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

TL;DR

This work addresses robust adaptive control for linear parameter-varying (LPV) systems subject to unmatched nonlinear uncertainties and unknown input gain. It merges ${\mathcal{L}_1}$ adaptive control with a peak-to-peak gain (PPG) minimization framework to attenuate unmatched disturbances through a dynamic LPV feedforward map ${\bar{\mathcal{H}}}(\theta)$, complemented by a low-pass filter ${\mathcal{C}}(s)$ to decouple estimation from control. The authors derive uniform transient and steady-state performance bounds relative to a nominal reference system, establish a stability condition via a LPV small-gain bound, and propose a practical LPV-LMI based synthesis workflow including gridding to handle parameter dependence and uncertain input gain. The approach is demonstrated on the short-period dynamics of an F-16 aircraft across a large operating envelope, with simulations using both LPV and full nonlinear models showing robust tracking and smoother control signals. The framework offers a systematic path to scheduling desired dynamics in the presence of large uncertainties, with implications for high-performance flight control and other aerospace applications, and suggests future work on extending to output-feedback cases.

Abstract

In controlling systems with large operating envelopes, it is often necessary to adjust the desired dynamics according to operating conditions. This paper presents a robust adaptive control architecture for linear parameter-varying (LPV) systems that allows for the desired dynamics to be systematically scheduled, while being able to handle a broad class of uncertainties, both matched and unmatched, which can depend on both time and states. The proposed controller adopts an L1 adaptive control architecture for designing the adaptive control law and peak-to-peak gain (PPG) minimization for designing the robust control law to mitigate the effect of unmatched uncertainties. Leveraging the PPG bound of an LPV system, 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 nominal system. The efficacy of the proposed method is validated by extensive simulations using the short-period dynamics of an F-16 aircraft operating in a large envelope.

Figures (12)

• Figure 1: Proposed robust adaptive control architecture
• Figure 2: Scheme for unmatched uncertainty attenuation
• Figure 3: Open-loop (left) and closed-loop (right) poles when $\bar{q}_s$ changes from $-1$ to $1$ with an increment of $0.2$
• Figure 4: Trajectories of scheduling parameters
• Figure 5: Trajectories of $x_1$ (top) and $x_2$ (bottom) under different references

Theorems & Definitions (54)

• Remark 1
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• Lemma 1
• Definition 1
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• Lemma 2