Professor Lihua Xie, Professor Huanshui Zhang (auth.)'s Control and Estimation of Systems with Input/Output Delays PDF

By Professor Lihua Xie, Professor Huanshui Zhang (auth.)

ISBN-10: 354071118X

ISBN-13: 9783540711186

ISBN-10: 3540711198

ISBN-13: 9783540711193

Time delays exist in lots of engineering platforms resembling transportation, verbal exchange, technique engineering and networked regulate structures. lately, time hold up platforms have attracted habitual pursuits from learn group. a lot of the trouble has been all for balance research and stabilization of time hold up structures utilizing the so-called Lyapunov-Krasovskii useful including a linear matrix inequality method, which gives an effective numerical instrument for dealing with structures with delays in country and/or inputs.

Recently, a few extra fascinating and basic improvement for structures with input/output (i/o) delays has been made utilizing time area or frequency area techniques. those methods result in analytical ideas to time hold up difficulties when it comes to Riccati equations or spectral factorizations.

This monograph provides uncomplicated analytical recommendations to manage and estimation difficulties for platforms with a number of i/o delays through ordinary instruments reminiscent of projection. we suggest a re-organized innovation research process for hold up platforms and determine a duality among optimum keep watch over of platforms with a number of enter delays and smoothing estimation for hold up unfastened structures. those attractive new thoughts are utilized to resolve keep an eye on and estimation difficulties for structures with a number of i/o delays and kingdom delays less than either the H2 and H-infinity functionality standards.

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6) · · · Γ(l) ] , t ≥ hl . 2) can be rewritten as N JN = x (N + 1)P x(N + 1) + N u (t)Rt u(t) + t=0 where Rt = x (t)Qx(t), ⎧ ⎨ diag{R · · · , R(i) }, hi ≤ t < hi+1 , ⎩ diag{R · · · , R(l) }, t ≥ hl . 4). 30 3. 10) where x(t) is the state and y(t) is the measurement output. The initial state x(N + 1), q(t) and v(t) are white noises with zero means and covariance matrices x(N + 1), x(N + 1) = P , q(t), q(s) = Qδt,s and v(t), v(s) = Rt δt,s , respectively. 11) ⎩ (l + 1)m × 1, t ≥ h , l and v(t) has the same dimension as y(t).

We note that in the absence of input delays, the solution to the LQR problem is well known and is related to one backward RDE. In the case of single input delay, the optimal tracking problem has been studied in [75] and a solution is also given in terms of one backward RDE. Here, we aim to give a similar solution for systems with multiple input delays. It is worth pointing out that the presence of delays in multiple input channels makes the control problem much more challenging due to interactions among various input channels.

1 29 Duality Between Linear Quadratic Regulation and Smoothing Estimation In this section, we shall convert the LQR problem into an optimization problem in a linear space for an associated stochastic system and establish a duality between the LQR problem and a smoothing problem. The duality will allow us to derive a solution for the LQR problem via standard smoothing estimation in the next section. 3) x(t + 1) = ⎩ Φx(t) + Γ u(t), t≥h, t where l ⎧⎡ ⎤ u0 (t − h0 ) ⎪ ⎪ ⎪ ⎢ ⎪ ⎥ .. ⎪ ⎪ ⎣ ⎦ , hi ≤ t < hi+1 , .

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Control and Estimation of Systems with Input/Output Delays by Professor Lihua Xie, Professor Huanshui Zhang (auth.)


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