Data assimilation (DA) and uncertainty quantification (UQ) are extensively used in analysing and reducing error propagation in high-dimensional spatial-temporal dynamics. Typical applications span from computational fluid dynamics (CFD) to geoscience and climate systems. Recently, much effort has been given in combining DA, UQ and machine learning (ML) techniques. These research efforts seek to address some critical challenges in high-dimensional dynamical systems, including but not limited to dynamical system identification, reduced order surrogate modelling, error covariance specification and model error correction. A large number of developed techniques and methodologies exhibit a broad applicability across numerous domains, resulting in the necessity for a comprehensive guide. This paper provides the first overview of state-of-the-art researches in this interdisciplinary field, covering a wide range of applications. This review is aimed at ML scientists who attempt to apply DA and UQ techniques to improve the accuracy and the interpretability of their models, but also at DA and UQ experts who intend to integrate cutting-edge ML approaches to their systems. Therefore, this article has a special focus on how ML methods can overcome the existing limits of DA and UQ, and vice versa. Some exciting perspectives of this rapidly developing research field are also discussed.

High-dimensional and incomplete (HDI) data subject to the nonnegativity constraints are commonly encountered in a big data-related application concerning the interactions among numerous nodes. A nonnegative latent factor analysis (NLFA) model can perform representation learning to HDI data efficiently. However, existing NLFA models suffer from either slow convergence rate or representation accuracy loss. To address this issue, this paper proposes a proximal alternating-direction-method-of-multipliers-based nonnegative latent factor analysis (PAN) model with two-fold ideas: 1) adopting the principle of alternating-direction-method-of-multipliers to implement an efficient learning scheme for fast convergence and high computational efficiency; and 2) incorporating the proximal regularization into the learning scheme to suppress the optimization fluctuation for high representation learning accuracy to HDI data. Theoretical studies verify that PAN converges to a Karush-Kuhn-Tucker (KKT) stationary point of its nonnegativity-constrained learning objective with its learning scheme. Experimental results on eight HDI matrices from real applications demonstrate that the proposed PAN model outperforms several state-of-the-art models in both estimation accuracy for missing data of an HDI matrix and computational efficiency.

Quanta image sensors (QIS) are a new type of single-photon imaging device that can oversample the light field to generate binary bit-streams. The reconstruction for QIS refers to the recovery of original scenes from these binary measurements. Conventional reconstruction algorithms for QIS generally depend solely on one instantiated prior and are certainly insufficient for capturing the statistical properties over high-dimensional space. On the other hand, deep learning-based methods have shown promising performance, due to their excellent ability to learn feature representations from relevant databases. However, most deep models only focus on exploring local features while generally overlooking long-range similarity. In view of this, a dual-prior integrated reconstruction algorithm for QIS (DPI-QIS) is proposed, which combines a deep prior with a non-local self-similarity one using the multi-agent consensus equilibrium (MACE) framework. In comparison to the approaches that utilize a single prior, DPI-QIS fits the reconstruction model sufficiently by leveraging the respective merits of both priors. An effective yet flexible MACE framework is employed to integrate the physical forward model allying with the two prior-based models to achieve an overall better result. Extensive experiments demonstrate that the proposed algorithm achieves state-of-the-art performance in terms of objective and visual perception at multiple oversampling factors, while having stronger robustness to noise.

This paper considers the mean square output containment control problem for heterogeneous multi-agent systems (MASs) with randomly switching topologies and nonuniform distributed delays. By modeling the switching topologies as a continuous-time Markov process and taking the distributed delays into consideration, a novel distributed containment observer is proposed to estimate the convex hull spanned by the leaders’ states. A novel distributed output feedback containment controller is then designed without using the prior knowledge of distributed delays. By constructing a novel switching Lyapunov functional, the output containment control problem is then solved in the sense of mean square under an easily-verifiable sufficient condition. Finally, two numerical examples are given to show the effectiveness of the proposed controller.

This paper explores the problem of distributed Nash equilibrium seeking in games, where players have limited knowledge on other players’ actions. In particular, the involved players are considered to be high-order integrators with their control inputs constrained within a pre-specified region. A linear transformation for players’ dynamics is firstly utilized to facilitate the design of bounded control inputs incorporating multiple saturation functions. By introducing consensus protocols with adaptive and time-varying gains, the unknown actions for players are distributively estimated. Then, a fully distributed Nash equilibrium seeking strategy is exploited, showcasing its remarkable properties: 1) ensuring the boundedness of control inputs; 2) avoiding any global information/parameters; and 3) allowing the graph to be directed. Based on Lyapunov stability analysis, it is theoretically proved that the proposed distributed control strategy can lead all the players’ actions to the Nash equilibrium. Finally, an illustrative example is given to validate effectiveness of the proposed method.

The existing containment control has been widely developed for several years, but ignores the case for large-scale cooperation. The strong coupling of large-scale networks will increase the costs of system detection and maintenance. Therefore, this paper is concerned with an extensional containment control issue, hierarchical containment control. It aims to enable a multitude of followers achieving a novel cooperation in the convex hull shaped by multiple leaders. Firstly, by constructing the three-layer topology, large-scale networks are decoupled. Then, under the condition of directed spanning group-tree, a class of dynamic hierarchical containment control protocol is designed such that the novel group-consensus behavior in the convex hull can be realized. Moreover, the definitions of coupling strength coefficients and the group-consensus parameter in the proposed dynamic hierarchical control protocol enhance the adjustability of systems. Compared with the existing containment control strategy, the proposed hierarchical containment control strategy improves dynamic control performance. Finally, numerical simulations are presented to demonstrate the effectiveness of the proposed hierarchical control protocol.

The attitude tracking operations of an on-orbit spacecraft with degraded performance exhibited by potential actuator uncertainties (including failures and misalignments) can be extraordinarily challenging. Thus, the control law development for the attitude tracking task of spacecraft subject to actuator (namely reaction wheel) uncertainties is addressed in this paper. More specially, the attitude dynamics model of the spacecraft is firstly established under actuator failures and misalignment (without a small angle approximation operation). Then, a new non-singular sliding manifold with fixed time convergence and anti-unwinding properties is proposed, and an adaptive sliding mode control (SMC) strategy is introduced to handle actuator uncertainties, model uncertainties and external disturbances simultaneously. Among this, an explicit misalignment angles range that could be treated herein is offered. Lyapunov-based stability analyses are employed to verify that the reaching phase of the sliding manifold is completed in finite time, and the attitude tracking errors are ensured to converge to a small region of the closest equilibrium point in fixed time once the sliding manifold enters the reaching phase. Finally, the beneficial features of the designed controller are manifested via detailed numerical simulation tests.