Reduced Order Observer for Linear Time-Invariant Multivariable Systems with Unknown Inputs

Lungu, Mihai; Lungu, Romulus

doi:10.1007/s00034-013-9618-z

Cited by 26 publications

(17 citation statements)

References 15 publications

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“…Due to the presence of the unknown-inputs, there are more constraints that should be satisfied and the observer design is thus more complicated and can be more conservative ( [24], [15], [25]). As far as the authors know, only two algorithms are available that attempt to find a reduced order UIFO for a system that does not satisfy Darouach's conditions ( [16], [7]). However, these methods do not necessarily lead to the design of the minimum possible order UIFO.…”

Section: Introductionmentioning

confidence: 99%

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On unknown-Input Functional Observability of linear systems

Mohajerpoor

Asayesh

Nahavandi

2015

2015 American Control Conference (ACC)

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Finding the least possible order of a stable Unknown-Input Functional Observer (UIFO) has always been a challenge in observer design theory. A practical recursive algorithm is proposed in this technical note to design a minimal multi-functional observer for multi-input multi-output (MIMO) linear time-invariant (LTI) systems with unknown-inputs. The concept of unknown-input functional observability is introduced, and it is used as a certificate of the convergence of our algorithm. The proposed procedure looks for a number of additional auxiliary functions to be augmented to the original functions desired for reconstruction. The resulting UIFO is proper, and minimal (of minimum possible order). Moreover, the algorithm does not need the system to be unknown-input observable. A numerical example shows the procedure as well as the effectiveness of the proposed algorithm.Keywords: Unknown-input functional observers, functional observability, invariant zeros and transmission zeros, null space and range space

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Section: Introductionmentioning

confidence: 99%

“…The observer is independent of the values of the unknown-inputs. UIFOs have even more importance than regular observers due to their wide range of applications and designing robust observers ( [4], [5], [6], [7], [8]). …”

Section: Introductionmentioning

confidence: 99%

On unknown-Input Functional Observability of linear systems

Mohajerpoor

Asayesh

Nahavandi

2015

2015 American Control Conference (ACC)

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“…Meanwhile, the approaches to designing positive observers seem to have received relatively less attention despite their practical significance. The observer design problem for general linear systems has been solved in the works of Lungu and Lungu . However, the observer may not be applicable to the case of positive systems since the state estimates may escape from the nonnegative orthant in some time interval, which, in turn, implies that the estimation is not valid.…”

Section: Introductionmentioning

confidence: 99%

“…The observer design problem for general linear systems has been solved in the works of Lungu and Lungu. 39,40 However, the observer may not be applicable to the case of positive systems since the state estimates may escape from the nonnegative orthant in some time interval, which, in turn, implies that the estimation is not valid. Therefore, the observer should be designed in such a way that the estimated state is nonnegative like the system state itself.…”

Section: Introductionmentioning

confidence: 99%

State‐bounding observer design for uncertain positive systems under ℓ₁ performance

Chen

Shen

2017

Optim Control Appl Methods

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Summary This paper investigates the ℓ1‐induced positive observer design problem for uncertain positive systems. First, we present the ℓ1‐induced performance indicator for positive systems, which fits well into the linear Lyapunov function. Then, a novel ℓ1‐induced performance characterization is developed for uncertain positive systems. Furthermore, a linear programming–based method is proposed to solve the ℓ1‐induced positive observer synthesis problem for positive systems with interval uncertainties. A pair of positive state‐bounding observers is designed to estimate the state of uncertain positive systems. Finally, we provide a numerical example to demonstrate the validity and efficiency of the derived methods.

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“…Essentially, Riccati equation‐based H ∞ control and linear matrix inequality techniques can solve the linear quadratic (LQ) regulator problem for the square system with direct transmission terms from input to both (i) measured output ( Y ( z ) = [ C ( I n − G ) −1 H + D ] u ( z ), where I − D T D − H T P H > 0, P is the solution of H ∞ control‐type Riccati equation, which implies that the square system is invertible and (ii) controlled output; however, only the latter case is considered in , that is, the direct transmission term from input to measured output is not considered in . H ∞ control technique‐based regulator can be applied to solve the tracking problem for the square system, that is, the number of control input equals to the number of measured output under the assumption I − D T D − H T P H > 0; however, it does not directly extend to the case where the number of control input is more than the number of measured output.…”

Section: Introductionmentioning

confidence: 99%

A new optimal linear quadratic observer‐based tracker under input constraint for the unknown system with a direct feed‐through term

Tsai

Lee

et al. 2014

Optim Control Appl Methods

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SUMMARYThis paper develops a new optimal linear quadratic observer-based tracker with input constraint for the linear unknown system with a direct transmission term from input to measured output. The off-line observer/Kalman filter identification method is used to determine the linear sampled-data model with a direct feed-through term. On the basis of this model, a high-gain optimal linear quadratic analog observer-based tracker is proposed, so that it can effectively induce a high quality performance on the state estimation and the trajectory tracking design. Besides, the prediction-based digital redesign method is utilized to obtain a relatively low-gain and implementable observer and digital tracker from the theoretically well-designed high-gain analog observer and tracker for the linear system with a direct transmission term from input to output. To reduce the magnitude of control input, which is caused by the high-gain property to fit the requirement of the input constraint, the modified linear quadratic analog tracker is proposed. Thus, the control input can be compressed effectively without losing the original high performance of tracking much.

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Reduced Order Observer for Linear Time-Invariant Multivariable Systems with Unknown Inputs

Cited by 26 publications

References 15 publications

On unknown-Input Functional Observability of linear systems

On unknown-Input Functional Observability of linear systems

State‐bounding observer design for uncertain positive systems under ℓ₁ performance

A new optimal linear quadratic observer‐based tracker under input constraint for the unknown system with a direct feed‐through term

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Reduced Order Observer for Linear Time-Invariant Multivariable Systems with Unknown Inputs

Cited by 26 publications

References 15 publications

On unknown-Input Functional Observability of linear systems

On unknown-Input Functional Observability of linear systems

State‐bounding observer design for uncertain positive systems under ℓ1 performance

A new optimal linear quadratic observer‐based tracker under input constraint for the unknown system with a direct feed‐through term

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State‐bounding observer design for uncertain positive systems under ℓ₁ performance