observability ?

Estimation of states and events in randomly switching systems is studied under irregular and random sampling schemes. Probabilistic characterization of observability is presented under various sampling schemes and regime-switching processes. The characterization is derived on the basis of our recent results on sampling complexity for system observability. Observer design and algorithms are developed.

[1]  Eugene Lukacs STOCHASTIC CONVERGENCE CONCEPTS AND THEIR PROPERTIES , 1975 .

[2]  Benjamin C. Kuo,et al.  Digital Control Systems , 1977 .

[3]  John G. Proakis,et al.  Probability, random variables and stochastic processes , 1985, IEEE Trans. Acoust. Speech Signal Process..

[4]  D.S. Naidu,et al.  Digital control system analysis and design , 1986, Proceedings of the IEEE.

[5]  Walter Murray Wonham,et al.  On observability of discrete-event systems , 1988, Inf. Sci..

[6]  M. Mariton,et al.  Jump Linear Systems in Automatic Control , 1992 .

[7]  S. Marcus,et al.  On controllability and normality of discrete event dynamical systems , 1991 .

[8]  Charles R. Johnson,et al.  Topics in Matrix Analysis , 1991 .

[9]  J. Raisch Controllability and observability of simple hybrid control systems-FDLTI plants with symbolic measurements and quantized control inputs , 1994 .

[10]  J. Gauthier,et al.  Erratum Observability and Observers for Nonlinear Systems , 1995 .

[11]  Lei Guo,et al.  Convergence and logarithm laws of self-tuning regulators , 1995, Autom..

[12]  C. Berenstein Complex Analysis and Special Topics in Harmonic Analysis , 1995 .

[13]  Joono Sur,et al.  State Observer for Linear Time-Invariant Systems With Quantized Output , 1998 .

[14]  K. Åström,et al.  Comparison of Periodic and Event Based Sampling for First-Order Stochastic Systems , 1999 .

[15]  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).

[16]  Fredrik Gustafsson,et al.  Event based sampling with application to vibration analysis in pneumatic tires , 2001, 2001 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings (Cat. No.01CH37221).

[17]  Xenofon Koutsoukos,et al.  Estimation of hybrid systems using discrete sensors , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[18]  Le Yi Wang,et al.  System identification using binary sensors , 2003, IEEE Trans. Autom. Control..

[19]  Magda Peligrad,et al.  Maximal Inequalities and an Invariance Principle for a Class of Weakly Dependent Random Variables , 2003 .

[20]  H. Kushner,et al.  Stochastic Approximation and Recursive Algorithms and Applications , 2003 .

[21]  G. Yin,et al.  Discrete-Time Markov Chains: Two-Time-Scale Methods and Applications , 2004 .

[22]  Jean-Claude Vivalda,et al.  On the preservation of observability under sampling , 2004, Syst. Control. Lett..

[23]  S. Ethier,et al.  Markov Processes: Characterization and Convergence , 2005 .

[24]  John G. Proakis,et al.  Digital Signal Processing 4th Edition , 2006 .

[25]  Le Yi Wang,et al.  State reconstruction for linear time-invariant systems with binary-valued output observations , 2007, 2007 46th IEEE Conference on Decision and Control.

[26]  Jim Hefferon,et al.  Linear Algebra , 2012 .

[27]  Le Yi Wang,et al.  State reconstruction for linear time-invariant systems with binary-valued output observations , 2008, Syst. Control. Lett..

[28]  An Jun,et al.  Complete convergence of weighted sums for ρ∗ -mixing sequence of random variables , 2008 .

[29]  Le Yi Wang,et al.  Identification of Systems With Regime Switching and Unmodeled Dynamics , 2009, IEEE Transactions on Automatic Control.

[30]  Shaobai Kan,et al.  System identification: Regime switching, unmodeled dynamics, and binary sensors , 2009 .

[31]  Le Yi Wang,et al.  Irregular sampling, active observability, and convergence rates of state observers for systems with binary-valued observations , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

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

[33]  G. Yin,et al.  System Identification with Quantized Observations , 2010 .

[34]  Le Yi Wang,et al.  State Observability and Observers of Linear-Time-Invariant Systems Under Irregular Sampling and Sensor Limitations , 2011, IEEE Transactions on Automatic Control.

[35]  Wei Feng,et al.  Joint State and Event Observers for Irregularly Sampled Switching Systems , 2012 .

[36]  Le Yi Wang,et al.  Joint state and event observers for linear switching systems under irregular sampling , 2013, Autom..