Switched Nonlinear Systems with All Unstable Modes

The stabilization problem of SNS with all unstable modes is much more challenging than that in Chap. 2 since we cannot utilize the tradeoff between stable modes and unstable modes. This motivates us to analyze the internal behavior of each mode. Section 3.1 proposes a time-dependent switching law for general SNS based on interconnected system approach, followed by Sect. 3.2 where both time-dependent and state-dependent switching laws are provided for nonminimum phase SNS. The results are applied to supervisory control design of nonlinear systems in Sect. 3.3 and target aggregation problem of multi-agent systems in Sect. 3.4.

[1]  S. Tafazoli,et al.  Nonlinear control and stability analysis of spacecraft attitude recovery , 2006, IEEE Transactions on Aerospace and Electronic Systems.

[2]  Jian Xiao,et al.  Stabilization of switched continuous-time systems with all modes unstable via dwell time switching , 2014, Autom..

[3]  Bin Jiang,et al.  Fault Tolerant Control Design for Hybrid Systems , 2010 .

[4]  S. Di Gennaro,et al.  Output stabilization of flexible spacecraft with active vibration suppression , 2003 .

[5]  Jun Zhao,et al.  On stability, L2-gain and Hinfinity control for switched systems , 2008, Autom..

[6]  Marcel Staroswiecki,et al.  From control to supervision , 2000, Annu. Rev. Control..

[7]  Alessandro Astolfi,et al.  Stabilization of continuous-time switched nonlinear systems , 2008, Syst. Control. Lett..

[8]  Youmin Zhang,et al.  Fault-Tolerant Attitude Control for Flexible Spacecraft Without Angular Velocity Magnitude Measurement , 2011 .

[9]  Zhang Wei-guo,et al.  An adaptive backstepping design for longitudinal flight path control , 2008, 2008 7th World Congress on Intelligent Control and Automation.

[10]  Israel Koren,et al.  A Continuous-Parameter Markov Model and Detection Procedures for Intermittent Faults , 1978, IEEE Transactions on Computers.

[11]  Michel Kinnaert,et al.  Diagnosis and Fault-Tolerant Control , 2006 .

[12]  Guangming Xie,et al.  Periodic stabilizability of switched linear control systems , 2009, Autom..

[13]  Claire J. Tomlin,et al.  Switching in nonminimum phase systems: applications to a VSTOL aircraft , 2000, Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334).

[14]  Nagarajan Kandasamy,et al.  Transparent recovery from intermittent faults in time-triggered distributed systems , 2003 .

[15]  Jun Zhao,et al.  Hybrid control for global stabilization of the cart-pendulum system , 2001, Autom..

[16]  Panagiotis D. Christofides,et al.  Stability of nonlinear asynchronous systems , 2007, 2007 46th IEEE Conference on Decision and Control.

[17]  Thomas Parisini,et al.  Global asymptotic stabilization of the attitude and the angular rates of an underactuated non-symmetric rigid body , 2008, Autom..

[18]  Dennis S. Bernstein,et al.  Finite-Time Stability of Continuous Autonomous Systems , 2000, SIAM J. Control. Optim..

[19]  Marko Bacic,et al.  Dynamic non-minimum phase compensation for SISO nonlinear, affine in the input systems , 2006, Autom..

[20]  P. Crouch,et al.  Spacecraft attitude control and stabilization: Applications of geometric control theory to rigid body models , 1984 .

[21]  W.G. Zanardelli,et al.  Identification of Intermittent Electrical and Mechanical Faults in Permanent-Magnet AC Drives Based on Time–Frequency Analysis , 2007, IEEE Transactions on Industry Applications.

[22]  Mario Innocenti,et al.  Autonomous formation flight , 2000 .

[23]  Youmin Zhang,et al.  Adaptive Sliding Mode Fault Tolerant Attitude Tracking Control for Flexible Spacecraft Under Actuator Saturation , 2012, IEEE Transactions on Control Systems Technology.

[24]  S. Ge,et al.  Stability Theory of Switched Dynamical Systems , 2011 .

[25]  Mohammad Farrokhi,et al.  Robust adaptive control of nonlinear non-minimum phase systems with uncertainties , 2011, Autom..

[26]  Yan-Wu Wang,et al.  Synchronization of complex dynamical networks under recoverable attacks , 2010, Autom..

[27]  Daniel Liberzon,et al.  Input/output-to-state stability and state-norm estimators for switched nonlinear systems , 2012, Autom..

[28]  Ilya Kolmanovsky,et al.  Developments in nonholonomic control problems , 1995 .

[29]  Michael J. Rycroft,et al.  Recent advances in global electric circuit coupling between the space environment and the troposphere , 2012 .

