**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**30135

##### Solutions to Probabilistic Constrained Optimal Control Problems Using Concentration Inequalities

**Authors:**
Tomoaki Hashimoto

**Abstract:**

**Keywords:**
Optimal control,
stochastic systems,
discrete-time systems,
probabilistic constraints.

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.1126940

**References:**

[1] D. Q. Mayne, J. B. Rawlings, C. V. Rao and P. O. M. Scokaert, Constrained Model Predictive Control: Stability and Optimality, Automatica, Vol. 36, pp. 789-814, 2000.

[2] T. Hashimoto, Y. Yoshioka, T. Ohtsuka, Receding Horizon Control with Numerical Solution for Thermal Fluid Systems, Proceedings of SICE Annual Conference, pp. 1298-1303, 2012.

[3] T. Hashimoto, Y. Yoshioka, T. Ohtsuka, Receding Horizon Control with Numerical Solution for Spatiotemporal Dynamic Systems, Proceedings of IEEE Conference on Decision and Control, pp. 2920-2925, 2012.

[4] T. Hashimoto, Y. Yoshioka and T. Ohtsuka, Receding Horizon Control for Hot Strip Mill Cooling Systems, IEEE/ASME Transactions on Mechatronics, Vol. 18, No. 3, pp. 998-1005, 2013.

[5] T. Hashimoto, Y. Yoshioka and T. Ohtsuka, Receding Horizon Control With Numerical Solution for Nonlinear Parabolic Partial Differential Equations, IEEE Transactions on Automatic Control, Vol. 58, No. 3, pp. 725-730, 2013.

[6] T. Hashimoto, Y. Takiguchi and T. Ohtsuka, Receding Horizon Control for High-Dimensional Burgers’ f Equations with Boundary Control Inputs, Transactions of the Japan Society for Aeronautical and Space Sciences, Vol. 56, No.3, pp. 137-144, 2013.

[7] T. Hashimoto, Y. Takiguchi and T. Ohtsuka, Output Feedback Receding Horizon Control for Spatiotemporal Dynamic Systems, Proceedings of Asian Control Conference, 2013.

[8] R. Satoh, T. Hashimoto and T. Ohtsuka, Receding Horizon Control for Mass Transport Phenomena in Thermal Fluid Systems, Proceedings of Australian Control Conference, pp. 273-278, 2014.

[9] T. Hashimoto, Receding Horizon Control for a Class of Discrete-time Nonlinear Implicit Systems, Proceedings of IEEE Conference on Decision and Control, pp. 5089-5094, 2014.

[10] T. Hashimoto, Optimal Feedback Control Method Using Magnetic Force for Crystal Growth Dynamics, International Journal of Science and Engineering Investigations, Vol. 4, Issue 45, pp. 1-6, 2015.

[11] T. Hashimoto, R. Satoh and T. Ohtsuka, Receding Horizon Control for Spatiotemporal Dynamic Systems, Mechanical Engineering Journal, Vol. 3, No. 2, 15-00345, 2016.

[12] M. V. Kothare, V. Balakrishnan and M. Morari, Robust Constrained Model Predictive Control Using Linear Matrix Inequalities, Automatica, Vol. 32, pp. 1361-1379, 1996.

[13] P. Scokaert and D. Mayne, Min-max Feedback Model Predictive Control for Constrained Linear Systems, IEEE Trans. Automat. Contr., Vol. 43, pp. 1136-1142, 1998.

[14] A. Bemporad, F. Borrelli and M. Morari, Min-max Control of Constrained Uncertain Discrete-time Linear Systems, IEEE Trans. Automat. Contr., Vol. 48, pp. 1600-1606, 2003.

[15] T. Alamo, D. Pe˜na, D. Limon and E. Camacho, Constrained Min-max Predictive Control: Modifications of the Objective Function Leading to Polynomial Complexity, IEEE Trans. Automat. Contr., Vol. 50, pp. 710-714, 2005.

[16] D. Pe˜na, T. Alamo, A. Bemporad and E. Camacho, A Decomposition Algorithm for Feedback Min-max Model Predictive Control, IEEE Trans. Automat. Contr., Vol. 51, pp. 1688-1692, 2006.

[17] D. Bertsimas and D. B. Brown, Constrained Stochastic LQC: A Tractable Approach, IEEE Trans. Automat. Contr., Vol. 52, pp. 1826-1841, 2007.

[18] P. Hokayema, E. Cinquemani, D. Chatterjee, F Ramponid and J. Lygeros, Stochastic Receding Horizon Control with Output Feedback and Bounded Controls, Automatica, Vol. 48, pp. 77-88, 2012.

[19] P. Li, M. Wendt and G. Wozny, A Probabilistically Constrained Model Predictive Controller, Automatica, Vol. 38, pp. 1171-1176, 2002.

[20] J. Yan and R. R. Bitmead, Incorporating State Estimation into Model Predictive Control and its Application to Network Traffic Control, Automatica, Vol. 41, pp. 595-604, 2005.

[21] J. A. Primbs and C. H. Sung, Stochastic Receding Horizon Control of Constrained Linear Systems with State and Control Multiplicative Noise, IEEE Trans. Automat. Contr., Vol. 54, pp. 221-230, 2009.

[22] M. Cannon, B. Kouvaritakis and X. Wu, Probabilistic Constrained MPC for Multiplicative and Additive Stochastic Uncertainty, IEEE Trans. Automat. Contr., Vol. 54, pp. 1626-1632, 2009.

[23] E. Cinquemani, M. Agarwal, D. Chatterjee and J. Lygeros, Convexity and Convex Approximations of Discrete-time Stochastic Control Problems with Constraints, Automatica, Vol. 47, pp. 2082-2087, 2011.

[24] J. Matuˇsko and F. Borrelli, Scenario-Based Approach to Stochastic Linear Predictive Control, Proceedings of the 51st IEEE Conference on Decision and Control, pp. 5194-5199, 2012.

[25] T. Hashimoto, I. Yoshimoto, T. Ohtsuka, Probabilistic Constrained Model Predictive Control for Schr¨odinger Equation with Finite Approximation, Proceedings of SICE Annual Conference, pp. 1613-1618, 2012.

[26] T. Hashimoto, Probabilistic Constrained Model Predictive Control for Linear Discrete-time Systems with Additive Stochastic Disturbances, Proceedings of IEEE Conference on Decision and Control, pp. 6434-6439, 2013.

[27] T. Hashimoto, Computational Simulations on Stability of Model Predictive Control for Linear Discrete-time Stochastic Systems, International Journal of Computer, Electrical, Automation, Control and Information Engineering, Vol. 9, No. 8, pp. 1385-1390, 2015.

[28] T. Hashimoto, Conservativeness of Probabilistic Constrained Optimal Control Method for Unknown Probability Distribution, International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering, Vol. 9, No. 9, pp. 11-15, 2015.

[29] T. Hashimoto, A Method for Solving Optimal Control Problems subject to Probabilistic Affine State Constraints for Linear Discrete-time Uncertain Systems, International Journal of Mechanical and Production Engineering, Vol. 3, Issue 12, pp. 6-10, 2015.

[30] B. Øksendal, Stochastic Differential Equations: An Introduction with Applications, Springer, 6th edition, 2010.

[31] S. Boucheron, G. Lugosi and P. Massart Concentration Inequalities: A Nonasymptotic Thepry of Independence, Oxford University Press, 2013.

[32] J. Nocedal and S. J. Wright, Numerical Optimization, Springer Series in Operation Research and Financial Engineering, Springer, 2006.