Adaptive control of feedback linearizable systems: a modelling error compensation approach

Biological pest control using a model‐based robust feedback

“…The control approach is based on MEC ideas that lead to controllers with a simple linear structure, good closed‐loop performance and robustness properties [34, 35].…”

“…The tuning of both parameters follows the simple rule [34, 35]: τ p > 0.5 τ c > 0.5 τ e , where τ p is a characteristic time constant of the controlled systems. τ c can be seen as a closed‐loop time constant and, determines the desired closed‐loop convergence, and τ e determines the smoothness of the modelling error estimation.…”

“…The stability analysis of closed‐loop systems is based on singular perturbation arguments. For the sake of completeness in presentation, a sketch of main ideas of the stability results for the MEC approach is provided as follows [34].…”

Robust sliding mode‐based extremum‐seeking controller for reaction systems via uncertainty estimation approach

“…Assumption The function η ≡ Θ( z , ς , u ) is locally smooth bounded, and its time derivative denoted by Ξ( z , η , ς , u ) is also bounded. Then once the uncertain function η is defined, it is possible to rewrite the system in the following extended state‐space representation: where η is interpreted as an augmented state whose dynamics can be reconstructed from measurements of the input and the output signals . (a) It can be proved that the solution of system is a projection of the solution of system ; (b) A feature of system is that the uncertainties have been lumped into an uncertain function Θ( z , ς , u ) that can be estimated by an unmeasurable but observable state η .…”

“…By following this idea, because represents the observable states , the problem of estimating z can be addressed by using a high‐gain observer. Thus, the dynamics of the states ( z , η ) can be reconstructed from the measurements of the output signal y = h ( x ) = z 1 in the following way where ( , ) denotes the estimate for z and the lumped uncertainty state η , respectively. The observer parameters κ i ′ s are chosen such that the polynomial κ r + 1 p r + κ r − 2 p r − 1 + … + κ 1 = 0 is Hurwitz, and Γ > 0 is a positive parameter (high‐gain observer).…”