Set-membership state estimation for discrete time piecewise affine systems using zonotopes

This paper presents a method for guaranteed state estimation of discrete time piecewise affine systems with unknown but bounded noise and disturbance. Using zonotopic set representations, the proposed method computes the set of states that are consistent with the model, observation, and bounds on the noise and disturbance such that the real state of the system is guaranteed to lie in this set. Because in piecewise affine systems, the state space is partitioned into a number of polyhedral sets, at each iteration the intersection of the zonotopes containing a set-valued estimation of the states with each of the polyhedral partitions must be computed. We use an analytic method to compute the intersection as a zonotope and minimize the size of the intersection. A numerical example is provided to illuminate the algorithm.

[1]  Pedro Casau,et al.  A set-valued approach to FDI and FTC: Theory and implementation issues , 2012 .

[2]  Vicenç Puig,et al.  Robust fault detection using zonotope‐based set‐membership consistency test , 2009 .

[3]  Qinghua Zhang,et al.  Robust Fault Diagnosis Based on Adaptive Estimation and Set-Membership Computations , 2007 .

[4]  Vicenç Puig,et al.  Worst-case state estimation and simulation of uncertain discrete-time systems using zonotopes , 2001, 2001 European Control Conference (ECC).

[5]  D. Mayne,et al.  State estimation for piecewise affine, discrete time systems with bounded disturbances , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[6]  F. Schweppe.  Recursive state estimation: Unknown but bounded errors and system inputs , 1967 .

[7]  Didier Dumur,et al.  Robust tube-based constrained predictive control via zonotopic set-membership estimation , 2011, IEEE Conference on Decision and Control and European Control Conference.

[8]  Luigi Chisci,et al.  Block recursive parallelotopic bounding in set membership identification , 1998, Autom..

[9]  Eduardo F. Camacho,et al.  Bounded error identification of systems with time-varying parameters , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[10]  Eduardo F. Camacho,et al.  Guaranteed state estimation by zonotopes , 2005, Autom..

[11]  Peter Fogh Odgaard,et al.  Fault Detection of Wind Turbines with Uncertain Parameters: A Set-Membership Approach , 2012 .

[12]  A. Vicino,et al.  Sequential approximation of feasible parameter sets for identification with set membership uncertainty , 1996, IEEE Trans. Autom. Control..

[13]  Vicenç Puig,et al.  Fault diagnosis and fault tolerant control using set-membership approaches: Application to real case studies , 2010, Int. J. Appl. Math. Comput. Sci..

[14]  Luigi Chisci,et al.  Recursive state bounding by parallelotopes , 1996, Autom..

[15]  Bart De Schutter,et al.  Equivalence of hybrid dynamical models , 2001, Autom..

[16]  Pramod P. Khargonekar,et al.  FILTERING AND SMOOTHING IN AN H" SETTING , 1991 .

[17]  M. Johansson,et al.  Piecewise Linear Control Systems , 2003 .

[18]  C. Combastel.  A state bounding observer based on zonotopes , 2003, 2003 European Control Conference (ECC).

[19]  Seyedmojtaba Tabatabaeipour,et al.  Fault detection of a benchmark wind turbine using interval analysis , 2012, 2012 American Control Conference (ACC).