Hybrid model reference adaptive control for unmatched uncertainties

Quindlen, John F.; Chowdhary, Girish; How, Jonathan P.

doi:10.1109/acc.2015.7170884

Cited by 14 publications

(12 citation statements)

References 12 publications

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“…Finally, Fig. 7 shows the actual lumped uncertainty and its estimation using the adaptive law in (41). We can see that due to the nonzero initialization error, i.e., x(0) = 0, the estimated uncertainty σ(t) deviated from its true value σ(t, x, u) (defined in (39)) significantly at the first sampling interval [0, T ), but became very close to the true value afterward.…”

Section: Simulation Results With the Lpv Plantmentioning

confidence: 99%

“…Based the estimation error bound defined later in (74), the smaller a is, the more accurate the uncertainty estimation is. On the other hand, setting a too small, together with a small sampling time (T near 0), will cause the estimation gain Υ(T ) in (41) to be close to ∞, potentially resulting in numerical issues.…”

Section: Remarkmentioning

confidence: 99%

“…where b ẋ(ρ, ρ u ) is defined in (70). From the prediction error dynamics in (64), we have for 0 where the second equality is due to the adaptive law in (41). Furthermore, considering that e −a((i+1)T −ξ) is always positive and σ(ξ) is continuous, we can apply the first mean value theorem in an element-wise manner 1 to (F.6).…”

Section: F Proof Of Lemma 10mentioning

confidence: 99%

“…The adaptive law in (41) and the equality (F.7) indicate that for any t ∈ (i + 1)T, (i + 2)T ∩ [0, τ ] with i ∈ Z 0 , there exist τ * j ∈ (iT, (i + 1)T ) (j ∈ Z n 1 ) such that σ(t) = − a e aT − 1…”

Section: F Proof Of Lemma 10mentioning

confidence: 99%

“…Besides, backstepping adaptive control and ADRC were combined in [64] to handle a nonlinear semi-strict-feedback system subject to both parametric and nonlinear uncertainties, where asymptotic output tracking was achieved when the nonlinear uncertainties were time-invariant. Alternative approaches, such as learning the unmatched uncertainties and incorporating the learned uncertainties to adapt the reference model have also been investigated in linear MRAC settings [65,41,28]. However, these approaches cannot handle time-dependent uncertainties, e.g., external disturbances.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Robust Adaptive Control of Linear Parameter-Varying Systems with Unmatched Uncertainties

Zhao¹,

Snyder²,

Hovakimyana³

et al. 2020

Preprint

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This paper presents a robust adaptive control solution for linear parameter-varying (LPV) systems with unknown input gain and unmatched nonlinear (state-and time-dependent) uncertainties based on the L1 adaptive control architecture and the idea of peak-to-peak gain (PPG) analysis/minimization from robust control. Specifically, we introduce new tools for stability and performance analysis leveraging the PPG bound of an LPV system that is computable using linear matrix inequality (LMI) techniques. A piecewise-constant estimation law is introduced to estimate the lumped uncertainty with quantifiable error bounds, which can be systematically improved by reducing the estimation sampling time. We also present a new approach to attenuate the unmatched uncertainty based on the PPG minimization that is applicable to a broad class of systems with linear nominal dynamics. In addition, we derive transient and steady-state performance bounds in terms of the input and output signals of the actual closed-loop system as compared to the same signals of a virtual reference system that represents the possibly best achievable performance. Under mild assumptions, we prove that the transient performance bounds can be uniformly reduced by decreasing the estimation sampling time, which is subject only to hardware limitations. The theoretical development is validated by extensive simulations on the short-period dynamics of an F-16 aircraft.

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Section: Simulation Results With the Lpv Plantmentioning

confidence: 99%

Section: Remarkmentioning

confidence: 99%

Section: F Proof Of Lemma 10mentioning

confidence: 99%

Section: F Proof Of Lemma 10mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Robust Adaptive Control of Linear Parameter-Varying Systems with Unmatched Uncertainties

Zhao¹,

Snyder²,

Hovakimyana³

et al. 2020

Preprint

View full text Add to dashboard Cite

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Model reference adaptive control for nonlinear time‐varying hybrid dynamical systems

L’Afflitto

2023

Adaptive Control & Signal

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Summary This paper presents the first model reference adaptive control system for nonlinear, time‐varying, hybrid dynamical plants affected by matched and parametric uncertainties, whose resetting events are unknown functions of time and the plant's state. In addition to a control law and an adaptive law, which resemble those of the classical model reference adaptive control framework for continuous‐time dynamical systems, the proposed framework allows imposing instantaneous variations in the reference model's trajectory to rapidly steer the trajectory tracking error to zero, while retaining the closed‐loop system's ability to follow a user‐defined signal. These results are enabled by the first extension of the classical LaSalle–Yoshizawa theorem to time‐varying hybrid dynamical systems, which is presented in this paper as well. A numerical simulation shows the key features of the proposed adaptive control system and highlights its ability to reduce both the control effort and the trajectory tracking error over a classical model reference adaptive control system applied to the same problem.

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