The Lyapunov stability theory-based adaptive filter (LST-AF) is a robust filtering algorithm which the tracking error quickly converges to zero asymptotically. Recently, the software module of the LST-AF algorithm is effectively used in engineering applications such as tracking, prediction, noise cancellation and system identification problems. Therefore, hardware implementation becomes necessary in many cases where real time procedure is needed. In this paper, an implementation of the LST-AF algorithm on Field Programmable Gate Arrays (FPGA) is realized for the first time to our knowledge. The proposed hardware implementation on FPGA is performed for two main benchmark problems; i) tracking of an artificial signal and a Henon chaotic signal, ii) estimation of filter parameters using a system identification model. Experimental results are comparatively presented to test accuracy, performance and logic occupation. The results show that our proposed hardware implementation not only conserves the capabilities of software versions of the LST-AF algorithm but also achieves a better performance than them.

Fuzzy cognitive maps (FCMs) are used to support decision-making, and the decision processes are performed by inference of FCMs. The inference greatly depends on activation functions such as sigmoid function, hyperbolic tangent function, step function, and threshold linear function. However, the sigmoid functions widely used for decision-making processes have been designed by experts. Therefore, we propose a method for designing sigmoid functions through Lyapunov stability analysis. We show the usefulness of the proposed method through the experimental results in inference of FCMs using the designed sigmoid functions.

In supervisory control, discrete event dynamic systems (DEDSs) are modeled by finite-state automata, and their behaviors described by the associated formal languages; control is exercised by a supervisor, whose control action is to enable or disable the controllable events. In this paper we present a general stability concept for DEDSs, stability in the sense of Lyapunov with resiliency, by incorporating Lyapunov stability concepts with the concept of stability in the sense of error recovery. We also provide algorithms for verifying stability and obtaining a domain of attraction. Relations between the notion of stability and the notion of fault-tolerance are addressed.