurement inaccuracy, mutations in the evolutionary processes, etc. The stochastic deviations can compound overtime and can lead to catastrophic results. In this chapter, we will present different approaches for decision-making in systems with uncertainties. We first consider model predictive control, which models and learns the system and uses the learned model to optimize the system. In many cases, a prior model of the system is not known. For such cases, we will also explain Gaussian process regression, which is one of the efficient modeling techniques. Further, we present constrained Markov decision process (CMDP) as an approach for decision-making with uncertainties, where the system is modeled as a MDP with constraints. The formalism of CMDP is extended to a model-free approach based on reinforcement learning to make decisions in the presence of constraints.

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References

  1. Altman, E.: Constrained Markov Decision Processes, vol. 7. CRC Press, Boca Raton (1999)

    MATH  Google Scholar 

  2. Farrell, R., Polli, A.: Comparison of unconstrained dynamic matrix control to conventional feedback control for a first order model. Adv. Instrum. Control 45(2), 1033 (1990)

    Google Scholar 

  3. Holkar, K., Waghmare, L.: An overview of model predictive control. Int. J. Control Autom. 3(4), 47–63 (2010)

    Google Scholar 

  4. Rachael, J., Rault, A., Testud, J., Papon, J.: Model predictive heuristic control: application to an industrial process. Automatica 14(5), 413–428 (1978)

    Google Scholar 

  5. Cutler, C.R., Ramaker, B.L.: Dynamic matrix control—a computer control algorithm. In: Joint Automatic Control Conference, vol. 17, p. 72 (1980)

    Google Scholar 

  6. Prett, D.M., Gillette, R.: Optimization and constrained multivariable control of a catalytic cracking unit. In: Joint Automatic Control Conference, vol. 17, p. 73 (1980)

    Google Scholar 

  7. Garcia, C.E., Prett, D.M., Morari, M.: Model predictive control: theory and practice—a survey. Automatica 25(3), 335–348 (1989)

    MATH  Google Scholar 

  8. Mayne, D.Q., Rawlings, J.B., Rao, C.V., Scokaert, P.O.: Constrained model predictive control: stability and optimality. Automatica 36(6), 789–814 (2000)

    MathSciNet  MATH  Google Scholar 

  9. Fernandez-Camacho, E., Bordons-Alba, C.: Model Predictive Control in the Process Industry. Springer, Berlin (1995)

    Google Scholar 

  10. Zadeh, L., Whalen, B.: On optimal control and linear programming. IRE Trans. Autom. Control 7(4), 45–46 (1962)

    Google Scholar 

  11. Propoi, A.: Application of linear programming methods for the synthesis of automatic sampled-data systems. Avtomat. i Telemeh 24, 912–920 (1963)

    MathSciNet  Google Scholar 

  12. Gutman, P.O.: Controllers for bilinear and constrained linear systems. PhD Thesis TFRT-1022 (1982)

    Google Scholar 

  13. Chang, T., Seborg, D.: A linear programming approach for multivariable feedback control with inequality constraints. Int. J. Control 37(3), 583–597 (1983)

    MATH  Google Scholar 

  14. Lorenzen, M., Cannon, M., Allgöwer, F.: Robust MPC with recursive model update. Automatica 103, 461–471 (2019)

    MathSciNet  MATH  Google Scholar 

  15. Bujarbaruah, M., Zhang, X., Tanaskovic, M., Borrelli, F.: Adaptive stochastic mpc under time varying uncertainty. IEEE Trans. Autom. Control (2020)

    MATH  Google Scholar 

  16. Kocijan, J., Murray-Smith, R., Rasmussen, C.E., Girard, A.: Gaussian process model based predictive control. In: Proceedings of the 2004 American Control Conference, vol. 3, pp. 2214–2219. IEEE (2004)

    Google Scholar 

  17. Cao, G., Lai, E.M.K., Alam, F.: Gaussian process model predictive control of an unmanned quadrotor. J. Intell. Robot. Syst. 88(1), 147–162 (2017)

