Explicit self-tuning methods

A general scheme, which allows the analysis of self-tuning controllers of linear systems with constant but unkonwn parameters, is presented. The emphasis is on explicit self-tuning methods applied to a given class of single-input/single-output, discrete-time stochastic systems. These methods involve the combination of a system parameter identifier and a control law calculation algorithm. A specific (stochastic gradient type) identification algorithm is analysed in order to establish what kind of properties one can expect from the identifier part of such an adaptive control scheme. A general control law structure is then considered and it is shown that any identification algorithm satisfying the previously obtained properties, combined with any control law calculation algorithm fulfilling some quite weak conditions leaads to an overall adaptive system stable in some satisfactory stochastic sense, under an additional `stabilisability assumption¿¿ on the estimated model of the system. This is summarised in a theorem which, we believe, should lead to new interesting results especially for non-minimum-phase systems. Similar approaches have been previously proposed for deterministic systems.