A parameterized polyhedra approach for explicit constrained predictive control

Olaru, Sorin; Dumur, Didier

doi:10.1109/cdc.2004.1430269

Cited by 48 publications

(44 citation statements)

References 6 publications

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“…Explicit model predictive control (MPC) has received significant attention in control community due to its relevance for rather small-dimensional systems [10], [17], [36], [37], [41]. However, even if the controllers are explicitly obtained, there exist major problems in terms of their implementation once the number of regions in the state-space partition becomes large.…”

Section: Motivationmentioning

confidence: 99%

Convex Lifting: Theory and Control Applications

Nguyễn

Gulan

Olaru

et al. 2018

IEEE Trans. Automat. Contr.

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Section: Motivationmentioning

confidence: 99%

Convex Lifting: Theory and Control Applications

Nguyễn

Gulan

Olaru

et al. 2018

IEEE Trans. Automat. Contr.

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“…Recall (see [4][5][6][7][8]) that a parametric linear/quadratic programming problem is defined as follows with respect to…”

Section: Parametric Linear/quadratic Programming Problemsmentioning

confidence: 99%

“…In control theory, this structure of control laws appeared in the last decade as an approximation of the classical nonlinear control laws with respect to a predefined error [1][2][3]. Then, it is shown that this PWA structure is inherited by the exact optimal solution of a linear model predictive control (MPC) problem with respect to a linear/quadratic cost function [4][5][6][7][8][9].…”

Section: Introductionmentioning

confidence: 99%

Constructive Solution of Inverse Parametric Linear/Quadratic Programming Problems

Nguyễn

Olaru

Rodríguez-Ayerbe

et al. 2016

J Optim Theory Appl

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Parametric convex programming has received a lot of attention, since it has many applications in chemical engineering, control engineering, signal processing, etc. Further, inverse optimality plays an important role in many contexts, e.g., image processing, motion planning. This paper introduces a constructive solution of the inverse optimality problem for the class of continuous piecewise affine functions. The main idea is based on the convex lifting concept. Accordingly, an algorithm to construct convex liftings of a given convexly liftable partition will be put forward. Following this idea, an important result will be presented in this article: any continuous piecewise affine function defined over a polytopic partition is the solution of a parametric linear/quadratic programming problem. Regarding linear optimal control, it will be shown that any continuous piecewise affine control law can be obtained via a linear optimal control problem with the control horizon at most equal to 2 prediction steps.

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“…It is known that in closed loop this class of controllers leads to a hybrid system formulation Heemels et al (2001). Another motivation for the study of the PWA controllers and their robustness is the recent interest in the optimization-based design via parametric convex programming Bemporad et al (2002); Tøndel et al (2003); Seron et al (2003); Olaru and Dumur (2004); Nguyen et al (2013) or the approximate explicit solutions in Model Predictive Control (MPC) Johansen and Grancharova (2003). Various types of uncertainties exist, in this paper, our interest is in parametric uncertainties, understood as variations of coefficients of a model with a pre-imposed structure.…”

Section: Introductionmentioning

confidence: 99%

Explicit robustness and fragility margins for linear discrete systems with piecewise affine control law

et al. 2016

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In this paper, we focus on the robustness and fragility problem for piecewise affine (PWA) control laws for discrete-time linear system dynamics in the presence of parametric uncertainty of the state space model. A generic geometrical approach will be used to obtain robustness/fragility margins with respect to the positive invariance properties. For PWA control laws defined over a bounded region in the state space, it is shown that these margins can be described in terms of polyhedral sets in parameter space. The methodology is further extended to the fragility problem with respect to the partition defining the controller. Finally, several computational aspects are presented regarding the transformation from the theoretical formulations to explicit representations (vertex/halfspace representation of polytopes) of these sets.

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A parameterized polyhedra approach for explicit constrained predictive control

Cited by 48 publications

References 6 publications

Convex Lifting: Theory and Control Applications

Convex Lifting: Theory and Control Applications

Constructive Solution of Inverse Parametric Linear/Quadratic Programming Problems

Explicit robustness and fragility margins for linear discrete systems with piecewise affine control law

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