Move blocking strategies in receding horizon control

Abstract

Abstract-In order to deal with the computational burden of optimal control, it is common practice to reduce the degrees of freedom by fixing the input or its derivatives to be constant over several time-steps. This policy is referred to as "move blocking". This paper will address two issues. First, a survey of various move blocking strategies is presented and the shortcomings of these blocking policies, such as the lack of stability and constraint satisfaction guarantees, will be illustrated. Second, a novel move blocking scheme, "Moving Window Blocking" (MWB), will be presented. In MWB, the blocking strategy is time-dependent such that the scheme yields stability and feasibility guarantees for the closed-loop system. Finally, the results of a large case-study are presented that illustrate the advantages and drawbacks of the various control strategies discussed in this paper.

Speed Tracking of a Linear Induction Motor-Enumerative Nonlinear Model Predictive Control

“…Other methods to reduce the number of optimization variables could also have been used, e.g. blocking of the input variables technique, [24]. The objective function (13) Increasing the prediction horizon N will lead to more accurate choice of control signals.…”

Optimal move blocking strategies for model predictive control

“…However, this prevents a terminal constraint from being enforced, so explicit guarantees of closed-loop convergence cannot be given. Cagienard et al (2007) and Shekhar and Maciejowski (2012b) present approaches that utilise timevarying blocking structures, where the changing structure allows a shifted version of the previously optimal input sequence to be feasible at the following time step. Guarantees of both recursive feasibility and closed-loop convergence can then be provided, with an appropriately designed terminal constraint and cost function.…”

“…One method of achieving the latter is to assume some form of input parameterisation, curtailing the number of degrees of freedom in the online optimisation problem. Various candidate parameterisations have been proposed, including move blocking (Cagienard, Grieder, Kerrigan, & Morari, 2007;Maciejowski, 2002), linear subspaces (Goebel & Allgöwer, 2014;Ong & Wang, 2014) and Laguerre polynomials (Rossiter & Wang, 2008). Move blocking is a candidate parameterisation that constrains groups of adjacent-in-time predicted inputs to have the same value.…”

Model Predictive Control with reduced number of variables for linear systems with bounded disturbances

“…Another approach to reduce online computations is to parameterize the control {u 0 , u 1 , · · · , u N −1 } of the MPC online optimization problem with a smaller set of variables. This approach is also known as the blocking parametrization [9], [10], [11] in the literature as the control {u 0 , u 1 , · · · , u N −1 } is divided into a union of several mutually exclusive blocks, each associated with one variable. This fewer number of variables naturally lead to a lower online computational effort.…”