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

Abstract 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 an

Integrated circuit implementation of multi-dimensional piecewise-linear functions

In this paper we present an integrated circuit implementing piecewise-linear (PWL) functions with three inputs, where each input can be either analog or digital. The PWL function to be implemented can be chosen by properly storing a set of coefficients in a 4 kB external memory. Experimental results are shown that demonstrate the circuit working up to 50 MHz with a maximum power consumption of 3.7 mW. Measurements corresponding to both static and time-varying inputs are provided and discussed. © 2010 Elsevier Inc. All rights reserved.Fil: Di Federico, Martin. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Investigaciones en Ingeniería Eléctrica "Alfredo Desages". Universidad Nacional del Sur. Departamento de Ingeniería Eléctrica y de Computadoras. Instituto de Investigaciones en Ingeniería Eléctrica "Alfredo Desages"; ArgentinaFil: Poggi, Tomaso. Università degli Studi di Genova; ItaliaFil: Julian, Pedro Marcelo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Investigaciones en Ingeniería Eléctrica "Alfredo Desages". Universidad Nacional del Sur. Departamento de Ingeniería Eléctrica y de Computadoras. Instituto de Investigaciones en Ingeniería Eléctrica "Alfredo Desages"; ArgentinaFil: Storace, Marco. Università degli Studi di Genova; Itali

Integrated circuit implementation of multi-dimensional piecewise-linear functions

In this paper we present an integrated circuit implementing piecewise-linear (PWL) functions with three inputs, where each input can be either analog or digital. The PWL function to be implemented can be chosen by properly storing a set of coefficients in a 4 kB external memory. Experimental results are shown that demonstrate the circuit working up to 50 MHz with a maximum power consumption of 3.7 mW. Measurements corresponding to both static and time-varying inputs are provided and discussed