A review of convex approaches for control, observation and safety of linear parameter varying and Takagi-Sugeno systems

This paper provides a review about the concept of convex systems based on Takagi-Sugeno, linear parameter varying (LPV) and quasi-LPV modeling. These paradigms are capable of hiding the nonlinearities by means of an equivalent description which uses a set of linear models interpolated by appropriately defined weighing functions. Convex systems have become very popular since they allow applying extended linear techniques based on linear matrix inequalities (LMIs) to complex nonlinear systems. This survey aims at providing the reader with a significant overview of the existing LMI-based techniques for convex systems in the fields of control, observation and safety. Firstly, a detailed review of stability, feedback, tracking and model predictive control (MPC) convex controllers is considered. Secondly, the problem of state estimation is addressed through the design of proportional, proportional-integral, unknown input and descriptor observers. Finally, safety of convex systems is discussed by describing popular techniques for fault diagnosis and fault tolerant control (FTC).Peer ReviewedPostprint (published version

A survey on gain-scheduled control and filtering for parameter-varying systems

Copyright © 2014 Guoliang Wei 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.This paper presents an overview of the recent developments in the gain-scheduled control and filtering problems for the parameter-varying systems. First of all, we recall several important algorithms suitable for gain-scheduling method including gain-scheduled proportional-integral derivative (PID) control, H 2, H ∞ and mixed H 2 / H ∞ gain-scheduling methods as well as fuzzy gain-scheduling techniques. Secondly, various important parameter-varying system models are reviewed, for which gain-scheduled control and filtering issues are usually dealt with. In particular, in view of the randomly occurring phenomena with time-varying probability distributions, some results of our recent work based on the probability-dependent gain-scheduling methods are reviewed. Furthermore, some latest progress in this area is discussed. Finally, conclusions are drawn and several potential future research directions are outlined.The National Natural Science Foundation of China under Grants 61074016, 61374039, 61304010, and 61329301; the Natural Science Foundation of Jiangsu Province of China under Grant BK20130766; the Program for Professor of Special Appointment (Eastern Scholar) at Shanghai Institutions of Higher Learning; the Program for New Century Excellent Talents in University under Grant NCET-11-1051, the Leverhulme Trust of the U.K., the Alexander von Humboldt Foundation of Germany

Gain-Scheduled Fault Detection Filter For Discrete-time LPV Systems

The present work investigates a fault detection problem using a gain-scheduled filter for discrete-time Linear Parameter Varying systems. We assume that we cannot directly measure the scheduling parameter but, instead, it is estimated. On the one hand, this assumption imposes the challenge that the fault detection filter should perform properly even when using an inexact parameter. On the other, it avoids the burden associated with designing a complex estimation process for this parameter. We propose three design approaches: the ${\mathcal {H}_{2}}$ , ${\mathcal {H}_{\infty }}$ , and mixed ${\mathcal {H}_{2}} / {\mathcal {H}_{\infty }}$ gain-scheduled Fault Detection Filters designed via Linear Matrix Inequalities. We also provide numerical simulations to illustrate the applicability and performance of the proposed novel methods

Observer-based controllers with data dropout rate adaptation

In this work, we address the observer-based control problem for networked control systems with an unknown time-varying packet arrival rate (PAR) and under root mean square-norm bounded disturbances. We assume packetized transmissions of both measurement and control input through a communication network with successful delivery acknowledgement. Using the measurement reception state and the control transmission acknowledgement, we derive a filter to estimate the PAR. We consider that the PAR changes sporadically from a constant value to another one; that is, it has two different behaviours: transient and steady state. While the observer only updates the state estimation using the current received measurements, the controller computes the control action employing the current state estimation and the previous applied control input. We propose to schedule both the observer and controller with rational functions of the PAR estimation. We show that the separation principle applies, and then, seeking higher performance accuracy, we develop an optimization math formula observer and controller design procedure that considers the two possible behaviours of the PAR. This optimization procedure attempts to maximize the estimation and control performances for each of the possible constant values of the PAR while offering robustness against PAR estimation errors and variations of the PAR. By exploiting sum-of-squares decomposition techniques, the design procedure involves an optimization problem over polynomials. A numerical example illustrates the effectiveness of the proposed approach.This work has been supported by MICINN project number TEC2015-69155-R from the Spanish government, project number P1·1B2015-42 and grant PI15734 from Universitat Jaume I

