IMT Institutional Repository: No conditions. Results ordered -Date Deposited. 2022-08-14T22:24:20ZEPrintshttp://eprints.imtlucca.it/images/logowhite.pnghttp://eprints.imtlucca.it/2011-07-27T10:51:01Z2011-08-04T07:29:08Zhttp://eprints.imtlucca.it/id/eprint/558This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5582011-07-27T10:51:01ZApproximate multiparametric convex programmingAlberto Bemporadalberto.bemporad@imtlucca.itCarlo Filippi2011-07-27T09:08:58Z2014-07-17T12:46:26Zhttp://eprints.imtlucca.it/id/eprint/586This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5862011-07-27T09:08:58ZSuboptimal explicit MPC via approximate multiparametric quadratic programmingAlgorithms for solving multiparametric quadratic programming (mp-QP) were proposed in Bemporad et al. (2001) and Tondel et al. (2001) for computing explicit model predictive control (MPC) laws. The reason for this interest is that the solution to mp-QP is a piecewise affine function of the state vector and thus it is easily implementable on-line. The main drawback of solving mp-QP exactly is that whenever the number of linear constraints involved in the optimization problem increases, the number of polyhedral cells in the piecewise affine partition of the parameter space may increase exponentially. We address the problem of finding approximate solutions to mp-QP, where the degree of approximation is arbitrary and allows a trade off between optimality and a smaller number of cells in the piecewise affine solutionAlberto Bemporadalberto.bemporad@imtlucca.itCarlo Filippi2011-07-27T09:02:47Z2011-08-04T07:29:08Zhttp://eprints.imtlucca.it/id/eprint/471This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/4712011-07-27T09:02:47ZSuboptimal Explicit Receding Horizon Control via Approximate Multiparametric Quadratic Programming Algorithms for solving multiparametric quadratic programming (MPQP) were recently proposed in Refs. 1–2 for computing explicit receding horizon control (RHC) laws for linear systems subject to linear constraints on input and state variables. The reason for this interest is that the solution to MPQP is a piecewise affine function of the state vector and thus it is easily implementable online. The main drawback of solving MPQP exactly is that, whenever the number of linear constraints involved in the optimization problem increases, the number of polyhedral cells in the piecewise affine partition of the parameter space may increase exponentially. In this paper, we address the problem of finding approximate solutions to MPQP, where the degree of approximation is arbitrary and allows to tradeoff between optimality and a smaller number of cells in the piecewise affine solution. We provide analytic formulas for bounding the errors on the optimal value and the optimizer, and for guaranteeing that the resulting suboptimal RHC law provides closed-loop stability and constraint fulfillment.Alberto Bemporadalberto.bemporad@imtlucca.itCarlo Filippi2011-07-27T08:53:28Z2014-07-08T13:58:48Zhttp://eprints.imtlucca.it/id/eprint/470This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/4702011-07-27T08:53:28ZInner and outer approximation of polytopes using boxesThis paper deals with the problem of approximating a convex polytope in any finite dimension by a collection of (hyper)boxes. More exactly, given a polytope by a system of linear inequalities, we look for two collections and of boxes with non-overlapping interiors such that the union of all boxes in is contained in and the union of all boxes in contains . We propose and test several techniques to construct and aimed at getting a good balance between two contrasting objectives: minimize the volume error and minimize the total number of generated boxes. We suggest how to modify the proposed techniques in order to approximate the projection of onto a given subspace without computing the projection explicitly.Alberto Bemporadalberto.bemporad@imtlucca.itCarlo FilippiFabio Danilo Torrisi2011-07-27T08:47:40Z2011-08-05T13:54:55Zhttp://eprints.imtlucca.it/id/eprint/565This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5652011-07-27T08:47:40ZRobust explicit MPC based on approximate multi-parametric convex programmingMany robust model predictive control (MPC) schemes require the online solution of a convex program, which can be computationally demanding. For deterministic MPC schemes, multi-parametric programming was successfully applied to move most computations offline. In this paper we adopt a general approximate multi-parametric algorithm recently suggested for convex problems and propose to apply it to a classical robust WC scheme. This approach enables one to implement a robust MPC controller in real time for systems with polytopic uncertainty, ensuring robust constraint satisfaction and robust convergence to a given bounded set.David Muñoz de la PeñaAlberto Bemporadalberto.bemporad@imtlucca.itCarlo Filippi2011-07-27T08:43:54Z2013-09-13T09:50:06Zhttp://eprints.imtlucca.it/id/eprint/492This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/4922011-07-27T08:43:54ZAn algorithm for approximate multiparametric convex programmingFor multiparametric convex nonlinear programming problems we propose a recursive algorithm for approximating, within a given suboptimality tolerance, the value function and an optimizer as functions of the parameters. The approximate solution is expressed as a piecewise affine function over a simplicial partition of a subset of the feasible parameters, and it is organized over a tree structure for efficiency of evaluation. Adaptations of the algorithm to deal with multiparametric semidefinite programming and multiparametric geometric programming are provided and exemplified. The approach is relevant for real-time implementation of several optimization-based feedback control strategies. Alberto Bemporadalberto.bemporad@imtlucca.itCarlo Filippi2011-07-27T08:40:40Z2011-08-05T13:20:31Zhttp://eprints.imtlucca.it/id/eprint/489This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/4892011-07-27T08:40:40ZRobust explicit MPC based on approximate multi-parametric convex programmingMany robust model predictive control (MPC) schemes require the online solution of a computationally demanding convex program. For deterministic MPC schemes, multiparametric programming was successfully applied to move offline most of the computation. In this paper, we adopt a general approximate multiparametric algorithm recently suggested for convex problems and propose to apply it to a classical robust MPC scheme. This approach enables one to implement a robust MPC controller in real time for systems with polytopic uncertainty, ensuring robust constraint satisfaction and robust convergence to a given bounded setDavid Muñoz de la PeñaAlberto Bemporadalberto.bemporad@imtlucca.itCarlo Filippi