Alberto Oliveri

Ultra-Fast Stabilizing Model Predictive Control via Canonical Piecewise Affine Approximations

This paper investigates the use of canonical piecewise affine (PWA) functions for approximation and fast implementation of linear MPC controllers. The control law is approximated in an optimal way over a regular simplicial partition of a given set of states of interest. The stability properties of the resulting closed-loop system are analyzed by constructing a suitable PWA Lyapunov function. The main advantage of the proposed approach to the implementation of MPC controllers is that the resulting stabilizing approximate MPC controller can be implemented on chip with sampling times in the order of tens of nanoseconds.

Circuit implementation of piecewise-affine functions based on a binary search tree

In this paper we introduce a digital architecture implementing piecewise-affine functions defined over domains partitioned into polytopes: the functions are linear affine over each polytope. The polytope containing the input vector is found by exploring a previously constructed binary search tree. Once the polytope is detected, the function is evaluated by addressing an affine map whose coefficients are stored in a memory. The architecture has been implemented on FPGA and experimental results for a benchmark example are shown.

FPGA Implementations of Piecewise Affine Functions Based on Multi-Resolution Hyperrectangular Partitions

In this paper we propose a digital architecture suited for fast, low-power and small-size electronic implementation of PieceWise Affine (PWA) functions defined over n-dimensional domains partitioned into multi-resolution hyperrectangles. The point location problem, which requires most of the computational effort, is solved through an orthogonal search tree, which is easily and efficiently implementable. In the case of domains partitioned into single-resolution hyperrectangles, a simpler and even faster architecture is proposed. After introducing the new architectures, their key features are discussed and compared to previous architectures implementing PWA functions with domains partitioned into different types of polytopes. Case studies concerning the FPGA implementation of so-called explicit Model Predictive Control (MPC) laws for constrained linear systems are used as benchmarks to compare the different architectures.

FPGA implementation of optimal and approximate model predictive control for a buck-boost DC-DC converter

This paper proposes a method for FPGA implementation of explicit, piecewise affine (PWA) model predictive control (MPC) laws for non-inverting buck-boost DC-DC converters. A novel approach to obtain a PWA model of the power converter is proposed and two explicit MPC laws are derived, i.e., one based on the standard approach to synthesis of explicit MPC and one based on a simplicial PWA approximation of the resulting MPC law, which permits a more efficient implementation. An FPGA circuit is designed for both the original and the approximating MPC control law. Two hardware architectures with different FPGA footprint and computation latency are developed for each control law. Extensive real-time experiments demonstrate the performance of the two MPC controllers and their computational characteristics.

Hardware-in-the-loop simulations of circuit architectures for the computation of exact and approximate explicit MPC control functions

Several circuit architectures have been proposed for the fast implementation of embedded control systems, but only simulated results of the stand-alone circuits are usually reported. In this work we perform a hardware-in-the-loop simulation of a closed-loop system in which the controller is physically implemented in an FPGA. We improve two different circuit architectures available in the literature, to make them suitable for the computation of exact and approximate Model Predictive Control and we test them with the FPGA-in-the-loop simulations. Control and circuit performances are discussed.

Low-complexity approximations of PWA functions: A case study on Adaptive Cruise Control

This paper applies recently developed techniques for the PieceWise-Affine (PWA) approximation of explicit Model Predictive Control (MPC) to an Adaptive Cruise Control system. The optimal MPC law is approximated by using a particular class of PWA functions defined over a domain partitioned into simplices, referred to as PieceWise-Affine Simplicial functions. This approximation technique allows a very fast circuit implementation of the control function, thereby enabling the usage of MPC in embedded systems with extremely small sampling periods.

MOBY-DIC : a Matlab toolbox for circuit-oriented design of explicit MPC

This paper describes a MATLAB Toolbox for the integrated design of Model Predictive Control (MPC) state-feedback control laws and the digital circuits implementing them. Explicit MPC laws can be designed using optimal and sub-optimal formulations, directly taking into account the specifications of the digital circuit implementing the control law (such as latency and size), together with the usual control specifications (stability, performance, constraint satisfaction). Tools for a-posteriori stability analysis of the closed-loop system, and for the simulation of the circuit in Simulink, are also included in the toolbox.

Two FPGA-Oriented High-Speed Irradiance Virtual Sensors for Photovoltaic Plants

Knowing solar irradiance value allows an optimized management of photovoltaic (PV) power plants in terms of produced energy. Unfortunately, although sensing temperature is easy, the measurement of solar irradiance is expensive. In this paper, two circuit architectures for the estimation of the solar irradiance based on simple measurements are proposed. They are thought to be part of a centralized system implemented on field programmable gate array (FPGA) for sensing and monitoring of solar irradiance in a whole PV plant. The FPGA centralized architecture could allow for a real-time irradiance mapping by exploiting information coming from several low-cost measuring circuits suitably allocated on the PV modules. Validations on real irradiance data collected by the U.S. Department of Energy’s National Renewable Energy Laboratory are presented.

A Circuit Model of Hysteresis and Creep

A circuit architecture that models hysteretic phenomena is proposed. The model is flexible enough to reproduce both rate-independent hysteresis and thermal relaxation effects (creep), commonly observed in many real-world physical systems such as piezoelectric actuators. By suitably tuning the nonlinear characteristics of the resistive elements of the network, the well-known log(t) time dependence of the creep relaxation dynamics can be accurately reproduced. An identification procedure is proposed, and two test cases are discussed.

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

This paper is focused on the theoretical development and the hardware implementation of low-complexity piecewise-affine direct virtual sensors for the estimation of unmeasured variables of interest of nonlinear systems. The direct virtual sensor is designed directly from measured inputs and outputs of the system and does not require a dynamical model. The proposed approach allows one to design estimators which mitigate the effect of the so-called ‘curse of dimensionality’ of simplicial piecewise-affine functions, and can be therefore applied to relatively high-order systems, enjoying convergence and optimality properties. An automatic toolchain is also presented to generate the VHDL code describing the digital circuit implementing the virtual sensor, starting from the set of measured input and output data. The proposed methodology is applied to generate an FPGA implementation of the virtual sensor for the estimation of vehicle lateral velocity, using a hardware-in-the-loop setting.