On sliding mode control of single input Markovian jump systems

In this paper, an equivalent control based sliding mode control is proposed for single input linear Markovian jump systems which guarantees the asymptotical stability. Furthermore, by using the stochastic system theory, a multi-step state transition conditional probability function is introduced for the continuous Markovian process, which is used to define the reaching and sliding probabilities. Furthermore, the formulas for calculating reaching and sliding probabilities are derived for situations where the control force may not be strong enough to ensure the fully asymptotical stability. Extensive simulations are conducted to validate the theoretical results and show the relationship between the control force and reaching and sliding probabilities.

[1]  Peng Shi,et al.  Kalman filtering for continuous-time uncertain systems with Markovian jumping parameters , 1999, IEEE Trans. Autom. Control..

[2]  Shengyuan Xu,et al.  Robust H∞ filtering for uncertain Markovian jump systems with mode-dependent time delays , 2003, IEEE Trans. Autom. Control..

[3]  Lixian Zhang,et al.  Stability and stabilization of Markovian jump linear systems with partly unknown transition probabilities , 2009, Autom..

[4]  Yugang Niu,et al.  Adaptive sliding mode control for stochastic Markovian jumping systems with actuator degradation , 2013, Autom..

[5]  Daniel W. C. Ho,et al.  Sliding mode control of singular stochastic hybrid systems , 2010, Autom..

[6]  Xingyu Wang,et al.  Sliding mode control for Itô stochastic systems with Markovian switching , 2007, Autom..

[7]  Huijun Gao,et al.  State Estimation and Sliding-Mode Control of Markovian Jump Singular Systems , 2010, IEEE Transactions on Automatic Control.

[8]  Yugang Niu,et al.  Design of Sliding Mode Control Subject to Packet Losses , 2010, IEEE Transactions on Automatic Control.

[9]  Fei Liu,et al.  Finite-time stabilisation for Markov jump systems with Gaussian transition probabilities , 2013 .

[10]  James Lam,et al.  Exponential filtering for uncertain Markovian jump time-delay systems with nonlinear disturbances , 2004, IEEE Transactions on Circuits and Systems II: Express Briefs.

[11]  Peng Shi,et al.  Asynchronous I2-I∞ filtering for discrete-time stochastic Markov jump systems with randomly occurred sensor nonlinearities , 2014, Autom..

[12]  Yuanqing Xia,et al.  On designing of sliding-mode control for stochastic jump systems , 2006, IEEE Transactions on Automatic Control.

[13]  Vadim I. Utkin,et al.  Adaptive sliding mode control with application to super-twist algorithm: Equivalent control method , 2013, Autom..

[14]  M. Mahmoud,et al.  Robust Kalman filtering for continuous time-lag systems with Markovian jump parameters , 2003 .

[15]  Changhong Wang,et al.  Nonfragile observer‐based H ∞  sliding mode control for Itô stochastic systems with Markovian switching , 2014 .

[16]  Sheldon M. Ross.  Introduction to Probability Models. , 1995 .

[17]  Sheldon M. Ross,et al.  Introduction to Probability Models, Eighth Edition , 1972 .

[18]  James Lam,et al.  On robust stabilization of Markovian jump systems with uncertain switching probabilities , 2005, Autom..

[19]  Shengyuan Xu,et al.  Delay-Dependent $H_{\infty }$ Control and Filtering for Uncertain Markovian Jump Systems With Time-Varying Delays , 2007, IEEE Transactions on Circuits and Systems I: Regular Papers.

[20]  Steven X. Ding,et al.  A Review on Basic Data-Driven Approaches for Industrial Process Monitoring , 2014, IEEE Transactions on Industrial Electronics.

[21]  Huijun Gao,et al.  Data-Based Techniques Focused on Modern Industry: An Overview , 2015, IEEE Transactions on Industrial Electronics.

[22]  Xinghuo Yu,et al.  Sliding-Mode Control With Soft Computing: A Survey , 2009, IEEE Transactions on Industrial Electronics.

[23]  H. Chizeck,et al.  Controllability, stabilizability, and continuous-time Markovian jump linear quadratic control , 1990 .

[24]  Hui Zhang,et al.  Robust H∞ sliding-mode control for Markovian jump systems subject to intermittent observations and partially known transition probabilities , 2013, Syst. Control. Lett..

[25]  Xinghuo Yu,et al.  Stability probability in sliding mode control of second order Markovian jump systems , 2014, The 26th Chinese Control and Decision Conference (2014 CCDC).

[26]  Fei Liu,et al.  Observer‐based H ∞  control on nonhomogeneous Markov jump systems with nonlinear input , 2014 .

[27]  Y. Niu,et al.  Sliding mode control for stochastic Markovian jumping systems with incomplete transition rate , 2013 .

[28]  Ligang Wu,et al.  Sliding mode control with bounded L2 gain performance of Markovian jump singular time-delay systems , 2012, Autom..

[29]  Zhi-Hong Guan,et al.  Guaranteed cost control for uncertain Markovian jump systems with mode-dependent time-delays , 2003, IEEE Trans. Autom. Control..

[30]  José Claudio Geromel,et al.  Output feedback control of Markov jump linear systems in continuous-time , 2000, IEEE Trans. Autom. Control..

[31]  Mario Lefebvre,et al.  Applied Stochastic Processes , 2006 .