This paper addresses the state estimation problem for a class of uncertain systems with unknown nonlinear and time-varying dynamics as well as large disturbances. Actually, without exact model information about dynamics or disturbances, the Kalman filter (KF) or extended Kalman filter (EKF) struggles to obtain the covariance matrix (CM) of the state estimation error, which is quite important to ensure stability and evaluate estimation precision. To this end, this paper proposes a framework of robust consistent Kalman filter (RCKF) with provable boundedness of the CM of the state estimation error. Moreover, it is shown that the proposed method can ensure consistency, i.e., the upper bound of the CM of the state estimation error can be provided online. In particular, compared to the traditional consistent Kalman filter (CKF), the RCKF features a more robust design method, despite the large uncertainties exceeding the nominal upper bound. Finally, the proposed algorithm is applied to the state estimation problem of a permanent magnet synchronous motor (PMSM). The experimental results show a significant improvement in accuracy compared to the traditional CKF and other typical parameter estimation algorithms.
This paper proposes a novel direct data-driven control algorithm for probability density function (PDF) shape control in general non-Gaussian nonlinear stochastic systems, based on the cumulant-generating function (CGF). Previous studies have shown that the performance of traditional PDF shape control algorithms is significantly affected by the accuracy of the PDF model, which is commonly approximated using neural networks (NN) and system identification approaches. Consequently, the acquisition of some offline data and the pre-training of the NN basis function parameters are essential. To avoid this issue, a CGF-based linear data model (CGF-LDM) is established with the aid of dynamic linearization technology, transforming the PDF shape control problem into an output tracking problem. The unknown pseudo partitioned Jacobian matrix (PPJM) in CGF-LDM is estimated using the variable-rate forgetting recursive least squares, which is insensitive to initial PPJM parameters. A model-free control scheme is then developed by integrating a radial basis function neural network, where the weights are updated using the gradient descent-Barzilai–Borwein algorithm, while the centers and widths are recursively updated online based on the mean recursion strategy. The boundedness analysis of parameter estimation and tracking errors is provided, and the effectiveness of the proposed algorithm is verified through two simulations.
In the analysis and design of large network systems, we often face the problem that the dynamics of each node is not fully known. In such a case, a structural approach can be taken to solve a given problem. The “structural approach” refers to solving a problem without using the exact model of each node, i.e., using only the information about the network structure and limited information about the nodes. This paper addresses the problem of finding informative nodes whose convergence to zero guarantees the convergence of pre-specified target nodes. The key to solving the problem is to characterize the nodes whose convergence results from the convergence of a candidate informative node. To do this, we classify the nodes into four categories in terms of the induced subgraph of the original network structure on the target nodes. Based on this, we present all the solutions parameterized by the target nodes and free parameters.
This paper considers the distributed Nash equilibrium (NE) seeking problem in a multi-robot system whose dynamics are subject to unknown disturbances and are interconnected via switching communication networks with time-varying delays. In many practical robotic applications, such as formation control, resource allocation, and task planning, robots must optimize their individual cost functions while satisfying operational constraints. In contrast to previous works that typically assume static or delay-free networks, our approach explicitly accommodates communication delays in switching networks. In addition, each robot’s strategy is confined to a compact and convex set, which naturally models physical or task-related limitations. To guarantee convergence to the Nash equilibrium, we design projection-based pseudo-gradient update laws augmented with Gaussian radial basis function neural networks. These neural networks are employed to approximate and counteract the impact of the unknown bounded disturbances in each robot’s dynamics. Analytical results of semi-global nature are established using Lyapunov analysis, with convergence conditions that relate to strong monotonicity and Lipschitz continuity properties of the cost functions. A numerical example in the context of noncooperative robotic positioning is provided to illustrate the effectiveness of the proposed control scheme.
In this article, we offer a constructive network-based extremum seeking (ES) control framework in the presence of periodic sampling and uncertain time-varying communication delays. Combining ES with networked control systems (NCSs), we consider two communication networks: from sensor to controller and from controller to actuator. The sampling and time-varying delays in network, when disregarded, may break the property of zero-mean averaging and render ES controlled systems unstable. In order to overcome this difficulty, square-wave-based modulation and demodulation excitation signals are carefully designed to estimate the dominant gradient for stabilization and keep the trivial perturbations to be small.