    Google Scholar 

  18. Hewing, L., Kabzan, J., Zeilinger, M.N.: Cautious model predictive control using gaussian process regression. IEEE Trans. Control Syst. Technol. (2019)

    Google Scholar 

  19. Matschek, J., Himmel, A., Sundmacher, K., Findeisen, R.: Constrained Gaussian process learning for model predictive control. IFAC-PapersOnLine 53(2), 971–976 (2020)

    Google Scholar 

  20. Kolesar, P.: A markovian model for hospital admission scheduling. Manag. Sci. 16(6), B-384 (1970)

    Google Scholar 

  21. Golabi, K., Kulkarni, R.B., Way, G.B.: A statewide pavement management system. Interfaces 12(6), 5–21 (1982)

    Google Scholar 

  22. Winden, C., Dekker, R.: Markov decision models for building maintenance: a feasibility study. J. Oper. Res. Soc. 49, 928–935 (1998)

    MATH  Google Scholar 

  23. Shi, B., Ozsoy, M.G., Hurley, N., Smyth, B., Tragos, E.Z., Geraci, J., Lawlor, A.: Pyrecgym: a reinforcement learning gym for recommender systems. In: Proceedings of the 13th ACM Conference on Recommender Systems, pp. 491–495 (2019)

    Google Scholar 

  24. Luketina, J., Nardelli, N., Farquhar, G., Foerster, J., Andreas, J., Grefenstette, E., Whiteson, S., Rocktäschel, T.: A survey of reinforcement learning informed by natural language. In: Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence, IJCAI-19, pp. 6309–6317. International Joint Conferences on Artificial Intelligence Organization (2019)

    Google Scholar 

  25. Al-Abbasi, A.O., Ghosh, A., Aggarwal, V.: Deeppool: Distributed model-free algorithm for ride-sharing using deep reinforcement learning. IEEE Trans. Intell. Transp. Syst. 20(12), 4714–4727 (2019)

    Google Scholar 

  26. Singh, A., Al-Abbasi, A.O., Aggarwal, V.: A distributed model-free algorithm for multi-hop ride-sharing using deep reinforcement learning. IEEE Trans. Intell. Transp. Syst. (2021)

    Google Scholar 

  27. Chen, J., Umrawal, A.K., Lan, T., Aggarwal, V.: Deepfreight: A model-free deep-reinforcement-learning-based algorithm for multi-transfer freight delivery. In: International Conference on Automated Planning and Scheduling (ICAPS) (2021)

    Google Scholar 

  28. Wang, Y., Li, Y., Lan, T., Aggarwal, V.: Deepchunk: Deep q-learning for chunk-based caching in wireless data processing networks. IEEE Trans. Cogn. Commun. Netw. 5(4), 1034–1045 (2019)

    Google Scholar 

  29. Geng, N., Lan, T., Aggarwal, V., Yang, Y., Xu, M.: A multi-agent reinforcement learning perspective on distributed traffic engineering. In: 2020 IEEE 28th International Conference on Network Protocols (ICNP), pp. 1–11. IEEE (2020)

    Google Scholar 

  30. Silver, D., Schrittwieser, J., Simonyan, K., Antonoglou, I., Huang, A., Guez, A., Hubert, T., Baker, L., Lai, M., Bolton, A., Chen, Y., Lillicrap, T., Hui, F., Sifre, L., Driessche, G.V.D., Graepel, T., Hassabis, D.: Mastering the game of go without human knowledge. Nature 550, 354 – 359 (2017)

    Google Scholar 

  31. Silver, D., Hubert, T., Schrittwieser, J., Antonoglou, I., Lai, M., Guez, A., Lanctot, M., Sifre, L., Kumaran, D., Graepel, T., et al.: A general reinforcement learning algorithm that masters chess, Shogi, and go through self-play. Science 362(6419), 1140–1144 (2018)

    MathSciNet  MATH  Google Scholar 

  32. Åström, K.J., Wittenmark, B.: Adaptive Control, 2nd edn. Addison-Wesley Longman Publishing, Boston (1994)

