In this paper, we provide a rigorous mathematical foundation for continuous approximations of a class of systems with piecewise continuous functions. By using techniques from the theory of differential inclusions, the...
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In this paper, we provide a rigorous mathematical foundation for continuous approximations of a class of systems with piecewise continuous functions. By using techniques from the theory of differential inclusions, the underlying piecewisefunctions can be locally or globally approximated. The approximation results can be used to model piecewisecontinuous-time dynamical systems of integer or fractional-order. In this way, by overcoming the lack of numerical methods for differential equations of fractional-order with discontinuous right-hand side, unattainable procedures for systems modeled by this kind of equations, such as chaos control, synchronization, anticontrol and many others, can be easily implemented. Several examples are presented and three comparative applications are studied.
This paper proves analytically that synchronization of a class of piecewisecontinuous fractional-order systems can be achieved. Since there are no dedicated numerical methods to integrate differential equations with ...
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This paper proves analytically that synchronization of a class of piecewisecontinuous fractional-order systems can be achieved. Since there are no dedicated numerical methods to integrate differential equations with discontinuous right-hand sides for fractional-order models, Filippov's regularization (Filippov, Differential Equations with Discontinuous Right-Hand Sides, 1988) is applied, and Cellina's Theorem (Aubin and Cellina, Differential Inclusions Set-valued Maps and Viability Theory, 1984;Aubin and Frankowska, Set-valued Analysis, 1990) is used. It is proved that the corresponding initial value problem can be converted to a continuous problem of fractional-order systems, to which numerical methods can be applied. In this way, the synchronization problem is transformed into a standard problem for continuous fractional-order systems. Three examples are presented: the Sprott's system, Chen's system, and Shimizu-Morioka's system.
In this article, a robust control algorithm using sliding modes is proposed for the efficient regulation on the trajectory tracking tasks, in the nonlinear, multivariable, quadrotor system model, that ensures the asym...
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ISBN:
(纸本)9781479923762
In this article, a robust control algorithm using sliding modes is proposed for the efficient regulation on the trajectory tracking tasks, in the nonlinear, multivariable, quadrotor system model, that ensures the asymptotic convergence to a desired trajectory (reference signal - r (t)) in presence of all possible uncertainties and external disturbances. A smooth piecewise continuous function trajectory is proposed where the corresponding derivatives are bounded. Furthermore, we assume that the disturbances on the vehicle are bounded and the signal r (t) are available on line. The proposed algorithm employs a sliding surface based on the errors generated from the current state of the path in order to reach the desired reference r (t). The stability analysis of the closed-loop control system is proven via the use of Lyapunov theory. Finally, a numerical simulation of tracking a smooth trajectory is performed to demonstrate the validity and effectiveness of the proposed robust algorithm in presence of disturbances onto the vehicle.
In this article, a robust control algorithm using sliding modes is proposed for the efficient regulation on the trajectory tracking tasks, in the nonlinear, multivariable, quadrotor system model, that ensures the asym...
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ISBN:
(纸本)9781479923779
In this article, a robust control algorithm using sliding modes is proposed for the efficient regulation on the trajectory tracking tasks, in the nonlinear, multivariable, quadrotor system model, that ensures the asymptotic convergence to a desired trajectory (reference signal - r(t)) in presence of all possible uncertainties and external disturbances. A smooth piecewise continuous function trajectory is proposed where the corresponding derivatives are bounded. Furthermore, we assume that the disturbances on the vehicle are bounded and the signal r(t) are available on line. The proposed algorithm employs a sliding surface based on the errors generated from the current state of the path in order to reach the desired reference r(t). The stability analysis of the closed-loop control system is proven via the use of Lyapunov theory. Finally, a numerical simulation of tracking a smooth trajectory is performed to demonstrate the validity and effectiveness of the proposed robust algorithm in presence of disturbances onto the vehicle.
In this paper, we obtain a Fredholm index formula for Toeplitz operators whose symbols are certain piecewise continuous function matrices on the unit ball. Moreover, using this formula, we discuss the automorphisms on...
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In this paper, we obtain a Fredholm index formula for Toeplitz operators whose symbols are certain piecewise continuous function matrices on the unit ball. Moreover, using this formula, we discuss the automorphisms on the corresponding Toeplitz algebra.
A universal approximator based on h MOS analog circuits which provides direct analog synthesis of nonlinear functions is described. For this purpose a mathematical approach, founded on rigorous theoretical results and...
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A universal approximator based on h MOS analog circuits which provides direct analog synthesis of nonlinear functions is described. For this purpose a mathematical approach, founded on rigorous theoretical results and able to approximate a continuousfunction with a given small error, is reported. Within the theory it is demonstrated that a piecewise continuous function can be represented with particular sequences of functions, called Dime functions, having certain useful properties. Moreover, it is shown that such functions can be implemented with MOS analog circuits, on the basis of which the architecture of a universal approximator of nonlinear functions is defined.
A mathematical analysis, including existence and uniqueness, is given for some boundary value problems which model the flow of a fluid-solute mixture in a tube which is placed in an interstitium. The model permits an ...
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A mathematical analysis, including existence and uniqueness, is given for some boundary value problems which model the flow of a fluid-solute mixture in a tube which is placed in an interstitium. The model permits an interchange of fluid and solute across the tube walls.
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