Distributed Zonotopic Set-Membership State Estimation based on Optimization Methods with Partial Projection

Abstract

A distributed set-membership approach is proposed for the state estimation of large-scale systems. The uncertain system states are bounded in a sequence of the distributed set-membership estimators considering unknown-but-bounded system disturbances and measurement noise. In the framework of the set-membership approach, the measurement consistency test is implemented by finding parameterized intersection zonotopes. The size of the intersection zonotope is minimized by solving an optimization problem including a sequence of linear/bilinear matrix inequalities based on the weighted 2-norm criterion of the generator matrix. Meanwhile, for the distributed set-membership estimators, the partial projection method is considered to correct the estimation of the neighbor state. On the other hand, an on-line method is also provided. Finally, the proposed distributed set-membership approach is verified in a case study based on a urban drainage network.