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Relaxed formulation of the design conditions for Takagi-Sugeno fuzzy virtual actuators

Filasova A., Krokavec D., Liscinsky P.

Archives of Control Sciences

2016

Vol. 26, no. 2

199--221

The H∞ norm approach to virtual actuators design, intended to Takagi-Sugeno fuzzy continuous-time systems, is presented in the paper. Using the second Ljapunov method, the design conditions are formulated in terms of linear matrix inequalities in adapted bounded real lemma structures. Related to the static output controller, and for systems under influence of single actuator faults, the design steps are revealed for a three-tank system plant.

An approach to the analysis of observability and controllability in nonlinear systems via linear methods

Zhirabok A., Shumsky A.

International Journal of Applied Mathematics and Computer Science

2012

Vol. 22, no. 3

507-522

The paper is devoted to the problem of observability and controllability analysis in nonlinear dynamic systems. Both continuous- and discrete-time systems described by nonlinear differential or difference equations, respectively, are considered. A new approach is developed to solve this problem whose features include (i) consideration of systems with non-differentiable nonlinearities and (ii) the use of relatively simple linear methods which may be supported by existing programming systems, e.g.,Matlab. Sufficient conditions are given for nonlinear unobservability/uncontrollability analysis. To apply these conditions, one isolates the linear part of the system which is checked to be unobservable/uncontrollable and, if the answer is positive, it is examined whether or not existing nonlinear terms violate the unobservability/uncontrollability property.

Simulation-based design of monotonically convergent iterative learning control for nonlinear systems

Delchev K.

Archives of Control Sciences

2012

Vol. 22, no. 4

467-480

This paper deals with a simulation-based design of model-based iterative learning control (ILC) for multi-input, multi-output nonlinear time-varying systems. The main problem of the implementation of the nonlinear ILC in practice is possible inadmissible transient growth of the tracking error due to a non-monotonic convergence of the learning process. A model-based nonlinear closed-loop iterative learning control for robot manipulators is synthesized and its tuning depends on only four positive gains of both controllers - the feedback one and the learning one. A simulation-based approach for tuning the learning and feedback controllers is proposed to achieve fast and monotonic convergence of the presented ILC. In the case of excessive growth of transient errors this approach is the only way for learning gains tuning by using classical engineering techniques for practical online tuning of feedback gains.