Discrete time immersion and invariance adaptive control for systems in strict feedback form

Immersion and invariance adaptive control for discrete‐time systems in strict‐feedback form with input delay and disturbances

“…In this section the control design is outlined for system (2) initially considering the case = 1 and then extending the result to the general case > 1. The parameter is estimated adaptively using the I&I method in its discrete-time form [17]. In case = 1 the stabilising control law for the un-delayed system with known parameter * (ref.…”

“…Proof: Exploiting the similarity to Proposition 1 in [17], the following Lyapunov function candidate is chosen, where the dependency of 1 , , 1 on the state is omitted for brevity (i.e. 1 stands for 1 ( ), while 1 − stands for 1 ( − )):…”

“…The main contribution of this work is a new adaptive control algorithm for nonlinear discretetime systems in strict feedback form with input delay and disturbances. In particular, the algorithm consists of a recursive control law that includes the adaptive compensation of the disturbances based on the I&I formulation [17], hence extending the scope of [15]. Differently from [2], the algorithm is applicable to multiple disturbances without assumptions on their bounds.…”

Stabilization of feedforward discrete-time dynamics through immersion and invariance

“…Here, the general non linear x 1 -dynamics is known to be stabilizable under a suitable state feedback but the knowledge of a control Lyapunov Function is not assumed. The problem is presently set in the context of Immersion and Invariance -I&I. I&I was proposed in [6]- [7] for stabilizing continuous-time systems and reformulated in [8]- [9] in discrete-time; the overall design results to be less demanding in such a context.…”

Nonlinear Sampled-Data Stabilization with Delays

“…Immersion and Invariance was firstly introduced in continuous time in [29] and then proposed for discrete-time adaptive control in [31]. It is reformulated below in the discrete-time and sampled contexts for completeness (see also [30,32,33]).…”