Reference Tracking MPC Using Dynamic Terminal Set Transformation

Abstract

Among the many different formulations of Model Predictive Control (MPC) with guaranteed stability, one that has attracted significant attention is the formulation with a terminal cost and terminal constraint set, the so called dual mode formulation.In this paper our goal is to make minimal changes to the dual mode framework, for the linear polytopic case, in order to develop a flexible reference tracking algorithm with guaranteed stability and low complexity, which is intuitive and easily understood. The main idea is to introduce a scaling variable that dynamically scales the terminal constraint set and therefore allows it to be centered around an arbitrary setpoint without violating the stability conditions. The main benefit of the algorithm is reduced complexity of the resulting QP compared to other state of art methods without loosing performance.

Distributed predictive control with minimization of mutual disturbances

“…Reconfigurable terminal sets have been proposed in the context of setpoint, reference or target tracking and fault tolerant forms of MPC [22][23][24][25][26]; the idea is to parameterize an invariant, admissible set in terms of a steady-state target equilibrium pair, so that when the target changes the terminal set can be adjusted accordingly and automatically. In [27], a novel reconfigurable terminal set that is an inner approximation to the maximal admissible set (MAS) [28], parameterized by the right-hand side of the polytopic input constraint set (i.e., here b i ), is proposed; the context is fault-tolerant control, wherein the failure of an actuator may be modelled as a change in the input constraint set.…”

Constrained Reference Tracking based on Homothetic Sets

“…Additionally, for non-linear systems such set can be rather difficult to calculate or the resulting set is overly conservative approximation of the true terminal set. To overcome the problem of the increased complexity of the terminal set an alternative approach is presented in [7,8] which utilizes the idea of scaling and translating the terminal set computed for the regulation problem to track a given reference signal. In this paper we combine the ideas of the reference governor [9] and the tracking MPC [7,8,16] to develop a predictive reference management solution to constrained reference tracking problem for a class of non-linear, parameter-varying systems, applicable in the form of both reference governor and tracking MPC.…”

“…The approach [7,8] assumes a unique (invertible) mapping between a fixed point (x,ū) and an active reference signal v:…”

“…The idea of utilizing a family of homothetic transformations S(X F ) can be further used to extend the tracking MPC proposed in [7,8] to the non-linear parameter-varying case. Given a positively-invariant terminal set X T for the system (1) under control law (3) and a suitable terminal cost ψ(·) we pose the tracking MPC problem as follows.…”

“…For linear systems, the reference-dependent terminal set can be obtained simply by translating and scaling the terminal set calculated for the regulation problem [7,8]. The main benefit of such an approach is in a less complex terminal set comparing to the one calculated in the augmented state-reference space.…”