A state-set estimation algorithm for linear systems in the presence of bounded disturbances

Spathopoulos, M.P.; Grobov, I. D.

doi:10.1080/00207179608921869

Cited by 14 publications

(11 citation statements)

References 10 publications

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“…The polyhedron description is given in the form of inequalities, see equation (5). However, instead of using polyhedron perturbation, see Spathopoulos et al (1996), one may consider shifting hyper planes along the direction of the vector e.…”

Section: Input Disturbance Estimation 509mentioning

confidence: 99%

“…Remark 1: In this section, see Spathopoulos et al (1996), the interval set F is assumed to be constant for all t. In the following, assuming that the input disturbance is modelled by equation (3), the bounded sets F (t) Í F ,t = 0,1,. . .…”

Section: S Tate Estimationmentioning

confidence: 99%

“…Let X be a closed convex polyhedron described in terms of inequalities, see Spathopoulos et al (1996) and e be a vector. L et Y Í X and : =Ä yÎ Y (y + el) ,l Î R n is a scalar such that´X = .…”

Section: Estimation Of the Bound S For The Input Disturbance Setmentioning

confidence: 99%

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Input disturbance estimation in the bounded noise context

Spathopoulos¹,

Grobov²

1998

International Journal of Control

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A method is presented for computing input disturbance estimates for a state-space system using noisy observations. The input disturbance and the measurement noise is assumed to be bounded. In addition, the input disturbance is time varying and the rate of change per sampling time is bounded. A recursive procedure for estimating the bounds of the inpu5t disturbance is derived. Based on these estimates, a disturbance rejection scheme is proposed which results in obtaining less conservative guaranteed state estimated sets. Simulation results demonstrate the performance of our technique.

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Section: Input Disturbance Estimation 509mentioning

confidence: 99%

Section: S Tate Estimationmentioning

confidence: 99%

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Input disturbance estimation in the bounded noise context

Spathopoulos¹,

Grobov²

1998

International Journal of Control

Self Cite

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“…However, in many cases the appropriate statistics of the noise corrupting the data is not available and therefore the disturbances cannot be suitably described by random noise [18]. A non-statistical description of the noise in the form of bounds is used in the so called theory of guaranteed set estimation or set theoretic approach [6,7,12,13,16]. In the set theoretic approach all information about the system behaviour is provided in the form of the sets of possible states which are consistent with observations and system dynamics.…”

Section: Introductionmentioning

confidence: 99%

“…Many techniques for set estimation have been developed (See. 3,9,[12][13][14][15] following the works of Witsenhausen [17] and Schweppe [12]. However, neither of these techniques allows constructing disturbance set estimates.…”

Section: Introductionmentioning

confidence: 99%

Input Disturbance Estimation For Linear Systems in The Bounded Noise Context

Grobov

2001

Asian Journal of Control

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A method is presented for constructing input disturbance estimates for a linear system using noisy observations. The input disturbance of the dynamic system and the observation noise are assumed to be unknown but bounded. In addition, the structural characteristics of the input disturbance are given in the form of the maximum possible change of its magnitude per sampling time. The input disturbance represents a wide category of system uncertainties. A recursive procedure for obtaining disturbance set estimates is derived. The procedure is easy to implement and is a competitive technique comparative to the classical estimation schemes. Simulation results demonstrate the performance of the given techniques.

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Set membership state estimation with improved zonotopic description of feasible solution set

Chai

Sun

Qiao

2012

Intl J Robust & Nonlinear

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SUMMARYThis paper proposes an improved zonotopic method to set membership state estimation for nonlinear discrete‐time systems with a bounded description of noise and parameters. According to the previous method, a zonotope containing the uncertain trajectory of the system is computed using interval arithmetic in the time update. In the observation update, an improved intersection algorithm of zonotope and strip is used to obtain a zonotope bounding the intersection of the uncertain trajectory with the region of the state space consistent with the observed output. This obtained zonotope is used to describe the feasible solution set of state. It is proven that the zonotope obtained by the improved algorithm can be tighter than the one obtained by the previous algorithm. Simulation experiments are conducted showing the performance of the improved state estimation method as compared with the previous one. Two types of noise distribution are considered. The results expose the weakness of the previous method and illustrate the effectiveness of the improvement. Copyright © 2012 John Wiley & Sons, Ltd.

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A state-set estimation algorithm for linear systems in the presence of bounded disturbances

Cited by 14 publications

References 10 publications

Input disturbance estimation in the bounded noise context

Input disturbance estimation in the bounded noise context

Input Disturbance Estimation For Linear Systems in The Bounded Noise Context

Set membership state estimation with improved zonotopic description of feasible solution set

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