    MATH  Google Scholar 

  33. Djonin, D.V., Krishnamurthy, V.: Mimo transmission control in fading channels: a constrained markov decision process formulation with monotone randomized policies. IEEE Trans. Signal Process. 55(10), 5069–5083 (2007)

    MathSciNet  MATH  Google Scholar 

  34. Lizotte, D., Bowling, M.H., Murphy, A.S.: Efficient reinforcement learning with multiple reward functions for randomized controlled trial analysis. In: Proceedings of the 27th International Conference on International Conference on Machine Learning, ICML’10, pp. 695–702. Omnipress, USA (2010)

    Google Scholar 

  35. Drugan, M.M., Nowe, A.: Designing multi-objective multi-armed bandits algorithms: a study. In: The 2013 International Joint Conference on Neural Networks (IJCNN), pp. 1–8. IEEE (2013)

    Google Scholar 

  36. Achiam, J., Held, D., Tamar, A., Abbeel, P.: Constrained policy optimization. In: Proceedings of the 34th International Conference on Machine Learning—Volume 70, ICML’17, pp. 22–31. JMLR.org (2017)

    Google Scholar 

  37. Abels, A., Roijers, D., Lenaerts, T., Nowé, A., Steckelmacher, D.: Dynamic weights in multi-objective deep reinforcement learning. In: K. Chaudhuri, R. Salakhutdinov (eds.) Proceedings of the 36th International Conference on Machine Learning. Proceedings of Machine Learning Research, vol. 97, pp. 11–20. PMLR, Long Beach (2019)

    Google Scholar 

  38. Raghu, R., Upadhyaya, P., Panju, M., Agarwal, V., Sharma, V.: Deep reinforcement learning based power control for wireless multicast systems. In: 2019 57th Annual Allerton Conference on Communication, Control, and Computing (Allerton), pp. 1168–1175. IEEE (2019)

    Google Scholar 

  39. Gattami, A., Bai, Q., Agarwal, V.: Reinforcement learning for multi-objective and constrained markov decision processes. In: Proceedings of AISTATS (2021)

    Google Scholar 

  40. Sastry, S., Bodson, M.: Adaptive Control: Stability, Convergence and Robustness. Courier Corporation (2011)

    MATH  Google Scholar 

  41. Kumar, P.R.: A survey of some results in stochastic adaptive control. SIAM J. Control Optim. 23(3), 329–380 (1985)

    MathSciNet  MATH  Google Scholar 

  42. Kalman, R.E.: A new approach to linear filtering and prediction problems. Trans. ASME-J. Basic Eng. 82, 35–45 (1960)

    MathSciNet  Google Scholar 

  43. Schulz, E., Speekenbrink, M., Krause, A.: A tutorial on gaussian process regression: Modelling, exploring, and exploiting functions. J. Math. Psychol. 85, 1–16 (2018)

    MathSciNet  MATH  Google Scholar 

  44. Williams, R.J.: Simple statistical gradient-following algorithms for connectionist reinforcement learning. Mach. Learn. 8(3–4), 229–256 (1992)

    MATH  Google Scholar 

  45. Sutton, R.S., McAllester, D.A., Singh, S.P., Mansour, Y.: Policy gradient methods for reinforcement learning with function approximation. In: Advances in Neural Information Processing Systems, pp. 1057–1063 (2000)

    Google Scholar 

  46. Watkins, C.J., Dayan, P.: Q-learning. Mach. Learn. 8(3-4), 279–292 (1992)

    MATH  Google Scholar 

  47. Sutton, R.S., Barto, A.G.: Reinforcement Learning: An Introduction. MIT Press (2018)

    Google Scholar 

  48. Di Cairano, S., Yanakiev, D., Bemporad, A., Kolmanovsky, I.V., Hrovat, D.: An MPC design flow for automotive control and applications to idle speed regulation. In: 2008 47th IEEE Conference on Decision and Control, pp. 5686–5691. IEEE (2008)

    Google Scholar 

  49. Fleming, W.H., Rishel, R.W.: Deterministic and Stochastic Optimal Control, vol. 1. Springer, Berlin (2012)

    MATH  Google Scholar 

  50. Koppang, P., Leland, R.: Linear quadratic stochastic control of atomic hydrogen masers. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 46(3), 517–522 (1999)

