  Various methods are nowadays available to design observers for broad classes
of systems. Nevertheless, the question of the tuning of the observer to achieve
satisfactory estimation performance remains largely open. This paper presents a
general supervisory design framework for online tuning of the observer gains
with the aim of achieving various trade-offs between robustness and speed of
convergence. We assume that a robust nominal observer has been designed for a
general nonlinear system and the goal is to improve its performance. We present
for this purpose a novel hybrid multi-observer, which consists of the nominal
one and a bank of additional observer-like systems, that are collectively
referred to as modes and that differ from the nominal observer only in their
output injection gains. We then evaluate on-line the estimation cost of each
mode of the multi-observer and, based on these costs, we select one of them at
each time instant. Two different strategies are proposed. In the first one,
initial conditions of the modes are reset each time the algorithm switches
between different modes. In the second one, the initial conditions are not
reset. We prove a convergence property for the hybrid estimation scheme and we
illustrate the efficiency of the approach in improving the performance of a
given nominal high-gain observer on a numerical example.
