Reset observers alleviating the peaking and the robustness tradeoffs: A case study on force estimation in teleoperation.

The peaking phenomenon is an undesirable effect appearing in observers and destroying controller performance. Several solutions have been proposed to mitigate peaking in state estimation. The literature shows that reset or impulsive observers are superior to linear (Luenberger) observers. However, the comparisons are based on particular choices of linear observers. This paper investigates this issue. First, comparative frameworks are proposed based on two traded-off performance indices: ensemble maximum-peak versus ensemble settling time for nominal conditions, and ensemble settling time versus size of the error asymptotic invariant set for quadratically bounded uncertain plants. Next, performance limitations of linear observers are represented by Pareto-optimal boundaries. In this way, not previously considered in the literature as far as known, the superiority of the chosen reset observer is more rigorously assessed. The framework is finally applied to force estimation in haptic teleoperation.