Stochastic optimal control for sampled‐data system under stochastic sampling

In this study, the problem of designing a stochastic optimal controller for sampled-data systems whose sampling interval is subjected to a certain probability distribution is addressed. To design the controller, the Kronecker product operation and the Vandermonde matrix were introduced. A design method of the stochastic optimal controller is proposed. It is shown that the controller guarantee that the closed-loop system has exponentially mean square stability. Finally, the simulation results illustrate the effectiveness and practicability of the proposed method.

[1]  Jiangping Hu,et al.  Brief paper: Leader-following consensus for multi-agent systems via sampled-data control , 2011 .

[2]  Fredrik Gustafsson,et al.  Identification with stochastic sampling time jitter , 2008, Autom..

[3]  Y. Shu.  Stability and stabilization of nonuniform sampling systems. , 2008 .

[4]  Zhigang Zeng,et al.  Sliding-Mode Control of Memristive Chua's Systems via the Event-Based Method , 2017, IEEE Transactions on Circuits and Systems II: Express Briefs.

[5]  Tingwen Huang,et al.  Stabilization for sampled-data systems under noisy sampling interval , 2016, Autom..

[6]  Zidong Wang,et al.  Event-triggered distributed ℋ ∞ state estimation with packet dropouts through sensor networks , 2015 .

[7]  Kun Liu,et al.  Wirtinger's inequality and Lyapunov-based sampled-data stabilization , 2012, Autom..

[8]  Emilia Fridman,et al.  Robust sampled-data stabilization of linear systems: an input delay approach , 2004, Autom..

[9]  Edward Boje.  Approximate models for continuous-time linear systems with sampling jitter , 2005, Autom..

[10]  Young Soo Suh.  Stability and stabilization of nonuniform sampling systems , 2008, Autom..

[11]  Hong Ye,et al.  Scheduling of networked control systems , 2001 .

[12]  João Pedro Hespanha,et al.  A Survey of Recent Results in Networked Control Systems , 2007, Proceedings of the IEEE.

[13]  Peter E. Caines,et al.  Stochastic optimal control under Poisson-distributed observations , 2000, IEEE Trans. Autom. Control..

[14]  M. Kim,et al.  On stochastic optimal control of linear sampled data systems , 1965 .

[15]  Jan Swevers,et al.  Robust high-order repetitive control: Optimal performance trade-offs , 2008, Autom..

[16]  José Claudio Geromel,et al.  Optimal H2 state feedback sampled-data control design of Markov Jump Linear Systems , 2015, Autom..

[17]  Karolos M. Grigoriadis,et al.  Optimal state feedback sampled-data control design for Markov jump linear systems , 2018, Int. J. Control.

[18]  Event-Triggered Distributed H∞ State Estimation with Packet Dropouts through Sensor Networks , 2018, Performance Analysis and Synthesis for Discrete-Time Stochastic Systems with Network-Enhanced Complexities.

[19]  Hisaya Fujioka,et al.  A Discrete-Time Approach to Stability Analysis of Systems With Aperiodic Sample-and-Hold Devices , 2009, IEEE Transactions on Automatic Control.

[20]  João Pedro Hespanha,et al.  Exponential stability of impulsive systems with application to uncertain sampled-data systems , 2008, Syst. Control. Lett..

[21]  Zhigang Zeng,et al.  Synchronization of Switched Neural Networks With Communication Delays via the Event-Triggered Control , 2017, IEEE Transactions on Neural Networks and Learning Systems.

[22]  Doreen Meier,et al.  Introduction To Stochastic Control Theory , 2016 .

[23]  Pramod P. Khargonekar,et al.  H 2 optimal control for sampled-data systems , 1991 .

[24]  Zhigang Zeng,et al.  Aperiodic Sampled-Data Sliding-Mode Control of Fuzzy Systems With Communication Delays Via the Event-Triggered Method , 2016, IEEE Transactions on Fuzzy Systems.

[25]  R. Schappelle.  The inverse of the confluent Vandermonde matrix , 1972 .

[26]  Feng Ding,et al.  Reconstruction of continuous-time systems from their non-uniformly sampled discrete-time systems , 2009, Autom..

[27]  Emilia Fridman,et al.  A refined input delay approach to sampled-data control , 2010, Autom..

[28]  Huijun Gao,et al.  Robust sampled-data H∞ control with stochastic sampling , 2009, Autom..

[29]  Alexandre Seuret,et al.  A novel stability analysis of linear systems under asynchronous samplings , 2012, Autom..

[30]  Tai C Yang,et al.  Networked control system: a brief survey , 2006 .

[31]  Björn Wittenmark,et al.  Stochastic Analysis and Control of Real-time Systems with Random Time Delays , 1999 .

[32]  Emilia Fridman,et al.  Recent developments on the stability of systems with aperiodic sampling: An overview , 2017, Autom..

[33]  Cleve B. Moler,et al.  Nineteen Dubious Ways to Compute the Exponential of a Matrix, Twenty-Five Years Later , 1978, SIAM Rev..

[34]  Bruce A. Francis,et al.  Optimal Sampled-Data Control Systems , 1996, Communications and Control Engineering Series.

[35]  Wei Zhang,et al.  Stability of networked control systems , 2001 .

[36]  Emmanuel Trélat,et al.  Linear-quadratic optimal sampled-data control problems: Convergence result and Riccati theory , 2016, Autom..