Identification of hybrid and linear parameter‐varying models via piecewise affine regression using mixed integer programming

This article presents a two‐stage algorithm for piecewise affine (PWA) regression. In the first stage, a moving horizon strategy is employed to simultaneously estimate the model parameters and to classify the training data by solving a small‐size mixed‐integer quadratic programming problem. In the second stage, linear multicategory separation methods are used to partition the regressor space. The framework of PWA regression is adapted to the identification of PWA AutoRegressive with eXogenous input (PWARX) models as well as linear parameter‐varying (LPV) models. The performance of the proposed algorithm is demonstrated on an academic example and on two benchmark experimental case studies. The first experimental example concerns modeling the placement process in a pick‐and‐place machine, while the second one consists in the identification of an LPV model describing the input‐output relationship of an electronic bandpass filter with time‐varying resonant frequency.     

F-substituted hydroxyapatite nanopowders: Thermal stability,sintering behaviour and mechanical properties

Fluorine-substituted hydroxyapatites are considered promising materials for bone scaffolding. In this study a systematic investigation on F-half substituted hydroxyapatite (F-HAp, Ca₁₀(PO₄)₆OHF) obtained by precipitation is reported. Results on composition analysis, thermal behaviour, and sinterability are presented for a comparison with the respective pure hydroxyapatite. Samples were characterised by electron microscopy, induced coupled plasma-atomic emission spectroscopy, thermal analysis, infrared spectroscopy, N₂ adsorption measurements, X-ray diffraction and dilatometry. A semicrystalline F-substituted hydroxyapatite powder made up of needle-like nanoparticles was obtained. Notwithstanding that it was thermally stable up to 1300 °C, it was sintered at relatively low temperatures obtaining a very fine microstructure with a relevant nano-porosity, beneficial in view of cell adhesion and in-growth.Hardness, elastic modulus and toughness of produced samples were investigated by Vickers–Knoop microhardness testing. Significant improvements of the mechanical properties were observed for the F-substituted hydroxyapatite, in comparison with pure hydroxyapatite.     

A Lyapunov method for stability analysis of piecewise-affine systems over non-invariant domains

This paper analyses stability of discrete-time piecewise-affine systems, defined on possibly non-invariant domains, taking into account the possible presence of multiple dynamics in each of the polytopic regions of the system. An algorithm based on linear programming is proposed, in order to prove exponential stability of the origin and to find a positively invariant estimate of its region of attraction. The results are based on the definition of a piecewise-affine Lyapunov function, which is in general discontinuous on the boundaries of the regions. The proposed method is proven to lead to feasible solutions in a broader range of cases as compared to a previously proposed approach. Two numerical examples are shown, among which a case where the proposed method is applied to a closed-loop system, to which model predictive control was applied without a-priori guarantee of stability.     

Internal waves and K---H instability in thermal layers of the Advanced Solar Pond (ASP)

The development of internal waves and instabilities of the Kelvin Helmholtz-type may prevent the density gradient maintenance which allows the proper functioning of the Advanced Solar Pond (ASP). The properties and characteristics of internal waves, of constant and growing amplitude, are quantitatively described in this paper. The numerical simulations made in this study are in good agreement with previous theoretical and experimental results.     

On hybrid systems and closed-loop MPC systems

The following five classes of hybrid systems were recently proven to be equivalent: linear complementarity, extended linear complementarity, mixed logical dynamical systems, piecewise affine systems and max-min-plus-scaling systems. Some of the equivalences were obtained under additional assumptions, such as boundedness of certain system variables. In this paper, for linear or hybrid plants in closed-loop with a model predictive control (MPC) controller based on a linear model fulfilling linear constraints on input and state variables and utilizing a quadratic cost criterion, we provide a simple and direct proof that the closed-loop system is a subclass of any of the former five classes of hybrid systems. This result is of extreme importance, as it opens up the use of tools developed for the mentioned hybrid model classes, such as (robust) stability and safety analysis tools, to study closed-loop properties of MPC     

From linear to nonlinear MPC: bridging the gap via the real-time iteration

ABSTRACT

Linear model predictive control (MPC) can be currently deployed at outstanding speeds, thanks to recent progress in algorithms for solving online the underlying structured quadratic programs. In contrast, nonlinear MPC (NMPC) requires the deployment of more elaborate algorithms, which require longer computation times than linear MPC. Nonetheless, computational speeds for NMPC comparable to those of MPC are now regularly reported, provided that the adequate algorithms are used. In this paper, we aim at clarifying the similarities and differences between linear MPC and NMPC. In particular, we focus our analysis on NMPC based on the real-time iteration (RTI) scheme, as this technique has been successfully tested and, in some applications, requires computational times that are only marginally larger than linear MPC. The goal of the paper is to promote the understanding of RTI-based NMPC within the linear MPC community.     

Stochastic model predictive control for constrained discrete-time Markovian switching systems

In this paper we study constrained stochastic optimal control problems for Markovian switching systems, an extension of Markovian jump linear systems (MJLS), where the subsystems are allowed to be nonlinear. We develop appropriate notions of invariance and stability for such systems and provide terminal conditions for stochastic model predictive control (SMPC) that guarantee mean-square stability and robust constraint fulfillment of the Markovian switching system in closed-loop with the SMPC law under very weak assumptions. In the special but important case of constrained MJLS we present an algorithm for computing explicitly the SMPC control law off-line, that combines dynamic programming with parametric piecewise quadratic optimization.     

Energy-aware robust model predictive control based on noisy wireless sensors

Wireless sensor networks (WSNs) are becoming fundamental components of modern control systems due to their flexibility, ease of deployment and low cost. However, the energy-constrained nature of WSNs poses new issues in control design; in particular the discharge of batteries of sensor nodes, which is mainly due to radio communications, must be taken into account. In this paper we present a novel transmission strategy for communication between controller and sensors which is intended to minimize the data exchange over the wireless channel. Moreover, we propose an energy-aware control technique for constrained linear systems based on explicit model predictive control (MPC), providing closed-loop stability in the presence of disturbances. The presented control schemes are compared to traditional MPC techniques. The results show the effectiveness of the proposed energy-aware approach, which achieves a profitable trade-off between energy savings and closed-loop performance.