Lazy learning for local modelling and control design

Abstract. This paper presents local methods for modeling and control of discrete-time unknown nonlinear dynamical systems, when only a limited amount of input-output data is available. We propose the adoption of lazy learning, a memory-based technique for local modeling. The modeling procedure uses a query-based approach to select the best model con guration by assessing and comparing dierent alternatives. A new recursive technique for local model identication and validation is presented, together with an enhanced statistical method for model selection. Also, three methods to design controllers based on the local linearization provided by the lazy learning algorithm are described. In the rst method the lazy technique returns the forward and inverse models of the system which are used to compute the control action to take. The second is an indirect method inspired to self-tuning regulators where recursive least squares estimation is replaced by a local approximator. The third method combines the linearization provided by the local learning techniques with optimal linear control theory, to control nonlinear systems about regimes which are far from the equilibrium points. Simulation examples of identication and control of nonlinear systems starting from observed data are given.