Observer-based input-to-state stabilization of networked control systems with large uncertain delays

TLDR: This work considers output-feedback predictor-based stabilization of networked control systems with large unknown time-varying communication delays and designs a sampled-data observer that gives an estimate of the system state, which is used in a predictor that partially compensates unknown network delays.

About: This article is published in Automatica.The article was published on 2016-12-01 and is currently open access. It has received 91 citations till now. The article focuses on the topics: Networked control system & State observer.

Figures

Fig. 1. NCS with two networks

Fig. 2. Time-delays and updating times

Fig. 4. NCS with a sensors-to-controller network

Fig. 3. NCS with a controller-to-actuators network

Table 1 Average numbers of sent control signals (SCS) for different control strategies (r1 = 0.1, µM = 0.005, α = 0.001, ‖w1(t)‖ ≤ 10 −3, ‖w2(t)‖ ≤ 10 −3)

Frequently asked questions

Q1. What are the contributions mentioned in the paper "Observer-based input-to-state stabilization of networked control systemswith large uncertain delays" ?

The authors consider output-feedback predictor-based stabilization of networked control systems with large unknown time-varying communication delays. This estimate is used in a predictor that partially compensates unknown network delays. For systems with only a controller-to-actuators network, the authors take advantage of continuously available measurements by using a continuous-time predictor and employing a recently proposed switching approach to event-triggered control. 

Q2. What is the idea of a switching approach to event-triggered control?

The idea of a switching approach to event-triggered control is to present the closed-loop system as a switching between a system with sampling h and a system with continuous event-triggering mechanism. 

Q3. What is the principle of a switching approach to event-triggered control?

Based on the available measurements, a controller continuously calculates a control signal and transmits it at the sampling times ξk. 

Q4. What is the simplest way to get the h of the system (6), (7)?

According to numerical simulations, the system (6), (7) under the control input ū(ξk) = Kx̂(sk) (without a predictor and eventtriggering) is not stable for r0 = r1 = 0.1, h = 0.035, and ηM = µM = 0. 

Q5. What is the simplest way to get the h of the system?

If σ = 0 (no event-triggering), the conditions of Theorem 1 are satisfied for the same h and larger r0 = r1 = 0.17, ηM = µM = 0.005. 

Q6. How many events can be triggered by the continuous predictor?

In Table 1 one can see that the switching event-triggering reduces the number of sent control signals by more than 20% compared to the sampled event-triggering and by almost 15% compared to the continuous predictor without event-triggering. 

Q7. What is the first inequality in Lemma 1?

Let a, b, α ∈ R, 0 ≤ W ∈ Rn×n, and f : [a, b] → Rn be an absolutely continuous function with a square integrable first derivative such that f(a) = 0 or f(b) = 0. Then ∫ ba e2αtfT (t)Wf(t) dt≤ e2|α|(b−a) 4(b−a) 2π2∫ ba e2αtḟT (t)Wḟ(t) dt. 

Q8. What is the purpose of this paper?

In Section 3, the authors proceed to NCSs with continuous measurements and controller-to-actuators networks, where the authors demonstrate that a recently proposed switching approach to event-triggered control [21] takes advantage of continuously available measurements and further reduces the number of sent control signals. 

Q9. What is the value of t r0?

the value of ẑ(t− r0) cannot be calculated by the controller for t ∈ [ξ∗k, ξk+1), where ξ∗k = min{ξk, sk+1 + r0}, since it depends on y(sk+1) that is not available to the controller. 

Q10. What is the simplest way to obtain the number of sentcontrol signals under the event-triggering?

To obtain the number of sentcontrol signals under the event-triggering, the authors perform 10 numerical simulations with random i.i.d. ηk and µk satisfying (3) and w1(t), w2(t) satisfying ‖w1(t)‖ ≤ 10−3, ‖w2(t)‖ ≤ 10−3. 

Q11. What is the simplest way to check that t t1 holds?

(11)It is easy to check that for t ≥ t1 the following holds:0 ≤ τ0(t) ≤ τ̄ = h+ ηM , r0 + r1 ≤ τ1(t) ≤ τ2(t) ≤ τM = r0 + r1 + h+ ηM + µM .To avoid some technical complications, the authors assume that τ̄ ≤ r0+r1. 

Q12. what is the ′ wI2n?

By takingβ=βw sup s∈[0,t]|eA(r0+r1)w1(t)| 2+βw sups∈[0,t]|eA(r0+r1)Lw2(t)| 2,substituting ˙̂z(t) and applying Schur’s complement formula, the authors obtain that if[Ξ