**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**32451

##### Stochastic Model Predictive Control for Linear Discrete-Time Systems with Random Dither Quantization

**Authors:**
Tomoaki Hashimoto

**Abstract:**

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

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.1339996

**References:**

[1] 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.

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

[5] 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.

[6] 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.

[7] 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.

[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] 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.

[15] 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.

[16] 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.

[17] 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.

[18] 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.

[19] 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.

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

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

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

[23] 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.

[24] 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.

[25] 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.

[26] 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.

[27] 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.

[28] 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.