This paper concerns distributed state estimation for linear systems over a sensor network. Two novel algorithms utilizing the framework of moving horizon estimation (MHE) are proposed, which are fully distributed, scalable and allow for taking into account constraints on the noises and the system states. The proposed methods estimate the state by minimizing a local quadratic objective function, which can be efficiently solved by quadratic programming (QP). Consensus technique is employed to fuse information to construct the local quadratic objective function for each node. The first algorithm, which minimizes a quadratic function involving consensus on measurement costs (CM), approaches the centralized MHE with a sufficiently large number of consensus steps. The second one involving consensus both on arrival costs (CA) and measurement costs , enjoys the benefits of both the CA and CM. To avoid directly running consensus on some functions, a novel consensus strategy for the CM is developed. The estimation errors of the proposed methods are proven to be stochastically ultimately bounded under certain conditions. Finally, numerical results are presented to verify the effectiveness of the developed algorithms.

This paper develops model-free optimal tracking policies for Markov jump systems by solving non-zero-sum games (NZSGs). First, coupled action and mode-dependent value functions (CAMDVFs) are built for solving a two-player NZSG and getting Nash equilibrium solutions. Second, we propose a value iteration (VI) algorithm to parallelly update policies under each mode by collecting data on different operation modes within each iterative window. Moreover, the iterative increasing convergence of the CAMDVFs is proved by introducing auxiliary functions between two adjacent iterations. It is worth pointing out that an influence function is introduced to remove abnormal data to improve the learning capability of the VI algorithm effectively. Finally, the tracking policies' validity, self-adaptability and application potential are verified by a numerical example and a generalized economic model.