Download e-book for kindle: L1 Adaptive Control Theory: Guaranteed Robustness with Fast by Naira Hovakimyan

By Naira Hovakimyan

ISBN-10: 0898717043

ISBN-13: 9780898717044

This booklet provides a entire evaluation of the lately built L1 adaptive regulate idea, together with special proofs of the most effects. the most important function of the L1 adaptive keep an eye on idea is the decoupling of model from robustness. The architectures of L1 adaptive keep an eye on conception have assured brief functionality and robustness within the presence of speedy edition, with out implementing power excitation, utilizing gain-scheduling, or resorting to high-gain suggestions. The booklet covers specified proofs of the most effects and in addition provides the flight attempt effects that experience used this conception and comprises effects no longer but released in technical journals and convention court cases. the cloth is equipped into six chapters and concludes with an appendix that summarizes the mathematical effects used to aid the proofs. software program is accessible on a supplementary website. viewers: L1 Adaptive keep an eye on thought is meant for graduate scholars; researchers; and aerospace, mechanical, chemical, business, and electric engineers attracted to pursuing new instructions in study and constructing know-how at lowered bills. Contents: Foreword; Preface; bankruptcy 1: creation; bankruptcy 2: kingdom suggestions within the Presence of Matched Uncertainties; bankruptcy three: nation suggestions within the Presence of unrivaled Uncertainties; bankruptcy four: Output suggestions; bankruptcy five: L1 Adaptive Controller for Time-Varying Reference structures; bankruptcy 6: functions, Conclusions, and Open difficulties; Appendix A: platforms idea; Appendix B: Projection Operator for variation legislation; Appendix C: simple evidence on Linear Matrix Inequalities; Bibliography

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Additional info for L1 Adaptive Control Theory: Guaranteed Robustness with Fast Adaptation (Advances in Design and Control)

Example text

Notice that for ωc > 40, we have λ2 < 1. 71. 8(b) for constant reference inputs r = 25, 100, 400, which are again scaled accordingly. 7 The example above illustrates that high-order filters C(s) may give the opportunity to use relatively small adaptive gains. While a rigorous relationship between the choice of the adaptive gain and the order of the filter cannot be derived, an insight into this can be gained from the following analysis. 6) that ˆ + xin (s) , x(s) = kg H (s)C(s)r(s) + H (s)θ x(s) − H (s)C(s)η(s) while the state predictor can be rewritten as ˆ + xin (s) .

2 Next, we compare the performance of the L1 adaptive controller to that of a linear high-gain feedback. Consider the scalar system dynamics x(t) ˙ = θx(t) + u(t) , x(0) = 0 , where θ ∈ [θmin , θmax ], and let the desired system have a pole at −2 and unity DC gain. Since for this example we have b = 1, it follows from the definition of H (s) that H (s) = 1 . s +2 Then, in order to ensure that the desired system has unity DC gain and the closed-loop system tracks step-reference signals with zero steady-state error, a feedforward gain kg is needed.

2. 42) where r(s) and ηref (s) are the Laplace transforms of r(t) and ηref (t) θ (t)xref (t) + σ (t), respectively. 42). 42) is BIBS stable with respect to r(t) and x0 . Proof. 42) that xref (s) = G(s)ηref (s) + H (s)C(s)kg r(s) + xin (s) , where, similar to previous analysis, we have set xin (s) (sI − Am )−1 x0 . Since Am is Hurwitz, xin (t) is uniformly bounded. 1 that xref τ L∞ ≤ G(s) L1 ηref τ L∞ + H (s)C(s)kg L1 r L∞ + xin L∞ . 37), we have the following upper bound for ηref (t): ηref τ L∞ Substituting and solving for xref τ xref τ L∞ ≤ ≤ L xref τ L∞ , H (s)C(s)kg L∞ + στ L∞ .

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L1 Adaptive Control Theory: Guaranteed Robustness with Fast Adaptation (Advances in Design and Control) by Naira Hovakimyan


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