Harmonic-Copuled Riccati Equations and its Applications in Distributed Filtering

The coupled Riccati equations are cosisted of multiple Riccati-like equations with solutions coupled with each other, which can be applied to depict the properties of more complex systems such as markovian systems or multi-agent systems. This paper manages to formulate and investigate a new kind of coupled Riccati equations, called harmonic-coupled Riccati equations (HCRE), from the matrix iterative law of the consensus on information-based distributed filtering (CIDF) algortihm proposed in [1], where the solutions of the equations are coupled with harmonic means. Firstly, mild conditions of the existence and uniqueness of the solution to HCRE are induced with collective observability and primitiviness of weighting matrix. Then, it is proved that the matrix iterative law of CIDF will converge to the unique solution of the corresponding HCRE, hence can be used to obtain the solution to HCRE. Moreover, through applying the novel theory of HCRE, it is pointed out that the real estimation error covariance of CIDF will also become steady-state and the convergent value is simplified as the solution to a discrete time Lyapunov equation (DLE). Altogether, these new results develop the theory of the coupled Riccati equations, and provide a novel perspective on the performance analysis of CIDF algorithm, which sufficiently reduces the conservativeness of the evaluation techniques in the literature. Finally, the theoretical results are verified with numerical experiments.Comment: 14 pages, 4 figure

Consensus-Based Distributed Filtering with Fusion Step Analysis

For consensus on measurement-based distributed filtering (CMDF), through infinite consensus fusion operations during each sampling interval, each node in the sensor network can achieve optimal filtering performance with centralized filtering. However, due to the limited communication resources in physical systems, the number of fusion steps cannot be infinite. To deal with this issue, the present paper analyzes the performance of CMDF with finite consensus fusion operations. First, by introducing a modified discrete-time algebraic Riccati equation and several novel techniques, the convergence of the estimation error covariance matrix of each sensor is guaranteed under a collective observability condition. In particular, the steady-state covariance matrix can be simplified as the solution to a discrete-time Lyapunov equation. Moreover, the performance degradation induced by reduced fusion frequency is obtained in closed form, which establishes an analytical relation between the performance of the CMDF with finite fusion steps and that of centralized filtering. Meanwhile, it provides a trade-off between the filtering performance and the communication cost. Furthermore, it is shown that the steady-state estimation error covariance matrix exponentially converges to the centralized optimal steady-state matrix with fusion operations tending to infinity during each sampling interval. Finally, the theoretical results are verified with illustrative numerical experiments

Cooperative Control of Multi-Channel Linear Systems with Self-Organizing Private Agents

Cooperative behavior design for multi-agent systems with collective tasks is a critical issue to promote swarm intelligence. This paper investigates cooperative control for a multi-channel system, where each channel is managed by an agent that can communicate with neighbors in a network. Each agent is expected to self-organize a controller based only on local information and local interaction to stabilize the multi-channel system collaboratively. A novel cooperative control strategy is designed for each agent by leveraging a decomposing technique and a fusion approach. Then, a privacy-preserving mechanism is incorporated into this strategy to shield all private information from eavesdropping. Moreover, a fully distributed designing method for the strategy parameters is developed. As a result, agents can self-design and self-perform their controllers with private information preserved. It is proved that the multi-channel system stability can be ensured by the proposed strategy with finite fusion steps during each control interval. In addition, the cost of introducing the privacy-preserving mechanism and the effect of adding more channels on the system performance are quantitatively analyzed, which benefits mechanism design and channel placement. Finally, several comparative simulation examples are provided to demonstrate the effectiveness of the theoretical results

Data-Driven Kalman Filter using Maximum Likelihood Optimization

This paper investigates the state estimation problem for unknown linear systems with process and measurement noise. A novel data-driven Kalman filter (DDKF) that combines model identification with state estimation is developed using pre-collected input-output data and uncertain initial state information of the unknown system. Specifically, the state estimation problem is first formulated as a non-convex maximum likelihood (ML) optimization problem. Then, to reduce the computational complexity, the optimization problem is broken down into a series of sub-problems in a recursive manner. Based on the optimal solutions to the sub-problems, a closed-form DDKF is designed for the unknown system, which can estimate the state of a physically meaningful state-space realization, rather than these up to an unknown similarity transformation. The performance gap between the DDKF and the traditional Kalman filter with accurate system matrices is quantified through a sample complexity bound. In particular, when the number of the pre-collected trajectories tends to infinity, this gap converges to zero. Moreover, the DDKF is used to facilitate data-driven control design. A data-driven linear quadratic Gaussian controller is defined and its closed-loop performance is characterized. Finally, the effectiveness of the theoretical results is illustrated by numerical simulations

Stochastic Event-triggered Variational Bayesian Filtering

This paper proposes an event-triggered variational Bayesian filter for remote state estimation with unknown and time-varying noise covariances. After presetting multiple nominal process noise covariances and an initial measurement noise covariance, a variational Bayesian method and a fixed-point iteration method are utilized to jointly estimate the posterior state vector and the unknown noise covariances under a stochastic event-triggered mechanism. The proposed algorithm ensures low communication loads and excellent estimation performances for a wide range of unknown noise covariances. Finally, the performance of the proposed algorithm is demonstrated by tracking simulations of a vehicle