Integrated circuit implementation of multi-dimensional piecewise-linear functions

Federico, Martın Di; Poggi, Tomaso; Julián, P.; Storace, Marco

doi:10.1016/j.dsp.2010.02.007

Cited by 13 publications

(17 citation statements)

References 21 publications

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“…As advocated in [16], [20], [22], [24]- [27], it can be very beneficial for the eventual (circuit) implementation to use canonical PWA controllers that are based on regular partitions using e.g. regular simplices [20], [22], [24]- [27] or (multiscale) hypercubes [16].…”

Section: B Motivationmentioning

confidence: 99%

“…In case of stability only, these are given in [38] and in [39], while an alternative technique for implementing the S-procedure in discrete time has been proposed in [40]. The extension to ISS follows in a straightforward way leading to (27).…”

Section: ) Euclidean Norms (P = Q = 2)mentioning

confidence: 99%

“…regular simplices [20], [22], [24]- [27] or (multiscale) hypercubes [16]. Essentially, any desired polytopic shape can be chosen in our approximation method that follows.…”

Section: B Motivationmentioning

confidence: 99%

“…The conditions (27) are in LMI-form in the variablesF j ,g j of the low-complexity controller corresponding to regionP j , and U ij . Together with (18) and (19), affirming (27) for allP j , j ∈ {1, .…”

Section: ) Euclidean Norms (P = Q = 2)mentioning

confidence: 99%

“…The approximate control law is defined on a regular (possibly multiscale) partition, which can be chosen in a desirable way, e.g. based on multiscale rectangles as in [16] or regular simplices as in [20], [22], [24]- [27]. Due to the choice of a regular partition, the resulting regular PWA functions inherently result in efficient, low-complexity on-line implementations in terms of both computational effort and memory requirements.…”

Section: Introductionmentioning

confidence: 99%

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Approximation of explicit model predictive control using regular piecewise affine functions: an input-to-state stability approach

Genuit

Heemels

2012

IET Control Theory &Amp; Applications

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Piecewise affine (PWA) feedback control laws defined on general polytopic partitions, as for instance obtained by explicit MPC, will often be prohibitively complex for fast systems. In this work we study the problem of approximating these high-complexity controllers by low-complexity PWA control laws defined on more regular partitions, facilitating faster on-line evaluation. The approach is based on the concept of input-to-state stability (ISS). In particular, the existence of an ISS Lyapunov function (LF) is exploited to obtain a priori conditions that guarantee asymptotic stability and constraint satisfaction of the approximate low-complexity controller. These conditions can be expressed as local semidefinite programs (SDPs) or linear programs (LPs), in case of 2-norm or 1, ∞-norm based ISS, respectively, and apply to PWA plants. In addition, as ISS is a prerequisite for our approximation method, we provide two tractable computational methods for deriving the necessary ISS inequalities from nominal stability. A numerical example is provided that illustrates the main results.The authors are with the Hybrid and

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Section: B Motivationmentioning

confidence: 99%

Section: ) Euclidean Norms (P = Q = 2)mentioning

confidence: 99%

“…regular simplices [20], [22], [24]- [27] or (multiscale) hypercubes [16]. Essentially, any desired polytopic shape can be chosen in our approximation method that follows.…”

Section: B Motivationmentioning

confidence: 99%

Section: ) Euclidean Norms (P = Q = 2)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Approximation of explicit model predictive control using regular piecewise affine functions: an input-to-state stability approach

Genuit

Heemels

2012

IET Control Theory &Amp; Applications

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Application specific integrated circuit solution for multi‐input multi‐output piecewise‐affine functions

Brox

Martínez-Rodríguez

Tena-Sánchez

et al. 2015

Circuit Theory & Apps

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Summary This paper presents a fully digital architecture and its application specific integrated circuit implementation for computing multi‐input multi‐output (MIMO) piecewise‐affine (PWA) functions. The work considers both PWA functions defined over regular hyperrectangular and simplicial partitions of the input domains and also lattice PWA representations. The proposed architecture is able to implement PWA functions following different realization strategies, using a common structure with a minimized number of blocks, thus reducing power consumption and hardware resources. Experimental results obtained with application specific integrated circuit (ASIC) integrated in a 90‐nm complementary metal‐oxide semiconductor standard technology are provided. The proposed architecture is compared with other digital architectures in the state of the art habitually used to implement model predictive control applications. The proposal is superior in power consumption (saving up to 86%) and economy of hardware resources (saving up to 40% in comparison with a mere replication of the three representations) to other proposals described in literature, being ready to be used in applications where high‐performance and minimum unitary cost are required. Copyright © 2015 John Wiley & Sons, Ltd.

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Low-complexity piecewise-affine virtual sensors: theory and design

Rubagotti

Poggi

Oliveri

et al. 2013

International Journal of Control

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Integrated circuit implementation of multi-dimensional piecewise-linear functions

Cited by 13 publications

References 21 publications

Approximation of explicit model predictive control using regular piecewise affine functions: an input-to-state stability approach

Approximation of explicit model predictive control using regular piecewise affine functions: an input-to-state stability approach

Application specific integrated circuit solution for multi‐input multi‐output piecewise‐affine functions

Low-complexity piecewise-affine virtual sensors: theory and design

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