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

Fault estimation and active fault tolerant control for linear parameter varying descriptor systems

Starting with the baseline controller design, this paper proposes an integrated approach of active fault tolerant control based on proportional derivative extended state observer (PDESO) for linear parameter varying descriptor systems. The PDESO can simultaneously provide the estimates of the system states, sensor faults, and actuator faults. The L₂ robust performance of the closed-loop system to bounded exogenous disturbance and bounded uncertainty is achieved by a two-step design procedure adapted from the traditional observer-based controller design. Furthermore, an LMI pole-placement region and the L₂ robustness performance are combined into a multiobjective formulation by suitably combing the appropriate LMI descriptions. A parameter-varying system example is given to illustrate the design procedure and the validity of the proposed integrated design approach

Actuator and sensor fault estimation based on a proportional-integral quasi-LPV observer with inexact scheduling parameters

© 2019. ElsevierThis paper presents a method for actuator and sensor fault estimation based on a proportional-integral observer (PIO) for a class of nonlinear system described by a polytopic quasi-linear parameter varying (qLPV) mathematical model. Contrarily to the traditional approach, which considers measurable or unmeasurable scheduling parameters, this work proposes a methodology that considers inexact scheduling parameters. This condition is present in many physical systems where the scheduling parameters can be affected by noise, offsets, calibration errors, and other factors that have a negative impact on the measurements. A H8 performance criterion is considered in the design in order to guarantee robustness against sensor noise, disturbance, and inexact scheduling parameters. Then, a set of linear matrix inequalities (LMIs) is derived by the use of a quadratic Lyapunov function. The solution of the LMI guarantees asymptotic stability of the PIO. Finally, the performance and applicability of the proposed method are illustrated through a numerical experiment in a nonlinear system.Peer ReviewedPostprint (author's final draft

An LPV Fault Tolerant control for semi-active suspension -scheduled by fault estimation

International audienceIn this paper, a novel fault tolerant control is proposed to accommodate damper faults (oil leakages) in a semi-active suspension system based on a quarter-car vehicle model. The fault accommodation is based on the Linear Parameter Varying (LPV) control strategy and involved in 2 steps. At first, a fast time-varying fault is estimated by using the fast adaptive fault estimation (FAFE) algorithm and based on an unknown input adaptive observer. Thanks to information about the estimated fault, the dissipativity domain of the semi-active suspension is adapted according to the fault. Then a single LPV fault tolerant controller is developed to manage the system performances. The controller solution, derived in the LPV/H ∞ framework, is based on the LMI solution for polytopic systems. Some simulation results are presented that show the effectiveness of this approach

Robust inversion based fault estimation for discrete-time LPV systems

The article presents a state-space based Fault Diagnosis (FD) method for discrete-time, affine Linear Parameter Varying (LPV) systems. The goal of the technical note is to develop a robust and dynamic inversion based technique for systems with parameter varying representations when an additive, exogenous disturbance signal perturbs the system. After applying geometric concepts for explicit fault inversion, a robust strategy is proposed to attenuate the effect of the unknown disturbance input signal on the fault estimation error. The proposed robust observer is derived as a solution of off-line Linear Matrix Inequality (LMI) conditions. The technical note demonstrates the viability of the novel methodology through a numerical example

Interval Prediction for Continuous-Time Systems with Parametric Uncertainties

The problem of behaviour prediction for linear parameter-varying systems is considered in the interval framework. It is assumed that the system is subject to uncertain inputs and the vector of scheduling parameters is unmeasurable, but all uncertainties take values in a given admissible set. Then an interval predictor is designed and its stability is guaranteed applying Lyapunov function with a novel structure. The conditions of stability are formulated in the form of linear matrix inequalities. Efficiency of the theoretical results is demonstrated in the application to safe motion planning for autonomous vehicles.Comment: 6 pages, CDC 2019. Website: https://eleurent.github.io/interval-prediction