Set-membership identification of block-structured nonlinear feedback systems

In this paper a three-stage procedure for set-membership identification of block-structured nonlinear feedback systems is proposed. Nonlinear block parameters bounds are computed in the first stage exploiting steady-state measurements. Then, given the uncertain description of the nonlinear block, bounds on the unmeasurable inner-signal are computed in the second stage. Finally, linear block parameters bounds are computed in the third stage on the basis of output measurements and computed inner signal bounds. Computation of both the nonlinear block parameters and the inner-signal bounds is formulated in terms of semialgebraic optimization and solved by means of suitable convex LMI relaxation techniques. Linear block parameters are bounded solving a number of linear programming problems

Bounding the parameters of block-structured nonlinear feedback systems

In this paper, a procedure for set-membership identification of block-structured nonlinear feedback systems is presented. Nonlinear block parameter bounds are first computed by exploiting steady-state measurements. Then, given the uncertain description of the nonlinear block, bounds on the unmeasurable inner signal are computed. Finally, linear block parameter bounds are evaluated on the basis of output measurements and computed inner-signal bounds. The computation of both the nonlinear block parameters and the inner-signal bounds is formulated in terms of semialgebraic optimization and solved by means of suitable convex LMI relaxation techniques. The problem of linear block parameter evaluation is formulated in terms of a bounded errors-in-variables identification problem

Design of experiments for nonlinear system identification: A set membership approach

Design of Experiments (DoE) is an important step in system identification. Regardless of the chosen model structure and identification method, the DoE quality determines an upper bound on the accuracy of the identified models. One of the greatest challenges in this context is to design an experiment which gives the maximum information about the dynamics of the system of interest. In this paper, a novel DoE algorithm for input-constrained MISO nonlinear systems, based on set membership identification, is proposed. The DoE algorithm is aimed to minimize the so-called radius of information, a quantity giving the worst-case model error. Two numerical examples are presented, showing the effectiveness of the approach and its potential in view of real-world applications

Universal Approximation of a Class of Interval Type-2 Fuzzy Neural Networks in Nonlinear Identification

Neural networks (NNs), type-1 fuzzy logic systems (T1FLSs), and interval type-2 fuzzy logic systems (IT2FLSs) have been shown to be universal approximators, which means that they can approximate any nonlinear continuous function. Recent research shows that embedding an IT2FLS on an NN can be very effective for a wide number of nonlinear complex systems, especially when handling imperfect or incomplete information. In this paper we show, based on the Stone-Weierstrass theorem, that an interval type-2 fuzzy neural network (IT2FNN) is a universal approximator, which uses a set of rules and interval type-2 membership functions (IT2MFs) for this purpose. Simulation results of nonlinear function identification using the IT2FNN for one and three variables and for the Mackey-Glass chaotic time series prediction are presented to illustrate the concept of universal approximation

Set membership fault detection for nonlinear dynamic systems

In this chapter, an innovative approach to fault detection for nonlinear dynamic systems is proposed, based on the recently introduced quasi-local set membership- identification method, overcoming some relevant issues proper of the “classical” techniques. The approach is based on the direct identification from experimental data of a suitable filter and related uncertainty bounds. These bounds are used to detect when a change (e.g., a fault) has occurred in the dynamics of the system of inter- est. The main advantage of the approach compared to the existing methods is that it avoids the utilization of complex modeling and filter design procedures, since the filter/observer is directly designed from data. Other advantages are that the approach does not require to choose any threshold (as typically done in many “classical” tech- niques), and it is not affected by under-modeling problems. An experimental study regarding fault detection for a drone actuator is finally presented to demonstrate the effectiveness of the proposed approach

New methods for the estimation of Takagi-Sugeno model based extended Kalman filter and its applications to optimal control for nonlinear systems

This paper describes new approaches to improve the local and global approximation (matching) and modeling capability of Takagi–Sugeno (T-S) fuzzy model. The main aim is obtaining high function approximation accuracy and fast convergence. The main problem encountered is that T-S identification method cannot be applied when the membership functions are overlapped by pairs. This restricts the application of the T-S method because this type of membership function has been widely used during the last 2 decades in the stability, controller design of fuzzy systems and is popular in industrial control applications. The approach developed here can be considered as a generalized version of T-S identification method with optimized performance in approximating nonlinear functions. We propose a noniterative method through weighting of parameters approach and an iterative algorithm by applying the extended Kalman filter, based on the same idea of parameters’ weighting. We show that the Kalman filter is an effective tool in the identification of T-S fuzzy model. A fuzzy controller based linear quadratic regulator is proposed in order to show the effectiveness of the estimation method developed here in control applications. An illustrative example of an inverted pendulum is chosen to evaluate the robustness and remarkable performance of the proposed method locally and globally in comparison with the original T-S model. Simulation results indicate the potential, simplicity, and generality of the algorithm. An illustrative example is chosen to evaluate the robustness. In this paper, we prove that these algorithms converge very fast, thereby making them very practical to use

A unified framework for solving a general class of conditional and robust set-membership estimation problems

In this paper we present a unified framework for solving a general class of problems arising in the context of set-membership estimation/identification theory. More precisely, the paper aims at providing an original approach for the computation of optimal conditional and robust projection estimates in a nonlinear estimation setting where the operator relating the data and the parameter to be estimated is assumed to be a generic multivariate polynomial function and the uncertainties affecting the data are assumed to belong to semialgebraic sets. By noticing that the computation of both the conditional and the robust projection optimal estimators requires the solution to min-max optimization problems that share the same structure, we propose a unified two-stage approach based on semidefinite-relaxation techniques for solving such estimation problems. The key idea of the proposed procedure is to recognize that the optimal functional of the inner optimization problems can be approximated to any desired precision by a multivariate polynomial function by suitably exploiting recently proposed results in the field of parametric optimization. Two simulation examples are reported to show the effectiveness of the proposed approach.Comment: Accpeted for publication in the IEEE Transactions on Automatic Control (2014

On the interpretation and identification of dynamic Takagi-Sugenofuzzy models

Dynamic Takagi-Sugeno fuzzy models are not always easy to interpret, in particular when they are identified from experimental data. It is shown that there exists a close relationship between dynamic Takagi-Sugeno fuzzy models and dynamic linearization when using affine local model structures, which suggests that a solution to the multiobjective identification problem exists. However, it is also shown that the affine local model structure is a highly sensitive parametrization when applied in transient operating regimes. Due to the multiobjective nature of the identification problem studied here, special considerations must be made during model structure selection, experiment design, and identification in order to meet both objectives. Some guidelines for experiment design are suggested and some robust nonlinear identification algorithms are studied. These include constrained and regularized identification and locally weighted identification. Their usefulness in the present context is illustrated by examples