[30]  Bo Hu,et al.  Stability analysis of switched systems with stable and unstable subsystems: An average dwell time approach , 2001, Int. J. Syst. Sci..

[31]  Jie Lin,et al.  Coordination of groups of mobile autonomous agents using nearest neighbor rules , 2003, IEEE Trans. Autom. Control..

[32]  A. Isidori.  Nonlinear Control Systems , 1985 .

[33]  Shihua Li,et al.  Stabilization of the attitude of a rigid spacecraft with external disturbances using finite-time control techniques , 2009 .

[34]  Kai-Yew Lum,et al.  Output trajectory tracking for a switched nonlinear non-minimum phase system: The VSTOL aircraft , 2007, 2007 IEEE International Conference on Control Applications.

[35]  João Pedro Hespanha,et al.  Switched seesaw control for the stabilization of underactuated vehicles , 2007, Autom..

[36]  Richard M. Murray,et al.  Consensus problems in networks of agents with switching topology and time-delays , 2004, IEEE Transactions on Automatic Control.

[37]  Marcel Staroswiecki,et al.  Fault Accommodation for Nonlinear Dynamic Systems , 2006, IEEE Transactions on Automatic Control.

[38]  P. Tsiotras,et al.  CONTROL OF SPACECRAFT SUBJECT TO ACTUATOR FAILURES : STATE-OFTHE-ART AND OPEN PROBLEMS , 2000 .

[39]  Guodong Shi,et al.  Global target aggregation and state agreement of nonlinear multi-agent systems with switching topologies , 2009, Autom..

[40]  Zhong-Ping Jiang,et al.  A generalization of the nonlinear small-gain theorem for large-scale complex systems , 2008, 2008 7th World Congress on Intelligent Control and Automation.

[41]  Alberto Isidori,et al.  A tool for semi-global stabilization of uncertain non-minimum-phase nonlinear systems via output feedback , 2000, IEEE Trans. Autom. Control..

[42]  A. Morse,et al.  Stability of switched systems with average dwell-time , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[43]  Ji-Feng Zhang,et al.  Stability analysis and stabilization control of multi-variable switched stochastic systems , 2006, Autom..

[44]  João Pedro Hespanha,et al.  Stabilization of nonholonomic integrators via logic-based switching , 1999, Autom..

[45]  Jun Zhao,et al.  Synchronization of Complex Dynamical Networks with Switching Topology: a Switched System Point of View , 2008 .

[46]  A. A. Ismaeel,et al.  Test for detection and location of intermittent faults in combinational circuits , 1997 .

[47]  Jun Liu,et al.  Uniform stability of switched nonlinear systems , 2009 .

[48]  Youmin Zhang,et al.  Engineering Notes Fault-Tolerant Attitude Control for Spacecraft Under Loss of Actuator Effectiveness , 2011 .

[49]  David Angeli,et al.  Nonlinear norm-observability notions and stability of switched systems , 2005, IEEE Transactions on Automatic Control.

[50]  Daniel Liberzon,et al.  Switching in Systems and Control , 2003, Systems & Control: Foundations & Applications.

[51]  Emanuel Parzen,et al.  Stochastic Processes , 1962 .

[52]  Hassan K. Khalil,et al.  Robust stabilization of non-minimum phase nonlinear systems using extended high gain observers , 2011, 2008 American Control Conference.

[53]  Huijun Gao,et al.  Asynchronously switched control of switched linear systems with average dwell time , 2010, Autom..

[54]  Youmin Zhang,et al.  Bibliographical review on reconfigurable fault-tolerant control systems , 2003, Annu. Rev. Control..

[55]  Long Wang,et al.  Group consensus in multi-agent systems with switching topologies and communication delays , 2010, Syst. Control. Lett..

[56]  Marcel Staroswiecki,et al.  Fault tolerant cooperative control for a class of nonlinear multi-agent systems , 2011, Syst. Control. Lett..

[57]  Bong Wie,et al.  Space Vehicle Dynamics and Control, Second Edition , 2008 .

[58]  Thomas Parisini,et al.  Stable hybrid control based on discrete-event automata and receding-horizon neural regulators , 2001, Autom..

[59]  Marios M. Polycarpou,et al.  Fault diagnosis of a class of nonlinear uncertain systems with Lipschitz nonlinearities using adaptive estimation , 2010, Autom..

[60]  Paul M. Frank,et al.  Issues of Fault Diagnosis for Dynamic Systems , 2010, Springer London.

[61]  David J. Hill,et al.  Decomposable Dissipativity and Related Stability for Discrete-Time Switched Systems , 2011, IEEE Transactions on Automatic Control.

[62]  Jun Zhao,et al.  H∞ control for a class of non-minimum-phase cascade switched nonlinear systems , 2008, 2008 American Control Conference.