Self-triggered continuous-discrete observer with updated sampling period

TLDR: This paper deals with the design of high gain observers for a class of continuous-time dynamical systems with discrete-time measurements, and a state estimation problem of an academic bioprocess is studied, and its simulation results are discussed.

About: This article is published in Automatica.The article was published on 2015-12-01 and is currently open access. It has received 29 citations till now. The article focuses on the topics: Observer (quantum physics) & State observer.

Figures

Fig. 3. S given by the model (22) compared to Ŝ given by system (5)-(7).

Fig. 4. Graph of the gain function L.

Fig. 2. Updated sampling time δk.

Fig. 1. Input u(t) = D(t) and output y(tk) = X(tk) with measurement noise.

Frequently asked questions

Q1. What have the authors contributed in "Self-triggered continuous discrete observer with updated sampling period" ?

This paper deals with the design of high gain observers for a class of continuous-time dynamical systems with discrete-time measurements. Moreover, the new idea of the proposed work is that the use of the output measurements by the observer follows an event based on an extended observer state component. As an application of this approach, a state estimation problem of an academic bioprocess is studied, and its simulation results are discussed. 

Q2. What is the bioprocess supposed to be?

The bioprocess is supposed to be continuous with a scalar dilution rate D and an input substrate concentration Sin (which is assumed to be constant). 

Q3. what is the problem of observer synthesis for these systems?

The problem of observer synthesis for these systems is related to the sampling time of the output measurement which is always uniform and should be small to guarantee the observer convergence. 

Q4. What is the function f2 in the system?

the function f2 can easily be extended to a global Lipschitz C1 function on the whole domain R2 ×3 Notice that system (22) can be put in normal form whatever the values of K1, K2 and K3. 

Q5. What is the proof of Lemma 3?

Taking a1 sufficiently small, there exists αm > 0 sufficiently small such that for all α < αm the authors haveQ(α)′ΨPΨQ(α) 6 P − α 1 4p2 P. (17)Proof of Lemma 3. 

Q6. What is the simplest way to estimate the state of a continuous observer?

In this work the authors consider the problem of designing an observer for nonlinear systems that are diffeomorphic to the following form:ẋ = Ax+ f(x, u), (1)where the state x is in Rn, u : R→ Rp is a known input in the space of essentially bounded measurable functions from R+ to Rp (denoted L∞(R+,Rp)), A is a matrix in Rn×n and f : Rn × Rp is a locally Lipschitz vector field both having the following triangular structure:A = 0 1 0 . . . 0 ... . . . . . . . . . ...0 · · · 0 1 0 0 · · · · · · 0 1 0 · · · · · · · · · 0 , f(x, u) = f1(x1, u) f2(x1, x2, u) ...fn(x, u) . 

Q7. What is the corresponding value in the sequence of times?

The measured output is given as a sequence of values (yk)k>0 in Ryk = Cx(tk), (2)where (tk)k>0 is a sequence of times to be selected and C = [1 0 · · · 0] is in Rn.