Active disturbance rejection control for nonlinear systems : by Bao-Zhu Guo, Zhi-Liang Zhao

By Bao-Zhu Guo, Zhi-Liang Zhao

A concise, in-depth creation to lively disturbance rejection keep watch over conception for nonlinear platforms, with numerical simulations and obviously labored out equations

  • Provides the basic, theoretical beginning for functions of lively disturbance rejection control
  • Features numerical simulations and obviously labored out equations
  • Highlights some great benefits of lively disturbance rejection regulate, together with small overshooting, speedy convergence, and effort savings

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Extra info for Active disturbance rejection control for nonlinear systems : an introduction

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If this is not true, then there exists a sequence tn : tn → ∞ such that limn→∞ x(tn ; x0 ) = x∗ = 0. 49), we can obtain that V (x(t; x0 )) is nonincreasing as t increases. This together with the positive definiteness and continuity of V (x) gives lim V (x(t; x0 )) = V (x∗ ) > 0. 45) starting from x∗ . 49), we have V (x(t; x∗ )) < V (x∗ ) for all t > 0. 52) which implies that {x(t; x∗ )| t ≥ 0} ⊂ Lf V −1 (0). This is a contradiction. Hence there exists t1 > 0 such that V (x(t1 ; x∗ )) < V (x∗ ).

2 is taken from [148]. Autonomous underwater vehicles (AUV) are modeled in [155]. The notation of the relative degree of nonlinear systems is taken from [79]. 2 For Lyapunov’s doctoral thesis, we refer to [101]. A large number of publications appeared after Cold War for Lyapunov stability in the control and systems literature Introduction 51 [92, 80, 91]. There is plenty of literature on this topic in monographs, see for instance, [84, 12, 70, and 98]. 4 The finite-time stability for continuous systems was investigated more recently in [112, 17, 67, 15, 12, 16, 109, and 116].

175) (ii) t1 + τ ≤ t2 . In this case, by Vq (t2 , x2 ) ≥ Gq ( x2 ∞ ), we obtain Vq (t1 , x1 ) − Vq (t2 , x2 ) ≤ [e2λτ Gq ( ψ(t1 + τ ) ∞) − Gq ( x2 ∞) ≤ e2λτ |Gq ( ψ(t1 + τ ) ∞) − Gq ( x2 ∞) + (e2λτ −1 )Gq ( x2 ∞) + σ. 178) we obtain Vq (t1 , x2 ) − Vq (t2 , x2 ) ≤ e2λT (M + 2λm(R + 1))|t1 − t2 | + σ ≤ e2λT (M eKT + 2λm(R + 1))|t1 − t2 | + σ. 168) is valid by the arbitrariness of σ. 168), |Vq (t1 , x1 ) − Vq (t2 , x2 )| ≤ |Vq (t1 , x1 ) − Vq (t1 , x2 )| + |Vq (t1 , x2 ) − Vq (t2 , x2 )| ≤ e(2λ+K)T x1 − x2 ∞ ≤ L (t1 − t2 , x1 − x2 ) + (M eKT + 2λm(R + 1)e2λT |t1 − t2 |) ∞.

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