Multi-Parametric Toolbox (MPT)

By Michal Kvasnica, Pascal Grieder, Mato Baotic, Manfred Morari. International Conference on Hybrid Systems: Computation and Control, 2004

1,019 citations recorded by the source corpus.

Subfields: Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/2d14ce511cddedf4b16e4146c647fdde9762535a

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In Control and Systems Engineering

Citations in the corpus

Invariant approximations of the minimal robust positively Invariant set (2005, methodology): “4.1]. The set Fs (and hence F(®,s)) is easily computed using standard computational geometry software for computing the Minkowski sum of polytopes, such as [19] and [ 20 ].”
Move blocking strategies in receding horizon control (2004, methodology): “All results were created with the MPT Toolbox [6].”
Design and Implementation of Model Predictive Control for Electrical Motor Drives (2009, methodology): “The new cost function (4) and the constraints (5) that have been obtained fit in the class of optimization problems called quadratic programming, for which efficient iterative solvers are available in the technical literature on nonlinear programming and optimization methods (see [14] and [ 15 ] and”
A survey on explicit model predictive control (2009, background): “Similar and other functionalities can be found in the Multi Parametric Toolbox for Matlab [ 48 ].”
An introduction to event-triggered and self-triggered control (2012, positive): “To implement Algorithm 1 in M ATLAB , we use the routine polytope of the MPT-toolbox [34], to handle the sets Ω( x ( t k )) .”
A survey on stability analysis of discrete-time piecewise affine systems (2005, methodology): “All tools as well as the random systems be downloaded from (Kvasnica et al., 2003).”
Constrained zonotopes: A new tool for set-based estimation and fault detection (2016, methodology): “Due to the difficulty of computing minimal enclosing balls for general polytopes, the radius is defined here as half the length of the longest edge of the interval hull, which is easily computed by solving 2n LPs. Volume computations were done by converting to H-rep and using the volume routine in M”
On the Virtual Element Method for three-dimensional linear elasticity problems on arbitrary polyhedral meshes (2013, methodology): “We use the open source MATLAB toolbox, Multi-Parametric Toolbox (MPT) [26], for generating the polyhedral meshes.”
Multi-Parametric Toolbox 3.0 (2013, background): “Since the initial release in 2004 [14] there has been a significant progress in the development of the toolbox and the scope of the toolbox has widened to deal also with problems arising in computational geometry.”
Receding Horizon Temporal Logic Planning (2012, methodology): “Reachability Problem: Given an initial continuous controlled state , discrete controlled states , the set of admissible control inputs , the set of exogenous disturbances , the matrices , and as in (1), a horizon length , determine a sequence of control signals such that for all and (7) If the above”
Analyzing operational flexibility of electric power systems (2014, neutral): “For the reach-set calculations, the reachability functions of the MPT Toolbox [17] have been used in Matlab.”
Analysis of event-driven controllers for linear systems (2008, methodology): “…for discrete-time linear systems (e.g., Blanchini (1994, 1999), Kolmanovsky and Gilbert (1998), Kerrigan (2000) and Rakovic et al. (2005), and piecewise linear systems see, e.g., Kvasnica et al. (2004) and Rakovic et al. (2004)), these results can be carried over to eventdriven controlled systems.”