State and parameter estimation for time-varying systems: A Takagi-Sugeno approach (original) (raw)
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State and Parameter Estimation for Nonlinear Systems: a Takagi-Sugeno Approach
The main contribution of this paper is to propose a systematic approach to observer design for nonlinear Takagi-Sugeno (T-S) time-varying systems. The proposed procedure is based on the sector nonlinearity approach using the convex polytopic transformation. The exact writing of the time-varying nonlinear system as a T-S model allows to provide a state and parameter estimation.
Polytopic Observers for LPV Discrete-Time Systems
Lecture Notes in Control and Information Sciences, 2013
The main goal of this work is to give a general treatment on observer synthesis for LPV systems in the framework of Linear Matrix Inequalities. A special Parameter Dependent Lyapunov Function, called poly-quadratic Lyapunov function, is considered. It incorporates the parameter variations for LPV systems with polytopic parameter dependence and allows to guarantee a so-called poly-quadratic stability which is sufficient to ensure Global Asymptotic Stability. The concept of polytopic observers is introduced. A LMI-based method for the synthesis of this type of observers is proposed. The case when LPV systems are subjected to disturbances or when the parameter is known with a bounded level of uncertainty is further addressed. Conditions to guarantee performances like Input-to-State Stability (ISS), bounded peak-to-peak gain and L2 gain are given. The design of polytopic Unknown Input Observers both in the deterministic and in the noisy or uncertain cases is also presented. Finally, two illustrative examples dealing with polytopic observers for chaos synchronization and air path management of a turbocharged Spark Ignition engine are detailed.
An adaptive observer design approach for discrete-time nonlinear systems
arXiv (Cornell University), 2018
We discuss a design approach for nonlinear discrete-time adaptive observer. This involves transforming a nonlinear system into a quasi-LPV (Linear Parameter Varying) polytopic model in Takagi-Sugeno (T-S) form using nonlinear embedding and sector nonlinearity (SNL) transformation. We then develop a discrete-time counterpart for a joint state and parameter estimation, based on design strategies developed for continuous time models in the existing literature. The design uses a Lyapunov approach and provides an error bounded by L2 gain. Based on this strategy, we propose a design for adaptive observers for nonlinear systems whose T-S form can have unmeasured premise variables.
An adaptive observer design approach for a class of discrete-time nonlinear systems
International Journal of Applied Mathematics and Computer Science, 2018
We consider the problem of joint estimation of states and some constant parameters for a class of nonlinear discrete-time systems. This class contains systems that could be transformed into a quasi-LPV (linear parameter varying) polytopic model in the Takagi-Sugeno (T-S) form. Such systems could have unmeasured premise variables, a case usually overlooked in the observer design literature. We assert that, for such systems in discrete-time, the current literature lacks design strategies for joint state and parameter estimation. To this end, we adapt the existing literature on continuous-time linear systems for joint state and time-varying parameter estimation. We first develop the discrete-time version of this result for linear systems. A Lyapunov approach is used to illustrate stability, and bounds for the estimation error are obtained via the bounded real lemma. We use this result to achieve our objective for a design procedure for a class of nonlinear systems with constant paramet...
An Adaptive Observer Design for Takagi-Sugeno type Nonlinear System
arXiv (Cornell University), 2017
Takagi-Sugeno (T-S) type of polytopic models have been used prominently in the literature to analyze nonlinear systems. With the sector nonlinearity approach, an exact representation of a nonlinear system within a sector could be obtained in a T-S form. Hence, a number of observer design strategies have been proposed for nonlinear systems using the T-S framework. In this work, a design strategy for adaptive observers is presented for a type of T-S systems with unknown parameters. The proposed approach improves upon the existing literature in two folds: reduce the computational burden and provide an algorithmic procedure that would seamlessly connect the state estimation and parameter estimation parts of the observer design. Lyapunov approach is used for the stability analysis and the design procedure. The results are illustrated on a simulation example.
Advances in Science, Technology and Engineering Systems Journal
This paper is an extension of work originally presented in conference name. The goal is to propose new fault detection and fault isolation techniques for a polytypic linear parametervarying system (LPV). In this work, an adaptive observer design is formulated for a given polyquadratic Lyapunov function. Subsequently, new sufficient conditions are given in terms of Linear Matrix Inequalities (LMIs). To show the effectiveness of the proposed algorithm, an illustrative example is included.
2010
This paper deals with the topic of qLPV state-space model based control design in which LMIs are used to optimize the multi-objective control performance. In this paper we investigate how the convex hull of the polytopic model influences the state value estimation of the LMI based control design. We examine these influences through the control design of the two dimensional aeroelastic system's example. First we define various TP type polytopic model representations of a wing section whose vertices define different convex hulls. In the second step we investigate how these models lead to different performances of the state value estimation.
Adaptive polytopic estimation for nonlinear systems under bounded disturbances using moving horizon
2019
This paper introduces an adaptive polytopic estimator design for nonlinear systems under bounded disturbances combining moving horizon and dual estimation techniques. It extends the moving horizon estimation results for LTI systems to polytopic LPV systems. The design and necessary conditions to guarantee the robust stability and convergence to the true state and parameters for the case of bounded disturbances and convergence to the true system and state are given for the vanishing disturbances.
Fixed-time Observer Design for LTI Systems by Time-varying Coordinate Transformation
2020 59th IEEE Conference on Decision and Control (CDC)
In this work, we present a novel fixed-time state observer for LTI systems based on a time-varying coordinate transformation yielding the cancellation of the effect of the unknown initial conditions from the state estimates. This coordinate transformation allows one to map the state of the original system into that of an auxiliary system that evolves from initial conditions that are known by construction. After a stable observer is designed in the transformed coordinates, an estimate for the state of the original system can be obtained by inverting the above-mentioned map. The invertibility of the map is guaranteed for any time strictly greater than zero, so that the convergence time can be made arbitrarily small in nominal conditions. The robustness of the observer with respect to bounded measurement disturbances is characterized in terms of both transient and norm bounds on the asymptotic stateestimation error. Compared to existing finite and fixed-time approaches, the proposed method does not require high-gain output-error injection, state augmentation, delay operators, or moving-windows. The dimensionality of the observer matches that of the observed system, and its realization takes the form of an LTV system.
Actuator fault estimation based adaptive polytopic observer for a class of LPV descriptor systems
International Journal of Robust and Nonlinear Control, 2014
This paper presents an Adaptive Polytopic Observer (APO) design in order to develop an actuator fault estimation method dedicated to polytopic Linear Parameter Varying (LPV) descriptor systems. This paper extends a Fault Diagnosis (FD) method developed for regular LTI systems to polytopic LPV descriptor systems. Here, time-varying actuator faults are also considered whereas in many papers actuator faults are generally assumed to be constant. The design and convergence conditions of this APO are provided. The design is formulated through Linear Matrix Inequalities (LMI) techniques under equality constraints. The performances of the proposed actuator fault estimation scheme are illustrated using an electrical circuit.