Control of Uncertain Sampled-Data Systems: An Adaptive Posicast Control Approach

Abstract

This technical note proposes a discrete-time adaptive controller for the control of sampled-data systems. The design is inspired from the Adaptive Posicast Controller (APC) which was designed for time-delay systems in continuous time. Due to the performance degradation caused by digital approximation of continuous laws, together with the problem of assuming time-delays as integer multiples of sampling intervals, the benefits of APC could not be fully realized. In this technical note, these approximations/assumptions are eliminated. In addition, a disturbance observer is incorporated into the controller design which minimizes the effect of disturbances on the system. Extension to the case of uncertain input time-delay is also presented. The proposed approach is verified in simulation studies.

Discrete-time Adaptive Regulation of Systems with Uncertain Upper-bounded Input Delay: A State Substitution Approach

“…From Lemma 1 and using the results in (Abidi et al, 2017), lim k→∞β −1 0,k−iφ k−i (β i,k −β i,k−1 ) = 0 and that implies that the augmented system (40) is stable and a bound onη k exists such that…”

“…and using the fact that P −1 (Abidi et al, 2017), it is obtained that (28) is simplified to the form…”

“…Discretisation of continuous-time control laws, especially those for time-delay compensation, is fraught with numerical pitfalls (Mirkin, 2004) (Zhong, 2004). It may be more straightforward to design controllers in discrete-time, for example the discrete-time APC (Abidi et al, 2017) (Abidi and Xu, 2015). This is a model-reference adaptive controller that achieves reference trajectory tracking on a plant with an unknown, constant, upper-bounded time delay.…”

Model‐based vs data‐driven adaptive control: An overview

“…To conclude this section about fully model‐based adaptation, we can cite other recent works, ie, post the latest general survey paper, which can be classified under the model‐based paradigm: for nonlinear models,) for models with time delay,) with parameter‐independent realization controllers, with input/output quantization,) under state constraints,) under inputs and actuator‐bandwidth constraints,) for Markovian jump systems,) for switched systems,) for partial differential equation (PDE)–based models,) for nonminimum/minimum‐phase systems,) to achieve adaptive regulation and disturbance rejection,) multiple‐model and switching adaptive control,) linear quadratic regulator (LQR)–based adaptive control, model predictive control–based adaptive control,) applications of model‐based adaptive control,) for sensor/actuator fault mitigation,) for rapidly time‐varying uncertainties, nonquadratic Lyapunov function–based MRAC, for stochastic systems,) retrospective cost adaptive control, persistent excitation–free/data accumulation–based control or concurrent adaptive control, sliding mode–based adaptive control,) set‐theoretic–based adaptive controller with performance guarantees, sampled data systems, and robust adaptive control …”

Discrete-Time Adaptive Control for Systems With Input Time-Delay and Non-Sector Bounded Nonlinear Functions

“…The approach is further extended to multivariable input delay systems. For the scalar case, the approach is based on the prediction of future signals through successive substitution of the system model as is shown in [27]. Following the approach in [1], a coefficient is introduced into the adaptive law that guarantees asymptotic convergence in the presence of non sector bounded nonlinearities.…”