Abstract
Real time system parameter estimation from the set of input-output data is usually solved by minimization of quadratic norm errors of system equations – known in the literature as least squares (LS) or its modification as total least squares (TLS) or mixed LS and TLS. It is known that the utilization of the p-norm (1?p
Highlights
The dynamic properties of a real plant are usually identified by making a model – choosing a model structure and estimating the unknown parameters of the model using data measured on the real plant [1]
The purpose of this paper is to show the influence of different p-norm selection on ARX model identification and control
When the measurements of the system output were damaged by outliers, it is shown that the Euclidean norm gives worse results than the p-norm for 1 < p < 2
Summary
The dynamic properties of a real plant are usually identified by making a model – choosing a model structure and estimating the unknown parameters of the model using data measured on the real plant [1]. The measurement of the system output is considered to be damaged by a number of outliers Another problem is optimal control of dynamic systems. Model predictive control (MPC) strategies are very popular [2, 4]. Optimal predictive control of an ARX or state space model is usually obtained by minimizing the quadratic criterion. Minimizing the l1 norm using linear programming in MPC control has been considered by many authors A connection between linear programming and optimal control is shown for example in [8, 9]. Optimal predictive control utilizing p-norm minimization of the criterion is shown, and the results are illustrated by simple examples.
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