The theoretical part of linear functional observer design problem is solved

Tsui, Chia-Chi

doi:10.1109/chicc.2014.6895512

Cited by 1 publication

(5 citation statements)

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“…The claims of [19,42,43] were repeatedly rejected before publication that was already many years after 1986. In addition, about a decade and half after 1986, some new results appeared [46,47] .…”

Section: Results Of Function Observer Design For Reduced Ordermentioning

confidence: 99%

“…Finally, [19] most formally and rigorously proved the above claims of [42,43], and then made the following two further clear-cut claims: 1) Just like the minimum value of r is a function of every given data of the problem k k k = Dc c c, there is no analytical formula for the minimal observer order (r) itself from problem (8). Thus, (8) and (9) are the best possible theoretical result of minimal order function observer design problem, and the theoretical part of this problem is solved.…”

Section: Results Of Function Observer Design For Reduced Ordermentioning

confidence: 99%

“…In addition, about a decade and half after 1986, some new results appeared [46,47] . According to [19], these results reformulated without simplification the original problem formulation (5) and (6) (such as merely combining (5) and (6) together or merely reformulating the solvability of (6) as rank [K : C ] = rank[C ]), proposed only exhaustive numerical search to compute the solution of the complicated reformulation, and cannot even achieve the analytical result of p(ν1 − 1) of 1980 [2] . The claim of [46] that it offered the only design solution to the minimal order functional observer design problem, is based only on the assumption that numerical search can yield the minimal order, and is obviously erroneous and misleading.…”

Section: Results Of Function Observer Design For Reduced Ordermentioning

confidence: 99%

“…Section 2 indicates that based on a general and decoupled solution (7) to the most important observer design equation (5), the minimal order function observer design problem was essentially solved in 1986 [19] . Subsection 1.3 proves that in addition to the generation of feedback control signal Kx x x(t), the observer must also realize the loop transfer function or the robust property of that Kx x x(t)-control.…”

Section: Discussionmentioning

confidence: 99%

“…This order reduction is possible if the observer estimates Kx x x(t) directly instead of x x x(t), and such an observer is named "function (or functional) observer". For thirty years since the last survey of observer design [18] , very significant progress was made in function observer design problem and the problem is claimed essentially solved [19] .…”

Section: State Feedback Control (Sfc) Is Defined As U U U(t) = −Kx X mentioning

confidence: 99%

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Observer design — A survey

Tsui

2015

Int. J. Autom. Comput.

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This paper surveys the results of observer design for linear time-invariant (L-T-I) deterministic irreducible open-loop systems (OLS), the most basic type of OLS. An observer estimates Kx x x(t) signal where K is a constant and x x x(t) is the state vector of the OLS. Thus, an observer can be used as a feedback controller that implements state feedback control (SFC) or Kx x x(t)-control, and observer design is therefore utterly important in all feedback control designs of state space theory. In this survey, the observer design results are divided into three categories and for three respective main purposes. The first category of observers estimate signal Kx x x(t) only with a given K, and this survey has four conclusions: 1) Function observer that estimates Kx x x(t) directly is more general than state observer that estimates x x x(t), and may be designed with order lower than that of state observer, and the additional design objective is to minimize observer order; 2) The function observer design problem has already been simplified to the solving of a single set of linear equations only while seeking the lowest possible number of rows of the solution matrix, and an apparently most effective and general algorithm of solving such a problem can guarantee unified upper and lower bounds of the observer order; 3) Because such a single set of linear equations is the simplest possible theoretical formulation of the design problem and such theoretical observer order bounds are the lowest possible, and because the general, simple, and explicit theoretical formula for the function observer order itself do not exist, the theoretical part of this design problem is solved; 4) Because the function observer order is generically near its upper bound, further improvement on the computational design algorithm so that the corresponding observer order can be further reduced, is generically not worthwhile. The second category of observers further realize the loop transfer function and robustness properties of the direct SFC, and the conclusion of this survey is also fourfold: 1) To fully realize the loop transfer function of a practically designed Kx x x(t)-control, the observer must be an output feedback controller (OFC) which has zero gain to OLS input; 2) If parameter K is separately designed before the observer design, as in the separation principle which has been followed by almost all people for over half of a century, then OFC that estimates Kx x x(t) does not exist for almost all OLS s; 3) As a result, a synthesized design principle that designs an OFC first and is valid for almost all OLS s, is proposed and fully developed, the corresponding K will be designed afterwards and will be constrained by the OFC order as well as the OFC parameters; 4) Although the Kx x x(t)-control is constrained in this new design principle and is therefore called the "generalized SFC" (as compared to the existing SFC in which K is unconstrained), it is still strong enough for most OLS s and this new design principle overcomes many fund...

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