Andreas Schwung

Stability Analysis of Recurrent Fuzzy Systems: A Hybrid System and SOS Approach

This paper presents a new approach to the stability analysis of recurrent fuzzy systems (RFSs). RFSs are rule-based dynamic fuzzy systems that are usually obtained from heuristic or data-driven modeling. In the presented approach, the stability of both continuous-time and discrete-time RFS can be analyzed in a common framework. It is based on the representation of an RFS as a hybrid polynomial system. Due to the polynomial structure, the recently developed method of sum-of-squares (SOS) decomposition along with semidefinite programming can be employed to derive sufficient conditions for the stability of equilibrium points. We consider stability analysis for known equilibrium points as well as unknown equilibrium points. The latter results in a two-step procedure. In the first step, a polynomial is constructed. In the second verification step, this polynomial is proven to be a Lyapunov function for the RFS. The applicability of the approach is shown by two systems formulated as a rule-based RFS.

Anwendung zeitdiskreter rekurrenter Fuzzy-Systeme zur Fehlerdiagnose

Zusammenfassung Dieser Beitrag beschreibt die Anwendung zeitdiskreter rekurrenter Fuzzy-Systeme (DRFS) zur Fehlerdetektion und Fehlerisolation. Zum einen wird gezeigt, wie auf Basis datengestützt entworfener DRFS geeignete Residuen gebildet werden können. Zum anderen wird ein Ansatz zur Mehrfehlerisolation mit DRFS präsentiert. Dieser Ansatz basiert auf der Erweiterung klassischer statischer Fuzzy-Systeme zu DRFS. Die Anwendungsmöglichkeiten des Ansatzes werden anhand des Dreitank-Benchmarksystems illustriert.

Stability analysis of continuous-time recurrent fuzzy systems

In this paper, we present a new approach for the stability analysis of continuous-time recurrent fuzzy systems (CTRFS). The approach is based on the representation of a CTRFS as a switched polynomial system, for which a Lyapunov function is constructed in a two step procedure. Both steps are based on semidefinite programming. The applicability is shown by an ecological system formulated as a rule based structure.

Fault diagnosis of dynamical systems using recurrent fuzzy systems with application to an electrohydraulic servo axis

This paper presents a novel approach for fault isolation based on discrete-time recurrent fuzzy systems (DTRFS) extending the well-known static fuzzy systems for fault isolation. The DTRFS additionally allows for the isolation of faults causing dynamic residuals and the isolation of multiple subsequently occurring faults. Due to the flexibility of the DTRFS, multiplicative as well as additive faults can be handled. The approach is applied to an electrohydraulic servo axis with a duplex valve system. Experimental results at the testbed underline the effectiveness and applicability of the approach and show the enhanced performance compared to static fuzzy systems and state automata.

Sum of squares approaches for control of continuous-time recurrent fuzzy systems

In recent years, a concise theory of recurrent fuzzy systems has emerged and methods for utilizing these fuzzy systems with dynamics for modeling and fault detection were developed. At the same time, sum of squares decompositions in conjunction with semidefinite programming were successfully applied for the synthesis of controllers for polynomial systems. In this paper, we combine both approaches and present sum of squares based control strategies for continuous-time recurrent fuzzy systems. The system dynamics under consideration is defined by gradients at discrete points in the input-state space. An alternative description as piecewise polynomial system is possible. This motivates to utilize a controller switching between local polynomial control laws. We propose three different approaches for controller synthesis based on this idea and demonstrate this new synthesis method by means of an example. In addition, advantages and drawbacks of the approaches are discussed.

Modeling with discrete-time recurrent fuzzy systems via mixed-integer optimization

In this paper, we present a new approach for modeling of dynamical systems with discrete-time recurrent fuzzy systems (DTRFS). The modeling problem is divided into two subproblems. The first subproblem considers the identification of the rule base of the DTRFS which can be interpreted as structural modeling. This problem is recast into integer and mixed-integer optimization problems respectively dependent on the chosen cost function and system structure. The second subproblem considers the optimization of the parameters of the system, i.e., quantitative modeling. As a result, we obtain a linguistically interpretable model of the dynamical system which additionally can be interpreted as a linguistic automaton. The applicability of the approach is shown by modeling a thermofluidic process.

Nonlinear system modeling via hybrid system representation of recurrent fuzzy systems

This paper proposes a new approach to system modeling using continuous-time recurrent fuzzy systems (CTRFS). The approach is based on the representation of CTRFS as hybrid systems. With this representation, various forms of a priori knowledge about the system to be modeled can be incorporated. This allows a reasonable reduction of optimization parameters and hence, avoids overfitting. Furthermore, the presented approach offers a deeper insight into the system structure on the basis of measurement data solely. This is illustrated by a selection algorithm for relevant input and state variables. The applicability of the approach is shown by modeling a chemical process.

Flatness-based feedforward control for fast operating point transitions of compressor systems

This paper presents a novel approach to the control of fast operating point transitions of compression systems for gas turbines. A nonlinear model of the compression system is derived and shown to be flat. Based on the flatness property a feedforward control for a two-degree of freedom controller is designed, which permits fast transitions between operating points. Results obtained with a complex nonlinear simulation model of the compressor system show the improved performance of the proposed control concept compared to an existing one.

Nonlinear decoupling control of compressor systems for fast load transients in combined cycle power plants

This paper presents a novel approach to the control of compressor systems used for the supply of fuel gas to gas turbines in combined cycle power plants. A model for the compression system is derived first and special attention is paid to an accurate description of the compressor map. Due to the strong coupling of the nonlinear dynamics of the compression system a nonlinear decoupling control concept is required. The presented approach is based on a gain-scheduled decoupling controller. The proposed control concept is validated with a complex nonlinear simulation model of an industrial compressor.

Modellierung dynamischer Systeme mit zeitkontinuierlichen rekurrenten Fuzzy-SystemenModeling of Dynamical Systems Using Continuous-time Recurrent Fuzzy Systems

Zusammenfassung In diesem Beitrag wird die Anwendung zeitkontinuierlicher rekurrenter Fuzzy-Systeme (KRFS) zur Modellbildung technischer Systeme beschrieben. Ausgehend von der Systembeschreibung rekurrenter Fuzzy-Systeme werden Verfahren vorgestellt, mit denen das KRFS das Verhalten des Prozesses anhand von Messdaten und qualitativem Prozesswissen erlernen kann. Die Leistungsfähigkeit wird anhand der Modellierung eines biotechnologischen Prozesses gezeigt.