Distributed Least Squares Algorithms for Achieving Linear and Nonlinear Conservation Constraints

This paper proposes distributed least squares (LS) algorithms to achieve the conservation constraint via multi-agent network. In particular, the conservation constraint is that the sum of all the local functions equals to a constant. We first consider the linear conservation constraint, where each local function is linear. Then, a distributed LS algorithm is developed, which guarantees that all the agents’ states converge exponentially to a LS solution of the conservation constraint. Secondly, we further consider the nonlinear conservation constraint that is summed of multiple local nonlinear functions. By using the dynamic average tracking method, we develop an alternative distributed algorithm such that a LS solution of the nonlinear conservation constraint can be obtained. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed algorithms.