this work proposes a neural-fuzzy sliding mode control scheme for a hydro-turbine speed governor system. considering the assumption of elastic water hammer, a nonlinear mode of the hydro-turbine governor system is established. by linearizing this mode, a sliding mode controller is designed. the linearized mode is subject to uncertainties. the uncertainties are generated in the process of linear...

In this paper we propose the definition of Mittag-Leffler stability and introduce the fractional Lyapunov direct method. Then we provide the fractional comparison principle. Third, we extend the application of Riemann-Liouville fractional systems by using Caputo fractional systems. Finally, an illustrative example is provided as a proof of concept. keywords Fractional order dynamic system, Nona...

A nonlinear chattering-free sliding mode control method is designed to stabilize fractional chaotic systems with model uncertainties and external disturbances. The main feature of this controller is rapid convergence to equilibrium point, minimize chattering and resistance against uncertainties. The frequency distributed model is used to prove the stability of the controlled system based on dir...

We prove optimality principles for continuous bounded nonnegative viscosity solutions of Hamilton-Jacobi-Bellman equations. In particular we provide a representation formula for viscosity supersolutions as value functions of suitable obstacle control problems. This representation formula is applied to extend the Lyapunov direct method for stability to controlled Ito stochastic differential equa...

This work proposes a neural-fuzzy sliding mode control scheme for a hydro-turbine speed governor system. Considering the assumption of elastic water hammer, a nonlinear mode of the hydro-turbine governor system is established. By linearizing this mode, a sliding mode controller is designed. The linearized mode is subject to uncertainties. The uncertainties are generated in the process of linear...

This paper deals with the stability of continuous-time multidimensional nonlinear systems in the Roesser form. The concepts from 1D Lyapunov stability theory are first extended to 2D nonlinear systems and then to general continuous-time multidimensional nonlinear systems. To check the stability, a direct Lyapunov method is developed. While the direct Lyapunov method has been recently proposed f...