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This study examines the asymmetric link between fiscal decentralization, environmental innovation, and carbon emissions in highly decentralized countries. Our preliminary findings strictly reject the preposition of data normality and highlight that the observed relationship is quantile-dependent, which may disclose misleading results in previous studies using linear methodologies. Therefore, a novel empirical estimation technique popularized as Method of Moments Quantile Regression is employed that simultaneously deal with non-normality and structural changes. The results exhibit that fiscal decentralization significantly mitigates carbon emissions only at lower to medium emissions quantiles. On the other hand, environmental innovation reduces carbon emissions only at medium to higher emissions quantiles. Interestingly, the emissions-reducing effect of fiscal decentralization is highest for lower emissions quantiles and lowest for higher emissions quantiles. In contrast, the impact of environmental innovation is lowest for lower emissions quantiles and highest for higher emission quantiles. Economic growth and population increase carbon emissions, and their emissions-increasing effect are lowest for lower emissions quantiles and highest for higher emissions quantiles. Moreover, the heterogeneous panel causality test confirms a one-way causal association, implying that any policy intervention regarding fiscal decentralization and environmental innovation significantly affects carbon emissions.

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Input saturation must be taken into account for applying rapid reorientation in the large angle manoeuvre of a quadrotor. In this paper, a backstepping-based inverse optimal attitude controller (BIOAC) is derived which has the property of a maximum convergence rate in the sense of a control Lyapunov function (CLF) under input torque limitation. In the controller, a backstepping technique is used for handling the complexity introducing by the unit quaternion representation of the attitude of a quadrotor with four parameters. Moreover, the inverse optimal approach is employed to circumvent the difficulty of solving the Hamilton-Jacobi-Bellman (HJB) equation. The performance of BIOAC is compared with a PD controller in which the input torque limitation is not considered under the same unit quaternion representation using numerical simulation while the results show that BIOAC gains faster convergence with less control effort. Next, BIOAC is realized on a test bed and the effectiveness of the control law is verified by experimental studies.

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