Current optical flow methods exploit the stable appearance of frame (or RGB) data to establish robust correspondences across time. Event cameras, on the other hand, provide high-temporal-resolution motion cues and excel in challenging scenarios. These complementary characteristics underscore the potential of integrating frame and event data for optical flow estimation. However, most cross-modal approaches fail to fully utilize the complementary advantages, relying instead on simply stacking information. This study introduces a novel approach that uses a spatially dense modality to guide the aggregation of the temporally dense event modality, achieving effective cross-modal fusion. Specifically, we propose an event-enhanced frame representation that preserves the rich texture of frames and the basic structure of events. We use the enhanced representation as the guiding modality and employ events to capture temporally dense motion information. The robust motion features derived from the guiding modality direct the aggregation of motion information from events. To further enhance fusion, we propose a transformer-based module that complements sparse event motion features with spatially rich frame information and enhances global information propagation. Additionally, a mix-fusion encoder is designed to extract comprehensive spatiotemporal contextual features from both modalities. Extensive experiments on the MVSEC and DSEC-Flow datasets demonstrate the effectiveness of our framework. Leveraging the complementary strengths of frames and events, our method achieves leading performance on the DSEC-Flow dataset. Compared to the event-only model, frame guidance improves accuracy by 10%. Furthermore, it outperforms the state-of-the-art fusion-based method with a 4% accuracy gain and a 45% reduction in inference time. The code is publicly available athttps://github.com/ZhouQianang/STFlow.

This paper focuses on solving the linear quadratic regulator problem for discrete-time linear systems without knowing system matrices. The classical Q-learning methods for linear systems can be divided into Q-learning value iteration and Q-learning policy iteration. Q-learning value iteration converges at a linear convergence rate. Q-learning policy iteration has a second-order convergence rate but requires an initial stabilizing control policy. This paper aims to propose efficient model-free algorithms for solving the optimal control problem without requiring an initial stabilizing control policy. In this paper, we first present an equivalent problem for an auxiliary system with the same optimal control policy as the LQR problem. A Q-learning algorithm is proposed to solve the equivalent problem, which is proven to converge monotonically to the optimal solution. The convergence rate of the Q-learning algorithm is heavily dependent on the auxiliary system, so we introduce a model-free homotopy method based on Q-learning to solve the LQR problem. This homotopy method can achieve the optimal solution in a finite number of iterations by solving an LQR problem in each iteration. Additionally, we propose a Q-learning Lyapunov iteration algorithm to solve the equivalent problem for an auxiliary system and analyze its properties. Finally, two examples are provided to demonstrate our results. Note to Practitioners—This paper proposes several Q-learning methods to solve the linear quadratic regulator problem for discrete-time linear systems. On the one hand, it is difficult to know the exact system dynamics knowledge in actual engineering, so this paper is devoted to developing model-free algorithms. On the other hand, this paper focuses on the LQR problem because it is widely spread in practical applications. We propose several model-free algorithms to solve the LQR problem, which provides the basis for optimal control of actual applications. Similar to policy iteration, our algorithms need to solve the Lyapunov equation. The advantage of our methods is that all of our algorithms do not have strict constraints on initial conditions compared with policy iteration. The properties of every algorithm proposed in this paper are provided. In addition, we focus on the efficiency of algorithms to obtain the optimal control policy faster. Two practical examples are used to verify the effectiveness of our methods. Finally, the applicable situations of each algorithm are summarized in the conclusion.

This brief studies the discounted stochastic linear quadratic regulator (LQR) problem for systems suffering from additive noise of unknown mean. A completely model-free (MF) value iteration (VI) algorithm is developed to learn the optimal control policy using off-line system trajectories. The generated control policies are proven to converge to a small neighborhood of the optimal ones with high probability. In addition, an MF algorithm is proposed to learn a feasible discount factor. The proposed MF algorithms are illustrated through several examples.

This article studies the optimal state estimation problem for interconnected systems. Each subsystem can obtain its own measurement in real time, while, the measurements transmitted between the subsystems suffer from random delay. The optimal estimator is analytically designed for minimizing the conditional error covariance. The boundedness of the expected error covariance (EEC) is analyzed. In particular, a new condition that is easy to verify is established for the boundedness of EEC. Further, the properties of EEC with respect to the delay probability are studied. We found that there exists a critical probability such that the EEC is bounded if the delay probability is below the critical probability. Also, a lower and upper bound of the critical probability is derived. Finally, the proposed results are applied to a power system, and the effectiveness of the designed methods is illustrated by simulations.

