A robust least squares based approach to min‐max model predictive control

Abstract

SummaryThis article deals with the model predictive control (MPC) of linear, time‐invariant discrete‐time polytopic (LTIDP) systems. The 2‐fold aim is to simplify the treatment of complex issues like stability and feasibility analysis of MPC in the presence of parametric uncertainty as well as to reduce the complexity of the relative optimization procedure. The new approach is based on a two degrees of freedom (2DOF) control scheme, where the output r(k) of the feedforward input estimator (IE) is used as input forcing the closed‐loop system ∑f. ∑f is the feedback connection of an LTIDP plant ∑p with an LTI feedback controller ∑g. Both cases of plants with measurable and unmeasurable state are considered. The task of ∑g is to guarantee the quadratic stability of ∑f, as well as the fulfillment of hard constraints on some physical variables for any input r(k) satisfying an “a priori” determined admissibility condition. The input r(k) is computed by the feedforward IE through the on‐line minimization of a worst‐case finite‐horizon quadratic cost functional and is applied to ∑f according to the usual receding horizon strategy. The on‐line constrained optimization problem is here simplified, reducing the number of the involved constraints and decision variables. This is obtained modeling r(k) as a B‐spline function, which is known to admit a parsimonious parametric representation. This allows us to reformulate the minimization of the worst‐case cost functional as a box‐constrained robust least squares estimation problem, which can be efficiently solved using second‐order cone programming.

Decomposition‐based over‐parameterization forgetting factor stochastic gradient algorithm for Hammerstein‐Wiener nonlinear systems with non‐uniform sampling

“…[19][20][21] For example, Xia et al proposed a maximum likelihood-based multi-innovation stochastic gradient method for multivariable systems with colored noises. 22 Differently from the recursive least squares methods, 23 this article studies the gradient-based recursive identification methods for the Hammerstein-Wiener nonlinear system by using the decomposition technique. The main idea is to decompose the considered system into two subsystems and to identify the parameter vector of each subsystem, separately.…”