Scheduling Dimension Reduction of LPV Models -- A Deep Neural Network Approach

In this paper, the existing Scheduling Dimension Reduction (SDR) methods for Linear Parameter-Varying (LPV) models are reviewed and a Deep Neural Network (DNN) approach is developed that achieves higher model accuracy under scheduling dimension reduction. The proposed DNN method and existing SDR methods are compared on a two-link robotic manipulator, both in terms of model accuracy and performance of controllers synthesized with the reduced models. The methods compared include SDR for state-space models using Principal Component Analysis (PCA), Kernel PCA (KPCA) and Autoencoders (AE). On the robotic manipulator example, the DNN method achieves improved representation of the matrix variations of the original LPV model in terms of the Frobenius norm compared to the current methods. Moreover, when the resulting model is used to accommodate synthesis, improved closed-loop performance is obtained compared to the current methods.Comment: Accepted to American Control Conference (ACC) 2020, Denve

Mathematical control of complex systems

Copyright © 2013 ZidongWang et al.This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited

LPV control and virtual-sensor-based fault tolerant strategies for a three-axis gimbal system

This paper deals with the LPV control of a three-axis gimbal including fault-tolerant capabilities. First, the derivation of an analytical model for the considered system based on the robotics Serial-Link (SL) theory is derived. Then, a series of simplifications that allow obtaining a quasi-LPV model for the considered gimbal is proposed. Gain scheduling LPV controllers with PID structure are designed using pole placement by means of linear matrix inequalities (LMIs). Moreover, exploiting the sensor redundancy available in the gimbal, a virtual-sensor-based fault tolerant control (FTC) strategy is proposed. This virtual sensor uses a Recursive Least Square (RLS) estimation algorithm and an LPV observer for fault detection and estimation. Finally, the proposed LPV control scheme including the virtual sensor strategy is tested in simulation in several scenarios.Peer ReviewedPostprint (published version

Restricted structure non-linear generalized minimum variance control

This research presents the Restricted Structure Non-linear Generalized Minimum Variance (RS-NGMV) algorithm for Linear Parameter-Varying (LPV) systems. The LPV systems are defined as linear plant subsystems within the control diagram and may include Non-linear (NL) input subsystems. The RS-NGMV control solution for the latter will be slightly different than the first one and have the capability of dealing with NL characteristics such as saturation, discontinuities and black-box terms. The controller is built in a low-order Restricted Structure (RS) in the form of a general z-transfer function. This brings forward two major advantages. First, it offers a high-order advanced control solution inside low-order control structures which are known for their natural robustness. Secondly, it is easier to operate and re-tune for the classically trained staff in the industry as it can be given the structures they are rather familiar with such as the PID. Another advantage of the RS-NGMV is its model-based design that enables a faster adaptation to implement different systems. Features of the RS-NGMV are investigated throughout the thesis with case studies from trends in engineering like robotics, autonomous and electric vehicles. The results show that the RS-NGMV is highly capable of adapting to set-point changes, parameter variations with its ability to update the control gains rapidly by using optimizations. Some extensions of algorithms have also been studied following recent directions in optimal/predictive control resulting in a new preview control approach and Scheduled RS-NGMV control.This research presents the Restricted Structure Non-linear Generalized Minimum Variance (RS-NGMV) algorithm for Linear Parameter-Varying (LPV) systems. The LPV systems are defined as linear plant subsystems within the control diagram and may include Non-linear (NL) input subsystems. The RS-NGMV control solution for the latter will be slightly different than the first one and have the capability of dealing with NL characteristics such as saturation, discontinuities and black-box terms. The controller is built in a low-order Restricted Structure (RS) in the form of a general z-transfer function. This brings forward two major advantages. First, it offers a high-order advanced control solution inside low-order control structures which are known for their natural robustness. Secondly, it is easier to operate and re-tune for the classically trained staff in the industry as it can be given the structures they are rather familiar with such as the PID. Another advantage of the RS-NGMV is its model-based design that enables a faster adaptation to implement different systems. Features of the RS-NGMV are investigated throughout the thesis with case studies from trends in engineering like robotics, autonomous and electric vehicles. The results show that the RS-NGMV is highly capable of adapting to set-point changes, parameter variations with its ability to update the control gains rapidly by using optimizations. Some extensions of algorithms have also been studied following recent directions in optimal/predictive control resulting in a new preview control approach and Scheduled RS-NGMV control

Analysis and design of quadratic parameter varying (QPV) control systems with polytopic attractive region