This article studies the distributed linear minimum mean square error (LMMSE) estimation problem for large-scale systems with local information (LSLI). Large-scale systems are composed of numerous subsystems. Each subsystem only transmits information to its neighbors. Thus, only the local information is available to each subsystem. This implies that the information available to different subsystems is different. Using local information to design an LMMSE estimator, the gains of the estimator must satisfy the sparse structure constraint, which makes the estimator design challenging and complicates the boundedness analysis of the estimation error covariance (EEC). In this article, a framework of the distributed LMMSE estimation for LSLI is established. The gains of the LMMSE estimator are effectively constructed by solving linear matrix equations. A gradient descent algorithm is exploited to design the gains of the LMMSE estimator numerically. Sufficient conditions are derived to ensure the boundedness of the EEC. Also, a gradient-based search algorithm is developed to verify whether the sufficient conditions hold or not. Finally, an example is used to illustrate the effectiveness of the proposed results.

This article studies the$\mathcal {H}_{\infty }$control problem for linear networked and quantized control systems (NQCSs) with both communication delays and random packet losses. To deal with network-induced constraints and random packet dropouts, a novel discrete-time stochastic system model is developed for continuous-time networked control systems, and further overapproximated to a polytopic system with norm-bounded uncertainty. Based on the overapproximated system model, sufficient conditions are established for linear NQCSs in different cases to guarantee both input-to-state stability and$\mathcal {H}_{\infty }$performance with respect to the network-induced errors. Furthermore, we propose an algorithm to minimize the stability gain and the$\mathcal {H}_{\infty }$attenuation level simultaneously. Finally, a numerical example is given to illustrate the developed results.

This article investigates the decentralized optimal linear quadratic regulation (LQR) control for large-scale systems. The large-scale system is defined over a weakly connected graph. Assume that the information is transmitted along the edges in the graph, and one sampling period is required for the information to travel across an edge. Under the above setup, the LQR control problem for the strongly connected graph case has been fully solved. However, for the weakly connected graph case, the existing results fail. In this article, a new decomposition approach for noise history is proposed. Then, the LQR control problem of large-scale systems defined over a weakly connected graph can be well solved. In addition, the decentralized realization of the control input is derived based on the decentralized information hierarchy graph (DIHG). The DIHG construction algorithm is also provided. Finally, the effectiveness of the developed design scheme is illustrated by a numerical example.

This article investigates the event-triggered output feedback control problem for unmanned aerial vehicle (UAV) systems over cognitive radio (CR) networks. A periodic event-triggered scheme is proposed in the presence of CR networks. By modeling the CR network as anon–offswitch, a new switched time-delay system model is developed for the event-triggered UAV. Based on the new model, the exponential stability and$H_{\infty }$performance criteria are derived by using the constructed Lyapunov function. Then, a co-design method is proposed to obtain mode-dependent controller gains and trigger parameters simultaneously. Finally, the proposed scheme is verified by a UAV system.

In this paper, we propose an efficient method to produce content-sensitive superpixels. Our method produces regular superpixels in relatively homogeneous regions and captures object boundaries in content-dense regions. Compared with the existing content-sensitive superpixel methods, a new adaptive regrowth strategy with an explicit boundary constraint is proposed. The boundary constraint limits the shapes and the sizes of superpixels to ensure semantic consistency. The adaptive regrowth strategy generates more superpixels to capture small objects in content-dense regions. Experiments on the BSDS500 benchmark show that our method outperforms the state-of-the-art superpixel methods in terms of content sensitivity and several standard evaluation metrics.

This paper concentrates on the linear least mean square (LLMS) filtered and smoothed estimators for networked linear stochastic systems. Multiple packet losses, Markovian communication constraints, and superposed process noise are considered simultaneously. In order to reduce the channel load during communication, at every step, just one transmission node is permitted to send data packets. Hence, a Markovian communication protocol is utilized to arrange the packets of these transmission nodes. Moreover, multiple data packet dropouts occur during transmission due to an imperfect communication channel. Therefore, the global observation information cannot be obtained by the state estimator. The real state of Markov chain is assumed to be unknown to the estimator except the transition probability matrix. By means of the innovation analysis approach and orthogonal projection principle, we design Kalman-like estimators in a recursive form. Finally, through simulation experiments, we verify the effectiveness and superiority of the designed algorithm.

