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Norma Lozada-Castillo,Alexander Poznyak,Isaac Chairez 제어·로봇·시스템학회 2014 International Journal of Control, Automation, and Vol.12 No.5
This article describes the application of the so-called attractive ellipsoidal method to solve the trajectory stabilization problem for a class of genetic network systems modelled by a stochastic model. The genetic network model is described by a stochastic quasi-linear system affected by additive and multiplicative noises simultaneously. The solution of the control design provided in this study is based on a linear feedback structure. In this paper the algorithm to construct a suboptimal gain for adjusting the control design is introduced. The attractive ellipsoidal method is the key stone for designing the so-called suboptimal gain. Moreover, the practical stability of the genetic network trajectories is demonstrated on the mean and in almost sure senses. Some numerical simulations show how a set of stochastic trajectories are stabilized by the controller suggested in this study and how the predicted ellipsoid region is achieved by these trajectories.
Yair Lozano Hernández,Octavio Gutiérrez Frías,Norma Lozada-Castillo,Alberto Luviano Juárez 제어·로봇·시스템학회 2019 International Journal of Control, Automation, and Vol.17 No.9
This paper presents a control algorithm for the taking off and landing manoeuvres of a quadrotor aircraft in open navigation environments. For this purpose, a combination of controllers based on nested saturations and a generalised proportional integral (GPI) controller is used. The first controller limits both the angular positions and angular velocities in a small compact set, which defines the closed-loop stability domain and guarantees the total convergence of the state, whereas the second is designed for the translational aspect, considering the presence of disturbances during landing. The proposed controller is designed considering the presence of disturbances; therefore, greater robustness is obtained regarding perturbations that may occur in open navigation environments. The algorithm convergence is proven by means of Lyapunov’s second method. Several numerical simulations are presented to demonstrate the effectiveness of our proposed algorithm, and a comparison test against an effective method for indoor environments is provided to illustrate its superior performance.