    Google Scholar 

  51. Duncan, T.E., Pasik-Duncan, B.: A direct approach to linear-quadratic stochastic control. Opuscula Math. 37(6), 821–827 (2017)

    MathSciNet  MATH  Google Scholar 

  52. Bank, P., Voß, M.: Linear quadratic stochastic control problems with stochastic terminal constraint. SIAM J. Control Optim. 56(2), 672–699 (2018)

    MathSciNet  MATH  Google Scholar 

  53. Hordijk, A., Kallenberg, L.C.: Constrained undiscounted stochastic dynamic programming. Math. Oper. Res. 9(2), 276–289 (1984)

    MathSciNet  MATH  Google Scholar 

  54. Neto, T.A., Pereira, M.F., Kelman, J.: A risk-constrained stochastic dynamic programming approach to the operation planning of hydrothermal systems. IEEE Trans. Power Apparatus Syst. (2), 273–279 (1985)

    Google Scholar 

  55. Chen, R.C., Blankenship, G.L.: Dynamic programming equations for discounted constrained stochastic control. IEEE Trans. Autom. Control 49(5), 699–709 (2004)

    MathSciNet  MATH  Google Scholar 

  56. Roijers, D.M., Vamplew, P., Whiteson, S., Dazeley, R.: A survey of multi-objective sequential decision-making. J. Artif. Int. Res. 48(1), 67–113 (2013)

    MathSciNet  MATH  Google Scholar 

  57. Paternain, S., Chamon, L., Calvo-Fullana, M., Ribeiro, A.: Constrained reinforcement learning has zero duality gap. In: H. Wallach, H. Larochelle, A. Beygelzimer, F. d’ Alché-Buc, E. Fox, R. Garnett (eds.) Advances in Neural Information Processing Systems, vol. 32, pp. 7555–7565. Curran Associates (2019)

    Google Scholar 

  58. Bai, Q., Agarwal, M., Aggarwal, V.: Joint optimization of multi-objective reinforcement learning with policy gradient Based algorithm. J. Artif. Intell. Res. 74, 1565–1597 (2022)

    MathSciNet  MATH  Google Scholar 

  59. Bai, Q., Bedi, A.S., Agarwal, M., Koppel, A., Aggarwal, V.: Achieving zero constraint violation for constrained reinforcement learning via primal-dual approach. In Proceedings of the AAAI Conference on Artificial Intelligence 36(4), 3682–3689 (2022)

    Google Scholar 

  60. Agarwal, M., Bai, Q., Aggarwal, V.: Concave utility reinforcement learning with zero-constraint violations (2021). arXiv preprint arXiv:2109.05439

    Google Scholar 

  61. Liu, C., Geng, N., Aggarwal, V., Lan, T., Yang, Y., Xu, M.: Cmix: Deep multi-agent reinforcement learning with peak and average constraints. In: Joint European Conference on Machine Learning and Knowledge Discovery in Databases, pp. 157–173. Springer, Berlin (2021)

    Google Scholar 

  62. Preindl, M.: Robust control invariant sets and Lyapunov-based MPC for IPM synchronous motor drives. IEEE Trans. Ind. Electron. 63(6), 3925–3933 (2016)

    Google Scholar 

  63. Sopasakis, P., Herceg, D., Bemporad, A., Patrinos, P.: Risk-averse model predictive control. Automatica 100, 281–288 (2019)

    MathSciNet  MATH  Google Scholar 

  64. Deisenroth, M., Rasmussen, C.E.: Pilco: A model-based and data-efficient approach to policy search. In: Proceedings of the 28th International Conference on Machine Learning (ICML-11), pp. 465–472 (2011)

    Google Scholar 

  65. Yiqing, L., Xigang, Y., Yongjian, L.: An improved PSO algorithm for solving non-convex NLP/MINLP problems with equality constraints. Comput. Chem. Eng. 31(3), 153–162 (2007)

