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A supervisory observer is a multiple-model architecture, which estimates theparameters and the states of nonlinear systems. It consists of a bank of stateobservers, where each observer is designed for some nominal parameter valuessampled in a known parameter set. A selection criterion is used to select asingle observer at each time instant, which provides its state estimate andparameter value. The sampling of the parameter set plays a crucial role in thisapproach. Existing works require a sufficiently large number of parametersamples, but no explicit lower bound on this number is provided. The aim ofthis work is to overcome this limitation by sampling the parameter setautomatically using an iterative global optimisation method, called DIvidingRECTangles (DIRECT). Using this sampling policy, we start with 1 + 2npparameter samples where np is the dimension of the parameter set. Then, thealgorithm iteratively adds samples to improve its estimation accuracy.Convergence guarantees are provided under the same assumptions as in previousworks, which include a persistency of excitation condition. The efficacy of thesupervisory observer with the DIRECT sampling policy is illustrated on a modelof neural populations.

Supervisory observer for parameter and state estimation of nonlinear systems using the DIRECT algorithm