Adaptive parameter estimation with guaranteed prescribed performance

This paper presents a novel adaptive parameter estimation framework for linearly parameterized nonlinear systems, which can guarantee the prescribed error convergence performance (e.g. overshoot, convergence rate). By introducing appropriate filter operations, an explicit expression of parameter estimation error is obtained. Then a prescribed performance function (PPF) and the associate transform are proposed, such that parameter estimation can be reduced as a regulation problem of the transformed system by designing an adaptive law. To this end, a novel adaptive law based on the obtained parameter estimation error is developed, such that the error convergence can be guaranteed to be within the prescribed bound. The parameter estimation is obtained without using the measurement of the state derivatives and is independent of any observer/predictor design. Simulation results illustrate that the proposed methods can achieve faster transient and better steady-state performance than some available results.