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Most of the advanced nonlinear control strategies reported in the literature for underactuated mechanisms, such as overhead cranes, require the knowledge of all state variables. For cranes, the state vector includes variables related to the load sway and its velocity. The flatness property of crane-like systems can be exploited to solve both motion planning and tracking problems, so that the load (whose coordinates are included in the set of the flat outputs) exponentially follows a rapid reference trajectory. However, unmodeled friction phenomena and limitations on the direct measurement of sway-related state variables usually impede the practical implementation of flatness-based control laws. This paper proposes the use of an adaptive unscented Kalman filter to estimate friction forces and unmeasured state variables. The convergence of the filter is improved using a novel technique, called condition-based selective scaling. The performance of the suggested scheme is verified through a set of computer simulations on a 2D overhead crane system.

This study introduces a fuzzy based optimal state estimation approach. The new method is based on two principles: Adaptive Unscented Kalman filter, and Fuzzy Adaptive Grasshopper Optimization Algorithm. The approach is designed for the optimization of an adaptive Unscented Kalman Filter. To find the optimal parameters for the filter, a fuzzy based evolutionary algorithm, named Fuzzy Adaptive Grasshopper Optimization Algorithm, is developed where its efficiency is verified by application to different benchmark functions. The proposed optimal adaptive unscented Kalman filter is applied to two nonlinear systems: a robotic manipulator, and a servo-hydraulic system. Different simulation tests are conducted to verify the performance of the filter. The results of simulations are presented and compared with a previous version of the unscented Kalman filter. For a realistic test, the proposed filter is applied on the practical servo-hydraulic system. Practical results are discussed, and presented results approve the capability of the presented method for practical applications.

Since the noise statistics of large-scale battery energy storage systems (BESSs) are often unknown or inaccurate in actual applications, the estimation precision of state of charge (SOC) of BESSs using extended Kalman filter (EKF) or unscented Kalman filter (UKF) is usually inaccurate or even divergent. To resolve this problem, a method based on adaptive UKF (AUKF) with a noise statistics estimator is proposed to estimate accurately SOC of BESSs. The noise statistics estimator based on the modified Sage-Husa maximum posterior is aimed to estimate adaptively the mean and error covariance of measurement and system process noises online for the AUKF when the prior noise statistics are unknown or inaccurate. The accuracy and adaptation of the proposed method is validated by the comparison with the UKF and EKF under different real-time conditions. The comparison shows that the proposed method can achieve better SOC estimation accuracy when the noise statistics of BESSs are unknown or inaccurate.