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Stochastic Model Predictive Control for Linear Discrete-Time Systems with Random Dither Quantization
Authors: Tomoaki Hashimoto
Abstract:Recently, feedback control systems using random dither quantizers have been proposed for linear discrete-time systems. However, the constraints imposed on state and control variables have not yet been taken into account for the design of feedback control systems with random dither quantization. Model predictive control is a kind of optimal feedback control in which control performance over a finite future is optimized with a performance index that has a moving initial and terminal time. An important advantage of model predictive control is its ability to handle constraints imposed on state and control variables. Based on the model predictive control approach, the objective of this paper is to present a control method that satisfies probabilistic state constraints for linear discrete-time feedback control systems with random dither quantization. In other words, this paper provides a method for solving the optimal control problems subject to probabilistic state constraints for linear discrete-time feedback control systems with random dither quantization.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1339996Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 937
 R. Morita, S. Azuma, T. Sugie, Performance Analysis of Random Dither Quantizers in Feedback Control Systems, Preprints of the 18th IFAC World Congress, pp. 11296-11301, 2011.
 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.
 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.
 T. Hashimoto, Y. Takiguchi and T. Ohtsuka, Output Feedback Receding Horizon Control for Spatiotemporal Dynamic Systems, Proceedings of Asian Control Conference, 2013.
 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.
 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.
 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, No.3, pp. 137-144, 2013.
 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.
 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.
 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.
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 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.
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 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.
 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.
 T. Hashimoto, Solutions to Probabilistic Constrained Optimal Control Problems Using Concentration Inequalities, International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering, Vol. 10, No. 10, pp. 441-446, 2016.
 S. Boucheron, G. Lugosi and P. Massart Concentration Inequalities: A Nonasymptotic Thepry of Independence, Oxford University Press, 2013.
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 T. Hashimoto, T. Amemiya and H. A. Fujii, Stabilization of Linear Uncertain Delay Systems with Antisymmetric Stepwise Configurations, Journal of Dynamical and Control Systems, Vol. 14, No. 1, pp. 1-31, 2008.
 T. Hashimoto, T. Amemiya and H. A. Fujii, Output Feedback Stabilization of Linear Time-varying Uncertain Delay Systems, Mathematical Problems in Engineering, Vol. 2009, Article ID. 457468, 2009.
 T. Hashimoto and T. Amemiya, Stabilization of Linear Time-varying Uncertain Delay Systems with Double Triangular Configuration, WSEAS Transactions on Systems and Control, Vol. 4, No.9, pp.465-475, 2009.
 T. Hashimoto, Stabilization of Abstract Delay Systems on Banach Lattices using Nonnegative Semigroups, Proceedings of the 50th IEEE Conference on Decision and Control, pp. 1872-1877, 2011.
 T. Hashimoto, A Variable Transformation Method for Stabilizing Abstract Delay Systems on Banach Lattices, Journal of Mathematics Research, Vol. 4, No. 2, pp.2-9, 2012.
 T. Hashimoto, An Optimization Algorithm for Designing a Stabilizing Controller for Linear Time-varying Uncertain Systems with State Delays, Computational Mathematics and Modeling, Vol.24, No.1, pp.90-102, 2013.