Comparative Study of Model-Free Predictive Control and Its Database Maintenance for Unstable Systems

Abstract

: This study provides a comparison of three methods, i.e., standard locally weighted averaging (LWA), leastnorm solutions, and 1 -minimization, for model-free predictive control based on Just-In-Time modeling and database maintenance for an unstable system. In contrast to conventional model predictive control, the model-free predictive control method does not use any mathematical model; rather, it uses the past input/output data stored in a database. Although conventional stabilizing feedback is used to obtain the input/output data of an unstable system, model-free predictive control is assumed to be used without it. Three methods based on standard LWA, least-norm solutions, and 1 -minimization are statistically compared using a simple model. The results show that the methods of least-norm solutions and 1 -minimization are superior to that of LWA. The method by 1 -minimization yields tracking errors smaller than that by least-norm solutions; however, the method by 1 -minimization requires a long computational time. In addition, the effectiveness of a method of database maintenance is illustrated by numerical simulations.

Model-Free Predictive Control Using Polynomial Regressors

“…This system was also used in [10] to compare the model-free predictive control methods. Clearly, when ε(k) ≡ 0, (33) has three fixed points (u, y) = (0, 0), (2 −1/3 , 1), and (−2 −1/3 , −1), and only the first is unstable.…”

“…Query vector b is updated according to the measured data, and vector w is determined in every sampling interval. In [10], a method to update A and C in real-time was proposed.…”

“…Model-free predictive control was proposed as a data-driven control method that does not explicitly require a mathematical model [1]- [10]. In contrast to the standard model predictive control, which uses mathematical modeling, the modelfree predictive control method uses the records of past input and output datasets and the current inputs and outputs to predict future inputs and outputs.…”

“…Recently, in [8] and [9], it has been suggested that the local linearly weighted average can be replaced by solving a linear algebraic equation using a least-norm and an 1 -norm approach, yielding a mathematically much simpler model-free predictive control algorithm. In [10], three methods for model-free predictive control were compared in terms of their control performance.…”

A model-free predictive control method based on polynomial regression

“…Model-free predictive control is data-driven control that does not explicitly require any mathematical model [1]- [10]. In contrast to standard model predictive control utilizing mathematical models, the model-free predictive control method uses past records of input and output datasets and the current input and output to predict future input and output.…”