Multi-Input Multi-Output Ellipsoidal State Bounding

Durieu, C.; Walter, Éric; Polyak, B. T.

doi:10.1023/a:1011978200643

Cited by 236 publications

(196 citation statements)

References 20 publications

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“…Under some input constraints, the collection of all possible states to which the system can be transferred from the origin is referred to as the reachable set. The bounding of reachable states was first considered for linear systems in the late 1960s in the context of state estimation and it has later received a lot of attention in parameter estimation (see [8] and references therein). For linear systems, an ellipsoidal bound of the reachable set is often used to contain all the reachable states under zero initial conditions [5], [11], [12], [17], [18], [21], [23], [27], [28].…”

Section: Introductionmentioning

confidence: 99%

On reachable sets for positive linear systems under constrained exogenous inputs

Lam

Shu

et al. 2016

Automatica

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This paper focuses on positive linear time-invariant systems with constant coefficients and specific exogenous disturbance. The problem of finding a hyper-pyramid to bound the set of the states that are reachable from the origin in the Euclidean space is addressed, subject to inputs whose (1, 1)-norm or (∞, 1)-norm is bounded by a prescribed constant. The Lyapunov approach is applied and a bounding hyper-pyramid is obtained by solving a set of inequalities. Iterative procedures (with an adjustable parameter) for reducing the hyper-volume of the bounding hyper-pyramid for the reachable set are proposed.

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Section: Introductionmentioning

confidence: 99%

On reachable sets for positive linear systems under constrained exogenous inputs

Lam

Shu

et al. 2016

Automatica

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“…In summary, the uncertainty ellipsoid at the (k + l)th step is computed using (18), (19), (20), and (21) as:…”

Section: Uncertainty Matrixmentioning

confidence: 99%

Global optimal attitude estimation using uncertainty ellipsoids

Sanyal

Lee

Leok

et al. 2008

Systems & Control Letters

102

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A deterministic attitude estimation problem for a rigid body in a potential field, with bounded attitude and angular velocity measurement errors is considered. An attitude estimation algorithm that globally minimizes the attitude estimation error is obtained. Assuming that the initial attitude, the initial angular velocity and measurement noise lie within given ellipsoidal bounds, an uncertainty ellipsoid that bounds the attitude and the angular velocity of the rigid body is obtained. The center of the uncertainty ellipsoid provides point estimates, and the size of the uncertainty ellipsoid measures the accuracy of the estimates. The point estimates and the uncertainty ellipsoids are propagated using a Lie group variational integrator and its linearization, respectively. The attitude and angular velocity estimates are optimal in the sense that the sizes of the uncertainty ellipsoids are minimized.

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“…The measurement update obtains a minimal ellipsoid that contains the vector sum of these uncertainty ellipsoids. Using expressions for such a minimal ellipsoid given in [8] and [9], we get:…”

Section: B Measurement Updatementioning

confidence: 99%

Deterministic Global Attitude Estimation

Lee¹,

Sanyal²,

Leok³

et al. 2006

Proceedings of the 45th IEEE Conference on Decision and Control

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Abstract-A deterministic attitude estimation problem for a rigid body in an attitude dependent potential field with bounded measurement errors is studied. An attitude estimation scheme that does not use generalized coordinate representations of the attitude is presented here. Assuming that the initial attitude, angular velocity and measurement noise lie within given ellipsoidal bounds, an uncertainty ellipsoid that bounds the attitude and the angular velocity of the rigid body is obtained. The center of the uncertainty ellipsoid provides point estimates, and its size gives the accuracy of the estimates. The point estimates and the uncertainty ellipsoids are propagated using a Lie group variational integrator and its linearization, respectively. The estimation scheme is optimal in the sense that the attitude estimation error and the size of the uncertainty ellipsoid is minimized at each measurement instant, and it is global since the attitude is represented by a rotation matrix.

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Multi-Input Multi-Output Ellipsoidal State Bounding

Cited by 236 publications

References 20 publications

On reachable sets for positive linear systems under constrained exogenous inputs

On reachable sets for positive linear systems under constrained exogenous inputs

Global optimal attitude estimation using uncertainty ellipsoids

Deterministic Global Attitude Estimation

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