© . This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/This paper proposes a gain-scheduling approach for systems with a quadratic structure. Both the stability analysis and the state-feedback controller design problems are considered for quadratic parameter varying (QPV) systems. The developed approach assesses/enforces the belonging of a polytopic region of the state space to the region of attraction of the origin, and relies on a linear matrix inequality (LMI) feasibility problem. The main characteristics of the proposed approach are illustrated by means of examples, which confirm the validity of the theoretical results.Peer ReviewedPostprint (author's final draft

Design of shifting output-feedback controllers for LPV systems subject to time-varying saturations

This paper considers the problem of designing a shifting output-feedback controller for polytopic linear parameter-varying (LPV) systems subject to time-varying saturations. By means of the LPV framework and the use of the Lyapunov theory, the shifting paradigm concept, and the ellipsoidal invariant theory, a linear matrix inequality (LMI)-based methodology for the controller's design is proposed. The resulting gain-scheduled controller holds the control action in the linearity region of the actuators and regulates online the closed-loop convergence taking into account the instantaneous saturation limit values. The proposed approach is validated by means of an illustrative example.This work has been partially funded by the Spanish State Research Agency (AEI) and the European Regional Development Fund (ERFD) through the project SaCoAV (ref. PID2020-114244RB-I00). This work has also been partially funded by AGAUR of Generalitat de Catalunya through the Advanced Control Systems (SAC) group grant (2017 SGR 482) and by the University of Stavanger through the project IN-12267. A. Ruiz is also supported by the Secretaria d’Universitats i Recerca de la Generalitat de Catalunya, the European Social Fund (ESF) and AGAUR under a FI SDUR grant (ref. 2020 FI-SDUR 00097).Peer ReviewedPostprint (published version

Linear Parameter-Varying Embedding of Nonlinear Models with Reduced Conservativeness

In this paper, a systematic approach is developed to embed the dynamical description of a nonlinear system into a linear parameter-varying (LPV) system representation. Initially, the nonlinear functions in the model representation are approximated using multivariate polynomial regression. Taking into account the residuals of the approximation as the potential scheduling parameters, a principle component analysis (PCA) is conducted to introduce a limited set of auxiliary scheduling parameters in coping with the trade-o? between model accuracy and complexity. In this way, LPV embedding of the nonlinear systems and scheduling variable selection are jointly performed such that a good trade-o? between complexity and conservativeness can be found. The developed LPV model depends polynomially on some of the state variables and affinely on the introduced auxiliary scheduling variables, which all together comprise the overall scheduling vector. The methodology is applied to a two-degree of freedom (2-DOf) robotic manipulator in addition to an academic example to reveal the effectiveness of the proposed method and to show the merits of the presented approach compared with some available results in the literature.Comment: 7 pages, 2 figures, IFAC World Congress, Berlin, 202

Development of linear parameter varying control system for autonomous underwater vehicle

The development and application of Linear Parameter Varying (LPV) control system for robust longitudinal control system on an Autonomous Underwater Vehicle (AUV) are presented. The LPV system is represented as Linear Fractional Transformation (LFT) on its parameter set. The LPV control system combines LPV theory based upon Linear Matrix Inequalities (LMIs) and - synthesis to form a robust LPV control system. The LPV control design is applied for a pitch control of the AUV to fulfill control design criteria on frequency and time domain. The final closed-loop system is tested for robust stability throughout the operational envelope

Flexible-Link Robot Control Using a Linear Parameter Varying Systems Methodology

This paper addresses the issues of the Linear Parameter Varying (LPV) modelling and control of flexible-link robot manipulators. The LPV formalism allows the synthesis of nonlinear control laws and the assessment of their closed-loop stability and performances in a simple and effective manner, based on the use of Linear Matrix Inequalities (LMI). Following the quasi-LPV modelling approach, an LPV model of a flexible manipulator is obtained, starting from the nonlinear dynamic model stemming from Euler-Lagrange equations. Based on this LPV model, which has a rational dependence in terms of the varying parameters, two different methods for the synthesis of LPV controllers are explored. They guarantee the asymptotic stability and some level of closed-loop ℒ 2 -gain performance on a bounded parametric set. The first method exploits a descriptor representation that simplifies the rational dependence of the LPV model, whereas the second one manages the troublesome rational dependence by using dilated LMI conditions and taking the particular structure of the model into account. The resulting controllers involve the measured state variables only, namely the joint positions and velocities. Simulation results are presented that illustrate the validity of the proposed control methodology. Comparisons with an inversion-based nonlinear control method are performed in the presence of velocity measurement noise, model uncertainties and high-frequency inputs