    Google Scholar 

  66. Madani, T., Benallegue, A.: Sliding mode observer and backstepping control for a quadrotor unmanned aerial vehicles. In: 2007 American Control Conference, pp. 5887–5892. IEEE (2007)

    Google Scholar 

  67. Manchella, K., Umrawal, A.K., Aggarwal, V.: Flexpool: A distributed model-free deep reinforcement learning algorithm for joint passengers and goods transportation. IEEE Trans. Intell. Transp. Syst. 22(4), 2035–2047 (2021)

    Google Scholar 

  68. Mnih, V., Kavukcuoglu, K., Silver, D., Graves, A., Antonoglou, I., Wierstra, D., Riedmiller, M.: Playing Atari with deep reinforcement learning (2013). arXiv preprint arXiv:1312.5602

    Google Scholar 

  69. Van Hasselt, H., Guez, A., Silver, D.: Deep reinforcement learning with double q-learning. In: Proceedings of the AAAI conference on artificial intelligence, vol. 30 (2016)

    Google Scholar 

  70. Hester, T., Vecerik, M., Pietquin, O., Lanctot, M., Schaul, T., Piot, B., Horgan, D., Quan, J., Sendonaris, A., Osband, I., et al.: Deep q-learning from demonstrations. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32 (2018)

    Google Scholar 

  71. Schrittwieser, J., Antonoglou, I., Hubert, T., Simonyan, K., Sifre, L., Schmitt, S., Guez, A., Lockhart, E., Hassabis, D., Graepel, T., et al.: Mastering Atari, Go, Chess and Shogi by planning with a learned model. Nature 588(7839), 604–609 (2020)

    Google Scholar 

  72. Kakade, S.M.: A natural policy gradient. Adv. Neural Inform. Process. Syst. 14, 1531–1538 (2001)

    Google Scholar 

  73. Schulman, J., Levine, S., Abbeel, P., Jordan, M., Moritz, P.: Trust region policy optimization. In: International Conference on Machine Learning, pp. 1889–1897 (2015)

    Google Scholar 

  74. Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms (2017). arXiv preprint arXiv:1707.06347

    Google Scholar 

  75. Moffaert, K.V., Nowé, A.: Multi-objective reinforcement learning using sets of pareto dominating policies. J. Mach. Learn. Res. 15, 3663–3692 (2014)

    MathSciNet  MATH  Google Scholar 

  76. Tessler, C., Mankowitz, D.J., Mannor, S.: Reward constrained policy optimization. In: International Conference on Learning Representations (2018)

    Google Scholar 

  77. Efroni, Y., Mannor, S., Pirotta, M.: Exploration-exploitation in constrained MDPs (2020). arXiv preprint arXiv:2003.02189

    Google Scholar 

  78. Zheng, L., Ratliff, L.: Constrained Upper Confidence Reinforcement Learning, pp. 620–629. PMLR, The Cloud (2020)

    Google Scholar 

  79. Parpas, P., Rustem, B.: An algorithm for the global optimization of a class of continuous minimax problems. J. Optim. Theory Appl. 141, 461–473 (2009)

    MathSciNet  MATH  Google Scholar 

  80. Morari, M., Lee, J.H.: Model predictive control: past, present and future. Comput. Chem. Eng. 23(4–5), 667–682 (1999)

    Google Scholar 

  81. Hewing, L., Wabersich, K.P., Menner, M., Zeilinger, M.N.: Learning-based model predictive control: Toward safe learning in control. Ann. Rev. Control Robot. Auton. Syst. 3, 269–296 (2020)

    Google Scholar 

  82. Darby, M.L., Nikolaou, M.: Mpc: Current practice and challenges. Control Eng. Practice 20(4), 328–342 (2012)

    Google Scholar 

  83. Incremona, G.P., Ferrara, A., Magni, L.: Mpc for robot manipulators with integral sliding modes generation. IEEE/ASME Trans. Mechatron. 22(3), 1299–1307 (2017)

