Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 30169
Conservativeness of Probabilistic Constrained Optimal Control Method for Unknown Probability Distribution

Authors: Tomoaki Hashimoto

Abstract:

In recent decades, probabilistic constrained optimal control problems have attracted much attention in many research fields. Although probabilistic constraints are generally intractable in an optimization problem, several tractable methods haven been proposed to handle probabilistic constraints. In most methods, probabilistic constraints are reduced to deterministic constraints that are tractable in an optimization problem. However, there is a gap between the transformed deterministic constraints in case of known and unknown probability distribution. This paper examines the conservativeness of probabilistic constrained optimization method for unknown probability distribution. The objective of this paper is to provide a quantitative assessment of the conservatism for tractable constraints in probabilistic constrained optimization with unknown probability distribution.

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

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1108827

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1501

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, 2000, pp.789-814.
[2] T. Hashimoto, Y. Yoshioka, T. Ohtsuka, Receding Horizon Control with Numerical Solution for Thermal Fluid Systems, Proceedings of SICE Annual Conference, 2012, pp.1298-1303.
[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, 2013, pp.2920-2925.
[4] T. Hashimoto, Y. Yoshioka and T. Ohtsuka, Receding Horizon Control for Hot Strip Mill Cooling Systems, IEEE/ASME Transactions on Mechatronics, vol. 18, 2013, pp. 998-1005.
[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, 2013, pp. 725-730.
[6] T. Hashimoto, Y. Takiguchi and T. Ohtsuka, Receding Horizon Control for High-Dimensional Burgers ’ Equations with Boundary Control Inputs, Transactions of the Japan Society for Aeronautical and Space Sciences, Vol. 56, 2013, pp. 137-144.
[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, 2014, pp.273-278.
[9] T. Hashimoto, Receding Horizon Control for a Class of Discrete-time Nonlinear Implicit Systems, Proceedings of IEEE Conference on Decision and Control, 2014, pp.5089-5094.
[10] M. V. Kothare, V. Balakrishnan and M. Morari, Robust Constrained Model Predictive Control Using Linear Matrix Inequalities, Automatica, Vol. 32, 1996, pp.1361-1379.
[11] P. Scokaert and D. Mayne, Min-max Feedback Model Predictive Control for Constrained Linear Systems, IEEE Trans. Automat. Contr., Vol. 43, 1998, pp.1136-1142.
[12] A. Bemporad, F. Borrelli and M. Morari, Min-max Control of Constrained Uncertain Discrete-time Linear Systems, IEEE Trans. Automat. Contr., Vol. 48, 2003, pp.1600-1606.
[13] 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, 2005, pp.710-714.
[14] 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, 2006, pp.1688-1692.
[15] D. Bertsimas and D. B. Brown, Constrained Stochastic LQC: A Tractable Approach, IEEE Trans. Automat. Contr., Vol. 52, 2007, pp.1826-1841.
[16] P. Hokayema, E. Cinquemani, D. Chatterjee, F Ramponid and J. Lygeros, Stochastic Receding Horizon Control with Output Feedback and Bounded Controls, Automatica, Vol. 48, 2012, pp.77-88.
[17] M. Cannon, B. Kouvaritakis and D. Ng, Probabilistic Tubes in Linear Stochastic Model Predictive Control, Systems & Control Letters, Vol. 58, 2009, pp.747-753.
[18] M. Cannon, B. Kouvaritakis and X. Wu, Model Predictive Control for Systems with Stochastic Multiplicative Uncertainty and Probabilistic Constraints, Automatica, Vol. 45, 2009, pp.167-172.
[19] M. Cannon, B. Kouvaritakis and X. Wu, Probabilistic Constrained MPC for Multiplicative and Additive Stochastic Uncertainty, IEEE Trans. Automat. Contr., Vol. 54, 2009, pp.1626-1632.
[20] E. Cinquemani, M. Agarwal, D. Chatterjee and J. Lygeros, Convexity and Convex Approximations of Discrete-time Stochastic Control Problems with Constraints, Automatica, Vol. 47, 2011, pp.2082-2087.
[21] M. Ono, L. Blackmore and B. C. Williams, Chance Constrained Finite Horizon Optimal Control with Nonconvex Constraints, Proceedings of American Control Conference, 2010, pp.1145-1152.
[22] G. C. Calafiore and M. C. Campi, The Scenario Approach to Robust Control Design, IEEE Trans. Automat. Contr., Vol. 51, 2006, pp.742-753.
[23] J. Matuˇsko and F. Borrelli, Scenario-Based Approach to Stochastic Linear Predictive Control, Proceedings of the 51st IEEE Conference on Decision and Control, 2012, pp.5194-5199.
[24] A. Nemirovski and A. Shapiro, Convex Approximations of Chance Constrained Programs, SIAM J. Control Optim., Vol. 17, 2006, pp.969-996.
[25] Z. Zhou and R. Cogill, An Algorithm for State Constrained Stochastic Linear-Quadratic Control, Proceedings of American Control Conference, 2011, pp.1476-1481.
[26] T. Hashimoto, I. Yoshimoto, T. Ohtsuka, Probabilistic Constrained Model Predictive Control for Schr¨odinger Equation with Finite Approximation, Proceedings of SICE Annual Conference, 2012, pp.1613-1618.
[27] T. Hashimoto, Probabilistic Constrained Model Predictive Control for Linear Discrete-time Systems with Additive Stochastic Disturbances, Proceedings of IEEE Conference on Decision and Control, 2013, pp.6434-6439.
[28] 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, 2015, pp.1385-1390.
[29] M. Farina, L. Giulioni, L. Magni and R. Scattolini, A Probabilistic Approach to Model Predictive Control, Proceedings of the 52nd IEEE Conference on Decision and Control, 2013, pp.7734-7739.
[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.