This paper is concerned with the optimal decentralized output-feedback control of the large-scale systems. A random information pattern is considered, where the information is transmitted among the subsystems with random communication delays. For the random information pattern, the optimal LQG problems for both global estimation case and local estimation case are studied. It is difficult to derive the optimal controller under random framework, because the gains of the controller must be designed to satisfy the random sparse structure constraints. In this paper, we design the optimal controller by Hadamard product method. For global estimation case, the gains of the controller are obtained by solving linear matrix equation. For local estimation case, an iterative algorithm is exploited to compute the gains. In addition, the value of the cost function achieved by the designed controller is found and shown to monotonically increase with the increase of the delay probability for both global and local estimation cases. Finally, the theoretical results are illustrated by two numerical examples.

This article investigates the event-triggered observer-based output feedback load frequency control (LFC) problem for power systems. To reduce the amount of the transmitted signals, a dynamic event-triggered scheme is proposed by adding an exponential term. Moreover, an adaptive event-triggered scheme is proposed to provide a balance between the control performance and the number of the transmitted signals. Under the proposed schemes, a new model is formulated for the observer-based output feedback LFC system via a time-delay system method. By employing the Lyapunov functional method, sufficient conditions are derived for global asymptotical stability and$\mathcal L_{\infty }$performance. Then, a controller design method is developed. Finally, two examples are given to illustrate the effectiveness of the proposed schemes.

This paper focuses on the linear minimum mean square estimator for a networked discrete time-varying linear system subject to data quantification and communication constraints. The communication limitation is that only one transmission node can get access to the shared communication channel at each time step, and that different transmission nodes in the networked systems are scheduled to transmit information according to a Markov protocol. Then the remote estimator completes the estimation with only partially available observations, which are quantified. Suppose that the Markov chain is unknown to the remote estimator. By using orthogonal projection principle and innovation analysis method, a Kalman type filter is designed in a recurrence form. It is shown that estimation performance depends on the transition probability matrix of the Markov chain, quantization error, and the shared channel weighting parameter. Finally, an illustrative example is given to show the effectiveness of the proposed method.

This paper studies the discrete-time lossless positive real properties of transfer functions with minimal state-space realizations. Firstly, necessary and sufficiency conditions are established to characterize the discrete-time lossless positive real properties of a transfer function in terms of its behavior on the unit circle. Secondly, a DT-LPR lemma is given based on the QR decomposition and the Kalman reachability decomposition. This lemma provides necessary and sufficiency conditions for state-space systems to be DT-LPR. Finally, a numerical example is given to illustrate the developed theory.

In this paper, the moment matching model reduction problem for negative imaginary systems is considered in the time-domain framework. For a given high order negative imaginary system with poles at the origin, our goal is to find a reduced-order negative imaginary system such that a prescribed number of the moments and the poles at the origin are preserved. The reduced-order negative imaginary systems was constructed by the parameterized reduced-order systems that match the moments. It shows that a desired reduced-order system can be obtained by using the unique solution of a Sylvester equation. Finally, the proposed model reduction method is illustrated by an RLC network and a train system.

Digital networked control systems are of growing importance in safety-critical systems and perform indispensable function in most complex systems today. Networked degradations such as transmission delay and packet dropout cause such systems to fail to satisfy performance requirements, and eventually affect the overall reliability. It is necessary to get a model to verify and evaluate the system reliability in early design phase, prior to its implementation. However, existing probabilistic models only provide partial descriptions of such coupled networks and control system. In this paper, a new stochastic model represented by linear discrete-time approach is proposed, considering data packet transmissions in both channels: controller-to-actuator and sensor-to-controller. Different from pervious works, the historical behaviors of networked degradations are modeled by multistate Markov chains with uncertainties, releasing the assumption that faults of all periods are independent of each other. The concept of domain requirements for such systems is considered here, contributing to the integration of control and reliability engineering. Methodologies for quantitatively assessing the reliability of the single- and sequential-control goal are derived from the Monte Carlo method. An example of an industrial heat exchanger digital networked control system is provided to illustrate the effectiveness of the model and method.

This paper dears with the decentralized stabilization problem for a class of uncertain Markovian jump large-scale systems. The local controllers use local subsystem outputs and neighboring mode information to produce local control inputs. A sufficient condition is given in terms of rank constrained linear matrix inequalities (rank constrained LMIs) for the design of such controllers.