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Data assimilation techniques are widely used to predict complex dynamical systems with uncertainties, based on time-series observation data. Error covariance matrices modeling is an important element in data assimilation algorithms which can considerably impact the forecasting accuracy. The estimation of these covariances, which usually relies on empirical assumptions and physical constraints, is often imprecise and computationally expensive, especially for systems of large dimensions. In this work, we propose a data-driven approach based on long short term memory (LSTM) recurrent neural networks (RNN) to improve both the accuracy and the efficiency of observation covariance specification in data assimilation for dynamical systems. Learning the covariance matrix from observed/simulated time-series data, the proposed approach does not require any knowledge or assumption about prior error distribution, unlike classical posterior tuning methods. We have compared the novel approach with two state-of-the-art covariance tuning algorithms, namely DI01 and D05, first in a Lorenz dynamical system and then in a 2D shallow water twin experiments framework with different covariance parameterization using ensemble assimilation. This novel method shows significant advantages in observation covariance specification, assimilation accuracy, and computational efficiency.

We aim to control the differential mobile robot system to follow a class of pre-specified constraints sufficiently closely in the presence of system uncertainties. The mass and the moment of inertia of the differential mobile robot are considered as the uncertain parameters, which are (possibly) fast time-varying. In the first step, based on Udwadia and Kalaba’s approach, an adaptive robust control scheme is proposed to deal with the system uncertainties. The adaptive law is of leakage type, which can adjust itself based on the tracking error. Using this adaptive robust control scheme, we can obtain the desired armature currents of the two direct current (DC) motors, which are not the real control inputs. In the second step, taking the motor dynamics into account, a Lyapunov Minimax approach for the required actual control inputs (i.e., the input voltages of the two DC motors) is proposed to generate the desired armature currents. This two-step control methodology guarantees uniform boundedness and uniform ultimate boundedness, and renders the system to follow a class of pre-specified constraints approximately.