Discrete-time controller for stochastic polynomial systems with Poisson noises

This paper presents a solution to the optimal control problem for discrete-time stochastic nonlinear polynomial systems confused with white Poisson noises subject to a quadratic criterion. The solution is obtained in the following way: a nonlinear optimal controller is first developed for polynomial systems, considering the state vector completely available for control design. Then, based on the solution of the state estimation problem for polynomial systems with white Poisson noises, the state estimate vector is used in the control law to obtain a closed-form solution. Performance of this controller is compared to that of the controller employing the extended Kalman filter and the linear-quadratic regulator and the controller designed for polynomial systems confused with white Gaussian noises.

[1]  Dan Simon,et al.  Optimal State Estimation: Kalman, H∞, and Nonlinear Approaches , 2006 .

[2]  Bikash C. Pal,et al.  An extended linear quadratic regulator and its application for control of power system dynamics , 2016, 2016 IEEE First International Conference on Control, Measurement and Instrumentation (CMI).

[3]  Bo Song,et al.  Global Synchronization of Complex Networks Perturbed by Brown Noises and Poisson Noises , 2014, Circuits Syst. Signal Process..

[4]  S. D. Dvoenko,et al.  A method of total variation to remove the mixed Poisson-Gaussian noise , 2016, Pattern Recognition and Image Analysis.

[5]  Ichiro Nagashima,et al.  Optimal displacement feedback control law for active tuned mass damper , 2001 .

[6]  W. Fleming,et al.  Deterministic and Stochastic Optimal Control , 1975 .

[7]  C. Tung,et al.  RANDOM RESPONSE OF HIGHWAY BRIDGES TO VEHICLE LOADS , 1967 .

[8]  S. Nguang,et al.  Robust H∞ state feedback control of NCSs with Poisson noise and successive packet dropouts , 2014, International Journal of Control, Automation and Systems.

[9]  Praveen Jain,et al.  Application of linear quadratic regulator theory to the stator field-oriented control of induction motors , 2010 .

[10]  苏军,et al.  The Stochastic stability of a Logistic model with Poisson white noise , 2011 .

[11]  Silvere Bonnabel,et al.  An invariant Linear Quadratic Gaussian controller for a simplified car , 2014, 2015 IEEE International Conference on Robotics and Automation (ICRA).

[12]  R.N. Paschall,et al.  Design of a linear quadratic Gaussian controller for an adaptive optics system , 1991, [1991] Proceedings of the 30th IEEE Conference on Decision and Control.

[13]  J. Chudley,et al.  Soft Computing Design of a Linear Quadratic Gaussian Controller for an Unmanned Surface Vehicle , 2006, 2006 14th Mediterranean Conference on Control and Automation.

[14]  Ligang Wu,et al.  State estimation and sliding mode control for semi-Markovian jump systems with mismatched uncertainties , 2015, Autom..

[15]  Yeung Sam Hung,et al.  Distributed $H_{\infty}$ Filtering for Polynomial Nonlinear Stochastic Systems in Sensor Networks , 2011, IEEE Transactions on Industrial Electronics.

[16]  Zidong Wang,et al.  H∞ state estimation with fading measurements, randomly varying nonlinearities and probabilistic distributed delays , 2015 .

[17]  Liying Liu,et al.  Variable gain linear quadratic regulator and its application , 2014, 2014 IEEE International Conference on Mechatronics and Automation.

[18]  I. Main,et al.  A Poisson model for earthquake frequency uncertainties in seismic hazard analysis , 2008, 0807.2396.

[19]  G. Kalogeropoulos,et al.  Guaranteed stability margins for discrete-time LQ optimal regulators for the performance index with cross-product terms , 1997 .

[20]  Bor-Sen Chen,et al.  Robust stabilization design for nonlinear stochastic system with Poisson noise via fuzzy interpolation method , 2013, Fuzzy Sets Syst..

[21]  Bo Shen,et al.  Fuzzy-Logic-Based Control, Filtering, and Fault Detection for Networked Systems: A Survey , 2015 .

[22]  Robert J. Elliott,et al.  Filtering and change point estimation for hidden Markov-modulated Poisson processes , 2014, Appl. Math. Lett..

[23]  Michael V. Basin,et al.  Optimal Controller for Uncertain Stochastic Linear Systems With Poisson Noises , 2014, IEEE Transactions on Industrial Informatics.

[24]  Guo-Ping Liu,et al.  Filtering for Discrete-Time Networked Nonlinear Systems With Mixed Random Delays and Packet Dropouts , 2011, IEEE Transactions on Automatic Control.

[25]  J. D. Gibson.  Performance effects of optimal LQG eigenvalue placement in ship control , 2003, IECON'03. 29th Annual Conference of the IEEE Industrial Electronics Society (IEEE Cat. No.03CH37468).

[26]  T. Başar,et al.  A New Approach to Linear Filtering and Prediction Problems , 2001 .

[27]  Michael V. Basin,et al.  Discrete-time optimal control for stochastic nonlinear polynomial systems , 2014, Int. J. Gen. Syst..

[28]  M. Basin,et al.  Mean-square filtering for polynomial discrete-time systems with Poisson noises , 2016 .

[29]  Wei Xu,et al.  Characterization of stochastic resonance in a bistable system with Poisson white noise using statistical complexity measures , 2015, Commun. Nonlinear Sci. Numer. Simul..

[30]  E. Yaz,et al.  Linear optimal control, H2 and H∞ methods, by Jeffrey B. Burl, Addison Wesley Longman, Inc. Menlo Park, CA, 1999 , 2000 .