    Google Scholar 

  84. Yin, X., Jindal, A., Sekar, V., Sinopoli, B.: A control-theoretic approach for dynamic adaptive video streaming over HTTP. In: Proceedings of the 2015 ACM Conference on Special Interest Group on Data Communication, pp. 325–338 (2015)

    Google Scholar 

  85. Elgabli, A., Aggarwal, V., Hao, S., Qian, F., Sen, S.: Lbp: Robust rate adaptation algorithm for SVC video streaming. IEEE/ACM Trans. Netw. 26(4), 1633–1645 (2018)

    Google Scholar 

  86. Elgabli, A., Aggarwal, V.: Fastscan: Robust low-complexity rate adaptation algorithm for video streaming over HTTP. IEEE Trans. Circuits Syst. Video Technol. 30(7), 2240–2249 (2020)

    Google Scholar 

  87. Širokỳ, J., Oldewurtel, F., Cigler, J., Prívara, S.: Experimental analysis of model predictive control for an energy efficient building heating system. Appl. Energy 88(9), 3079–3087 (2011)

    Google Scholar 

  88. Saponara, M., Barrena, V., Bemporad, A., Hartley, E., Maciejowski, J.M., Richards, A., Tramutola, A., Trodden, P.: Model predictive control application to spacecraft rendezvous in Mars sample return scenario. EDP Sciences (2013)

    Google Scholar 

  89. Ding, Y., Wang, L., Li, Y., Li, D.: Model predictive control and its application in agriculture: A review. Comput. Electron. Agric. 151, 104–117 (2018)

    Google Scholar 

  90. Chung, H.M., Maharjan, S., Zhang, Y., Eliassen, F.: Distributed deep reinforcement learning for intelligent load scheduling in residential smart grid. IEEE Trans. Ind. Inform. (2020)

    Google Scholar 

  91. Li, R., Zhao, Z., Sun, Q., Chih-Lin, I., Yang, C., Chen, X., Zhao, M., Zhang, H.: Deep reinforcement learning for resource management in network slicing. IEEE Access 6, 74429–74441 (2018)

    Google Scholar 

  92. Zeng, D., Gu, L., Pan, S., Cai, J., Guo, S.: Resource management at the network edge: a deep reinforcement learning approach. IEEE Netw. 33(3), 26–33 (2019)

    Google Scholar 

  93. Zhang, Y., Yao, J., Guan, H.: Intelligent cloud resource management with deep reinforcement learning. IEEE Cloud Comput. 4(6), 60–69 (2017)

    Google Scholar 

  94. Vamvoudakis, K.G., Modares, H., Kiumarsi, B., Lewis, F.L.: Game theory-based control system algorithms with real-time reinforcement learning: how to solve multiplayer games online. IEEE Control Syst. Mag. 37(1), 33–52 (2017)

    MathSciNet  Google Scholar 

  95. Koch, W., Mancuso, R., West, R., Bestavros, A.: Reinforcement learning for UAV attitude control. ACM Trans. Cyber-Phys. Syst. 3(2), 1–21 (2019)

    Google Scholar 

  96. Bai, W., Zhang, B., Zhou, Q., Lu, R.: Multigradient recursive reinforcement learning NN control for affine nonlinear systems with unmodeled dynamics. Int. J. Robust Nonlinear Control 30(4), 1643–1663 (2020)

    MathSciNet  MATH  Google Scholar 

  97. Redder, A., Ramaswamy, A., Quevedo, D.E.: Deep reinforcement learning for scheduling in large-scale networked control systems. IFAC-PapersOnLine 52(20), 333–338 (2019)

    Google Scholar 

  98. Bai, Q., Bedi, A. S., Aggarwal, V.: Achieving zero constraint violation for constrained reinforcement learning via conservative natural policy gradient primal-dual algorithm. arXiv preprint (2022) arXiv:2206.05850

    Google Scholar 

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    Vaneet Aggarwal & Mridul Agarwal

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    Aggarwal, V., Agarwal, M. (2023). Control of Uncertain Systems. In: Nof, S.Y. (eds) Springer Handbook of Automation. Springer Handbooks. Springer, Cham. https://doi.org/10.1007/978-3-030-96729-1_8

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