Approximation of PWA Control Laws Using Regular Partitions: An ISS Approach

Genuit, Bag Bart; Lu, Lerong; Heemels, W.P.M.H.

doi:10.3182/20110828-6-it-1002.03182

Cited by 9 publications

(15 citation statements)

References 14 publications

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“…Since then, many approaches were designed to map piecewise affine functions to FPGA using binary search trees [30,25], lattice-based representation [28,24], mix thereof [8] or hash functions [7]. Explicit solutions to MPC can be approximated to reduce the complexity of piece-wise affine controllers [23,19]. Also, search algorithms can be simplified and give an approximate solution [29,6].…”

Section: Related Workmentioning

confidence: 99%

“…As far as we know, this is the first time that semantic factorizations are used to optimize affine control, while keeping it exact. However, when approximation is allowed, the complexity of the controller can be reduced [23,19] and control algorithms can be simplified [29,6]. In our case, this would not apply: control has to be exact, no approximation is allowed.…”

Section: Introductionmentioning

confidence: 99%

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Optimizing Affine Control With Semantic Factorizations

Alias

Plesco²

2017

ACM Trans. Archit. Code Optim.

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Hardware accelerators generated by polyhedral synthesis make an extensive use of affine expressions (affine functions and convex polyhedra) in control and steering logic. Since the control is pipelined, these affine objects must be evaluated at the same time for different values, which forbids aggressive reuse of operators. In this report, we propose an algorithm to factorize a collection of affine expressions without preventing pipelining. Our key contributions are (i) to use semantic factorizations exploiting arithmetic properties of addition and multiplication and (ii) to rely on a cost function whose minimization ensures a correct usage of FPGA resources. Our algorithm is totally parametrized by the cost function, which can be customized to fit a target FPGA. Experimental results on a large pool of linear algebra kernels show a significant improvement compared to traditional low-level RTL optimizations. In particular, we show how our method reduces resource consumption by revealing hidden strength reductions.Key-words: High-level synthesis, polyhedral compilation, affine control, FPGA * CNRS/ENS-Lyon/Inria/UCBL/Université de Lyon † XtremLogic SAS Optimisation du contrôle affine avec des factorisations sémantiques Résumé :Les accélérateurs matériels compilés par les algorithmes de synthèse polyédrique utilisent intensivement des expressions affines (fonctions affines par morceaux, polyèdres convexes) dans leur contrôle. Comme le contrôle est pipeliné, ces objets affines doiventêtreévalués en même temps pour différentes valeurs d'entrée, ce qui interdit une réutilisation aggressive des opérateurs. Dans ce rapport, nous proposons un algorithme pour factoriser une collection d'expressions affines sans empêcher le pipeline. Nos contributions sont (i) l'utilisation de factorisations exploitant les propriétés arithmétiques de l'addition et de la multiplication et (ii) une fonction de coût dont la minimisation assure une utilisation efficace des ressources FPGA. Notre algorithme est totalement paramétré par la fonction de coût, qui peutêtre adaptéeà un FPGA cible donné. Les résultats expérimentaux montrent que notre algorithme complète avantageusement les optimisations RTL bas-niveau implantées dans les outils de synthèse industriels. En particulier, nous montrons comment notre algorithme reduit la taille du circuit en révélant des réductions de force cachées.

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Section: Related Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Optimizing Affine Control With Semantic Factorizations

Alias

Plesco²

2017

ACM Trans. Archit. Code Optim.

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“…Since the number of state space partitions so greatly affect the applicability of explicit MPC, lots of research have been performed on the task of defining a simple state space partition structure in order to reduce the complexity in the point location problem, see, e.g., Rubagotti et al [2012], Raimondo et al [2012], Genuit et al [2011]. In Figure 3.3 and 3.4 we have used the pitch dynamics of the same aircraft as in Section 4.3.1 to calculate a simple explicit MPC controller for stabilizing the unstable dynamics around the origin.…”

Section: Definitionmentioning

confidence: 99%

Model Predictive Control in Flight Control Design : Stability and Reference Tracking

