Zs. Lendek

Adaptive observers for TS fuzzy systems with unknown polynomial inputs

A large class of nonlinear systems can be well approximated by Takagi-Sugeno (TS) fuzzy models, with linear or affine consequents. However, in practical applications, the process under consideration may be affected by unknown inputs, such as disturbances, faults or unmodeled dynamics. In this paper, we consider the problem of simultaneously estimating the state and unknown inputs in TS systems. The inputs considered in this paper are (1) polynomials in time (such as a bias in the model or an unknown ramp input acting on the model) and (2) unmodeled dynamics. The proposed observer is designed based on the known part of the fuzzy model. Conditions on the asymptotic convergence of the observer are presented and the design guarantees an ultimate bound on the error signal. The results are illustrated on a simulation example.

Sequential stability analysis and observer design for distributed TS fuzzy systems

Many complex physical systems are the interconnection of lower-dimensional subsystems. For such systems, distributed stability analysis and observer design presents several advantages with respect to centralized approaches, such as modularity, easier analysis and design, and reduced computational complexity. Applications include distributed process control, traffic and communication networks, and economic systems. In this paper, we propose sequential stability analysis and observer design for distributed systems where the subsystems are represented by Takagi-Sugeno (TS) fuzzy models. The analysis and design are done sequentially for the subsystems, allowing for the online addition of new subsystems. The conditions are formulated as LMIs and are therefore easy to solve. The approach is illustrated on simulation examples.

Stability analysis and observer design for decentralized TS fuzzy systems

A large class of nonlinear systems can be well approximated by Takagi-Sugeno (TS) fuzzy models, with linear or affine consequents. It is well-known that the stability of these consequent models does not ensure the stability of the overall fuzzy system. Stability conditions developed for TS fuzzy systems in general rely on the feasibility of an associated system of linear matrix inequalities, whose complexity may grow exponentially with the number of rules. We study distributed systems, where the subsystems are represented as TS fuzzy models. For such systems, a centralized analysis is often unfeasible. We analyze the stability of the overall TS system based on the stability of the subsystems and the strength of the interconnection terms. For naturally distributed applications, such as multi-agent systems, when adding new subsystems ldquoon-linerdquo, the construction and tuning of a centralized observer is often intractable. Therefore, we also propose a decentralized approach to observer design. Applications of such systems include distributed process control, traffic networks, and economic systems.

Fuzzy observer for state estimation of the METANET traffic model

Traffic control has proven an effective measure to reduce traffic congestion on freeways. In order to determine appropriate control actions, it is necessary to have information on the current state of the traffic. However, not all traffic states can be measured (such as the traffic density) and so state estimation must be applied in order to obtain state information from the available measurements. Linear state estimation methods are not directly applicable, as traffic models are in general nonlinear. In this paper we propose a nonlinear approach to state estimation that is based on a Takagi-Sugeno (TS) fuzzy model representation of the METANET traffic model. By representing the METANET traffic model as a TS fuzzy system, a structured observer design procedure can be applied, whereby the convergence of the observer is guaranteed. Simulation results are presented to illustrate the quality of the estimate.

Fuzzy models and observers for freeway traffic state tracking

Traffic state estimation is a prerequisite for traffic surveillance and control. For macroscopic traffic flow models several estimation methods have been investigated, including extended and unscented Kalman filters and particle filters. In this paper we propose a fuzzy observer for the continuous time version of the macroscopic traffic flow model METANET. In order to design the observer, we first derive a dynamic Takagi-Sugeno fuzzy model that exactly represents the traffic model of a segment of a highway stretch. The fuzzy observer is designed based on the fuzzy model and applied to the traffic model. The simulation results are promising for the future development of fuzzy observers for a highway stretch or a whole traffic network.

Stability of Cascaded Takagi-Sugeno Fuzzy Systems

A large class of nonlinear systems can be well approximated by Takagi-Sugeno (TS) fuzzy models, with local models often chosen linear or affine. It is well-known that the stability of these local models does not ensure the stability of the overall fuzzy system. Therefore, several stability conditions have been developed for TS fuzzy systems. We study a special class of nonlinear dynamic systems, that can be decomposed into cascaded subsystems. These subsystems are represented as TS fuzzy models. We analyze the stability of the overall TS system based on the stability of the subsystems. For a general nonlinear, cascaded system, global asymptotic stability of the individual subsystems is not sufficient for the stability of the cascade. However, for the case of TS fuzzy systems, we prove that the stability of the subsystems implies the stability of the overall system. The main benefit of this approach is that it relaxes the conditions imposed when the system is globally analyzed, therefore solving some of the feasibility problems. Another benefit is, that by using this approach, the dimension of the associated linear matrix inequality (LMI) problem can be reduced. Applications of such cascaded systems include multi-agent systems, distributed process control and hierarchical large-scale systems.

Stability analysis and observer design for string-connected TS systems

Abstract Distributed systems consist of interconnected, lower-dimensional subsystems. For such systems, distributed analysis and design present several advantages, such as modularity, easier analysis, and reduced computational complexity. Applications include distributed process control, traffic and communication networks, irrigation systems, hydropower valleys, etc. A special case of distributed systems is when the subsystems are connected in a string. By exploiting such a structure, in this paper, we propose conditions for the distributed stability analysis of Takagi-Sugeno fuzzy systems connected in a string. These conditions are extended to observer design. Sufficient LMI conditions, which are easy to solve are also provided. The approach is illustrated on a simulation example.

Cascaded parameter estimation for a water treatment plant using particle filters

Advanced online control of drinking water treatment plants requires reliable models. These models in general involve temperature-dependent, uncertain parameters, which can only be measured in laboratory conditions. We propose to estimate these parameters online, using the available pH quality measurements. Since the pH measurements are a nonlinear combination of the systems states, a particle filter is used. Thanks to the cascaded nature of the plant, the estimation is also performed in a cascaded setting. The performance is evaluated both for simulated and real-world data. Results indicate that the filter can be effectively used to improve the model accuracy.

Erratum to “Adaptive observers for TS fuzzy systems with unknown polynomial inputs” Fuzzy Sets and Systems 161 (2010) 2043--2065]

The description of the error dynamics (30) in our paper 1] contains an omission that leads to some bounds used in the conditions of Theorem 8 and Corollary 2 in the paper to be incorrectly defined. In what follows, the correct error dynamics and the corresponding conditions are given.

Stability bounds for fuzzy estimation and control — Part I: State estimation

Analysis and observer design for nonlinear systems have long been investigated, but no generally applicable methods exist as yet. A large class of nonlinear systems can be well approximated by Takagi-Sugeno fuzzy models, for which methods and algorithms have been developed to analyze their stability and to design observers. However, results obtained for Takagi-Sugeno fuzzy models are in general not directly applicable to the original nonlinear system. In this paper, we investigate what conclusions can be drawn and what guarantees can be expected when an observer is designed based on an approximate fuzzy model and applied to the original nonlinear system. It is shown that in general, exponential stability of the estimation error dynamics cannot be obtained. However, the estimation error is bounded. This bound is computed based on the approximation error and the Lyapunov function used. The results are illustrated using simulation examples.