Security in H2-sense for polytopic uncertain systems with attacks based on model predictive control

Abstract In this paper, the problem of network security in H 2 - sense for a discrete-time linear uncertain system with a polytopic description and subject to randomly occurring deception attacks is discussed. A novel attack model is proposed to reflect the randomly occurring behaviors of the deception attacks by using a set of Bernoulli distributed white sequences with known conditional probabilities. In view of the difficulties in obtaining state values in practical system, we design a static output-feedback controller. However, some equation constraints are brought about and become a hinder in obtaining the upper bound of the objective function. To deal with the problem, a singular decomposition technique is applied. Then, the static output-feedback model predictive control (MPC) algorithm is presented by solving an optimization problem involving some linear matrix inequalities (LMIs), by which security of the network (or the stability of the closed-loop system) could be guaranteed. Finally, a simulation example is utilized to illustrate validity and effectiveness of the proposed technique.

[1]  William B. Dunbar,et al.  Distributed Receding Horizon Control of Dynamically Coupled Nonlinear Systems , 2007, IEEE Transactions on Automatic Control.

[2]  Manfred Morari,et al.  Robust constrained model predictive control using linear matrix inequalities , 1994, Proceedings of 1994 American Control Conference - ACC '94.

[3]  Daniel W. C. Ho,et al.  Robust stabilization for a class of discrete-time systems with nonlinear perturbations , 2002, Proceedings of the 4th World Congress on Intelligent Control and Automation (Cat. No.02EX527).

[4]  W. Heemels,et al.  Approximation of explicit model predictive control using regular piecewise affine functions : an input-to-state stability approach , 2012 .

[5]  Xavier Litrico,et al.  Cyber Security of Water SCADA Systems—Part I: Analysis and Experimentation of Stealthy Deception Attacks , 2013, IEEE Transactions on Control Systems Technology.

[6]  Wook Hyun Kwon,et al.  Robust one-step receding horizon control of discrete-time Markovian jump uncertain systems , 2002, Autom..

[7]  Chun Chen,et al.  Security Analysis and Improvement of a Secure and Distributed Reprogramming Protocol for Wireless Sensor Networks , 2013, IEEE Transactions on Industrial Electronics.

[8]  Jiming Chen,et al.  Energy-Efficient Intrusion Detection with a Barrier of Probabilistic Sensors: Global and Local , 2013, IEEE Transactions on Wireless Communications.

[9]  Jiming Chen,et al.  Energy-efficient intrusion detection with a barrier of probabilistic sensors , 2012, 2012 Proceedings IEEE INFOCOM.

[10]  Kok Kiong Tan,et al.  Computation delay compensation for real time implementation of robust model predictive control , 2013 .

[11]  B. Kouvaritakis,et al.  Receding horizon output feedback control for linear systems with input saturation , 2001 .

[12]  A. Garulli,et al.  Output-feedback predictive control of constrained linear systems via set-membership state estimation , 2000 .

[13]  Huijun Gao,et al.  Network-based feedback control for systems with mixed delays based on quantization and dropout compensation , 2011, Autom..

[14]  Wen-an Zhang,et al.  New results on stabilization of networked control systems with packet disordering , 2015, Autom..

[15]  P.J. Goulart,et al.  A Method for Robust Receding Horizon Output Feedback Control of Constrained Systems , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[16]  Sonia Martínez,et al.  On the Performance Analysis of Resilient Networked Control Systems Under Replay Attacks , 2013, IEEE Transactions on Automatic Control.

[17]  B. Ding,et al.  Constrained robust model predictive control via parameter-dependent dynamic output feedback , 2010, Autom..

[18]  Yan Song,et al.  Distributed model predictive control for polytopic uncertain systems with randomly occurring actuator saturation and packet loss , 2014 .

[19]  Huiping Li,et al.  Event-triggered robust model predictive control of continuous-time nonlinear systems , 2014, Autom..

[20]  Bohui Wang,et al.  Robust distributed model predictive control for uncertain networked control systems , 2014 .

[21]  S. Shankar Sastry,et al.  Security of interdependent and identical networked control systems , 2013, Autom..

[22]  Tongwen Chen,et al.  Network-based predictive control of multirate systems , 2010 .

[23]  David Q. Mayne,et al.  Robust output feedback model predictive control of constrained linear systems , 2006, Autom..

[24]  Wook Hyun Kwon,et al.  Robust Receding Horizon Control of Discrete-Time Markovian Jump Uncertain Systems , 2001 .

[25]  Guan Xiaohong,et al.  Quantitative Hierarchical Threat Evaluation Model for Network Security , 2006 .

[26]  S. Shankar Sastry,et al.  Safe and Secure Networked Control Systems under Denial-of-Service Attacks , 2009, HSCC.

[27]  André Teixeira,et al.  Networked control systems under cyber attacks with applications to power networks , 2010, Proceedings of the 2010 American Control Conference.

[28]  John Y. Hung,et al.  Denial of service attacks on network-based control systems: impact and mitigation , 2005, IEEE Transactions on Industrial Informatics.

[29]  He Huang,et al.  Design and input-to-state practically stable analysis of the mixed H 2 /H ∞ feedback robust model predictive control , 2012 .

[30]  Dewei Li,et al.  Synthesis of dynamic output feedback RMPC with saturated inputs , 2013, Autom..

[31]  Ping Wang,et al.  Model predictive control of non-linear systems over networks with data quantization and packet loss. , 2013, ISA transactions.

[32]  A. H. Tahoun.  Adaptive stabilizer for chaotic networked systems with network-induced delays and packet losses , 2015, Nonlinear Dynamics.