Multiple extended state observers with second-level adaptation: a convex combination framework for low-peaking state estimation

This paper proposes a novel design framework for multiple extended state observers(MESOs) that utilizes second-level adaptation techniques to enhance the transient response and mitigate undesirable peaking phenomenon associated with extended state observers. The proposed method treats state estimation as a convex combination of the information obtained from multiple extended state observers. In this regard, it is demonstrated that certain constant parameters exist within this combination, leading to precise state estimation; then, these parameters are estimated using an adaptive algorithm. The convergence of state estimation to the state of the plant is proved. Moreover, compared to a single extended state observer, MESO is proved to provide state estimates with significantly smaller peaking. Simulation results demonstrate that MESO can provide accurate state estimates with arbitrary low peaking.