Parameter and state identification in non-linearizable uncertain systems

Abstract

A dynamical process is modelled by a system of non-linearizable ordinary differential equations with uncertain but bounded state variables and variable parameters. When stochastic identification is not feasible (no assumptions upon random parameters, single run control, etc), the “worst case” design is required. To avoid this penalty, we propose to extend the Liapunov design technique of building adaptive (on-line) identifiers, so far developed for linear systems with constant parameters. The standard study of stability of an error-equation is replaced by investigating convergence to diagonal set in the Cartesian product of state-parameter spaces of the model and the identifier. We also attempt to stabilize the model. Conditions for the above are introduced together with proposing suitable Liapunov functions. The method is illustrated on two examples with wide applicability: a damped Hamiltonian system and the non-linear oscillator.