Simon

2014

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Aircraft are dynamic systems that naturally contain a variety of constraints and nonlinearities such as, e.g., maximum permissible load factor, angle of attack and control surface deflections. Taking these limitations into account in the design of control systems are becoming increasingly important as the performance and complexity of the controlled systems is constantly increasing. It is especially important in the design of control systems for fighter aircraft. These require maximum control performance in order to have the upper hand in a dogfight or when they have to outmaneuver an enemy missile. Therefore pilots often maneuver the aircraft very close to the limit of what it is capable of, and an automatic system (called flight envelope protection system) against violating the restrictions is a necessity.In other application areas, nonlinear optimal control methods have been successfully used to solve this but in the aeronautical industry, these methods have not yet been established. One of the more popular methods that are well suited to handle constraints is Model Predictive Control (MPC) and it is used extensively in areas such as the process industry and the refinery industry. Model predictive control means in practice that the control system iteratively solves an advanced optimization problem based on a prediction of the aircraft's future movements in order to calculate the optimal control signal. The aircraft's operating limitations will then be constraints in the optimization problem.In this thesis, we explore model predictive control and derive two fast, low complexity algorithms, one for guaranteed stability and feasibility of nonlinear systems and one for reference tracking for linear systems. In reference tracking model predictive control for linear systems we build on the dual mode formulation of MPC and our goal is to make minimal changes to this framework, in order to develop a reference tracking algorithm with guaranteed stability and low complexity suitable for implementation in real time safety critical systems.To reduce the computational burden of nonlinear model predictive control several methods to approximate the nonlinear constraints have been proposed in the literature, many working in an ad hoc fashion, resulting in conservatism, or worse, inability to guarantee recursive feasibility. Also several methods work in an iterative manner which can be quit time consuming making them inappropriate for fast real time applications. In this thesis we propose a method to handle the nonlinear constraints, using a set of dynamically generated local inner polytopic approximations. The main benefits of the proposed method is that while computationally cheap it still can guarantee recursive feasibility and convergence.v Populärvetenskaplig sammanfattningFlygplan är dynamiska system som naturligt innehåller en mängd begränsningar och olinjäriteter så som t.ex. max tillåten lastfaktor, anfallsvinkel och roderlägen. Att ta hänsyn till dessa begränsningar i designen av styrsystem blir allt viktiga...

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“…The control law proposed by Bemporad et al (2011) presents feasibility and local optimality properties, but the asymptotic stability of the origin of the closed-loop system and the evaluation of its domain of attraction can be determined only a posteriori (see, e.g., Rubagotti et al (2013) and the references therein). We would like to remark that PWAS functions are not the only choice for approximation of explicit MPC aimed June 16, 2014 17:28 International Journal of Control Rubagotti˙etal˙IJC 3 at hardware implementation: for example, two different approaches based on the use of PWA hyper-rectangular partitions have been recently proposed by Genuit et al (2011) and Lu et al (2011). In all of these approaches , Genuit et al 2011, the possible presence of disturbance terms acting on the system is not taken into account.…”

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confidence: 99%

Robust explicit model predictive control via regular piecewise-affine approximation

Rubagotti

Barcelli

Bemporad

2014

International Journal of Control

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This paper proposes an explicit model predictive control design approach for regulation of linear time-invariant systems subject to both state and control constraints, in the presence of additive disturbances. The proposed control law is implemented as a piecewise-affine function defined on a regular simplicial partition, and has two main positive features. Firstly, the regularity of the simplicial partition allows one to efficiently implement the control law on digital circuits, thus achieving extremely fast computation times. Moreover, the asymptotic stability (or the convergence to a set including the origin) of the closed-loop system can be enforced a-priori, rather than checked a-posteriori via Lyapunov analysis.

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Approximation of PWA Control Laws Using Regular Partitions: An ISS Approach

Cited by 9 publications

References 14 publications

Optimizing Affine Control With Semantic Factorizations

Optimizing Affine Control With Semantic Factorizations

Model Predictive Control in Flight Control Design : Stability and Reference Tracking

Robust explicit model predictive control via regular piecewise-affine approximation

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