Robust Guaranteed Cost Output-Feedback Gain-Scheduled Controller Design

In the paper a new robust guaranteed cost output-feedback gain-scheduled PID controller design technique is presented for affine linear parameter-varying systems under polytopic model uncertainty, with the assumption that the scheduled parameters are affected with absolute uncertainty. The proposed centralized or decentralized method is based on the Bellman-Lyapunov equation, guaranteed cost, and parameter-dependent quadratic stability. The robust stability and performance conditions are translated to an optimization problem subject to bilinear matrix inequalities, which can be solved or further linearized. As the main result, the suggested stability and performance conditions without any restrictions on the controller structure are convex functions of the scheduling and uncertainty parameters. Hence, there is no need for applying multi-convexity or other relaxation techniques and consequently the proposed solution delivers a less conservative design method. The viability of the novel design technique is demonstrated and evaluated through numerical examples

Design of state-feedback controllers for linear parameter varying systems subject to time-varying input saturation

All real-world systems are affected by the saturation phenomenon due to inherent physical limitations of actuators. These limitations should be taken into account in the controller’s design to prevent a possibly severe deterioration of the system’s performance, and may even lead to instability of the closed-loop system. Contrarily to most of the control strategies, which assume that the saturation limits are constant in time, this paper considers the problem of designing a state-feedback controller for a system affected by time-varying saturation limits with the objective to improve the performance. In order to tie variations of the saturation function to changes in the performance of the closed-loop system, the shifting paradigm is used, that is, some parameters scheduled by the time-varying saturations are introduced to schedule the performance criterion, which is considered to be the instantaneous guaranteed decay rate. The design conditions are obtained within the framework of linear parameter varying (LPV) systems using quadratic Lyapunov functions with constant Lyapunov matrices and they consist in a linear matrix inequality (LMI)-based feasibility problem, which can be solved efficiently using available solvers. Simulation results obtained using an illustrative example demonstrate the validity and the main characteristics of the proposed approach.Peer ReviewedPostprint (published version

Generalized robust gain-scheduled PID controller design for affine LPV systems with polytopic uncertainty

In the paper a generalized guaranteed cost output-feedback robust gain-scheduled PID controller synthesis is presented for affine linear parameter-varying systems under polytopic model uncertainty. The controller synthesis is generalized in a sense that it covers robust, robust gain-scheduled, and robust switched (with arbitrary switching algorithm) PID controller design. The proposed centralized/decentralized controller method is based on Bellman–Lyapunov equation, guaranteed cost, and parameter-dependent quadratic stability. The proposed sufficient robust stability and performance conditions are derived in the form of bilinear matrix inequalities (BMI) which can efficiently be solved or further linearized. As the main result, the suggested performance and stability conditions without any restriction on the controller structure are convex functions of the scheduling and uncertainty parameters. Hence, there is no need for applying multi-convexity or other relaxation techniques and consequently the proposed solution delivers a less conservative design method. The viability of the novel design technique is demonstrated and evaluated through numerical examples

Fault detection in uncertain LPV systems with imperfect scheduling parameter using sliding mode observers

This is the author accepted manuscript. The final version is available from the publisher via the DOI in this record.This paper presents a sliding mode fault detection scheme for linear parameter varying (LPV) systems with uncertain or imperfectly measured scheduling parameters. In the majority of LPV systems, it is assumed that the scheduling parameters are exactly known. In reality due to noise or possibly faulty sensors, it is sometimes impossible to have accurate knowledge of the scheduling parameters and a design based on the assumption of perfect knowledge of the scheduling parameters cannot be guaranteed to work well in this situation. This paper proposes a sliding mode observer scheme to reconstruct actuator and sensor faults in a situation where the scheduling parameters are imperfectly known. The efficacy of the approach is demonstrated on simulation data taken from the nonlinear RECONFIGURE benchmark model.This work is supported by the EU-FP7 Grant (FP7-AAT-2012-314544

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

Efficient LMI-based quadratic stabilization of interval LPV systems with noisy parameter measures

none2openL. IETTO; Valentina OrsiniIetto, Leopoldo; Orsini, Valentin