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Local exact controllability to the trajectories of the Navier-Stokes system with nonlinear Navier-slip boundary conditions

Sergio Guerrero (2006)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper we deal with the local exact controllability of the Navier-Stokes system with nonlinear Navier-slip boundary conditions and distributed controls supported in small sets. In a first step, we prove a Carleman inequality for the linearized Navier-Stokes system, which leads to null controllability of this system at any time T>0. Then, fixed point arguments lead to the deduction of a local result concerning the exact controllability to the trajectories of the Navier-Stokes system.

Local small time controllability and attainability of a set for nonlinear control system

Mikhail Krastanov, Marc Quincampoix (2001)

ESAIM: Control, Optimisation and Calculus of Variations

In the present paper, we study the problem of small-time local attainability (STLA) of a closed set. For doing this, we introduce a new concept of variations of the reachable set well adapted to a given closed set and prove a new attainability result for a general dynamical system. This provide our main result for nonlinear control systems. Some applications to linear and polynomial systems are discussed and STLA necessary and sufficient conditions are obtained when the considered set is a hyperplane....

Local small time controllability and attainability of a set for nonlinear control system

Mikhail Krastanov, Marc Quincampoix (2010)

ESAIM: Control, Optimisation and Calculus of Variations

In the present paper, we study the problem of small-time local attainability (STLA) of a closed set. For doing this, we introduce a new concept of variations of the reachable set well adapted to a given closed set and prove a new attainability result for a general dynamical system. This provide our main result for nonlinear control systems. Some applications to linear and polynomial systems are discussed and STLA necessary and sufficient conditions are obtained when the considered set...

Locally positive nonlinear systems

Tadeusz Kaczorek (2003)

International Journal of Applied Mathematics and Computer Science

The notion of locally positive nonlinear time-varying linear systems is introduced. Necessary and sufficient conditions for the local positiveness of nonlinear time-varying systems are established. The concept of local reachability in the direction of a cone is introduced, and sufficient conditions for local reachability in the direction of a cone of this class of nonlinear systems are presented.

Maxwell strata in sub-Riemannian problem on the group of motions of a plane

Igor Moiseev, Yuri L. Sachkov (2010)

ESAIM: Control, Optimisation and Calculus of Variations

The left-invariant sub-Riemannian problem on the group of motions of a plane is considered. Sub-Riemannian geodesics are parameterized by Jacobi's functions. Discrete symmetries of the problem generated by reflections of pendulum are described. The corresponding Maxwell points are characterized, on this basis an upper bound on the cut time is obtained.

Model following control system with time delays

Dazhong Wang, Shujing Wu, Wei Zhang, Guoqiang Wang, Fei Wu, Shigenori Okubo (2016)

Kybernetika

Design of model following control system (MFCS) for nonlinear system with time delays and disturbances is discussed. In this paper, the method of MFCS will be extended to nonlinear system with time delays. We set the nonlinear part f ( v ( t ) ) of the controlled object as | | f ( v ( t ) ) | | α + β | | v ( t ) | | γ , and show the bounded of internal states by separating the nonlinear part into γ 0 . Some preliminary numerical simulations are provided to demonstrate the effectiveness of the proposed method.

Modeling nonlinear road traffic networks for junction control

Tamás Péter (2012)

International Journal of Applied Mathematics and Computer Science

The paper introduces a method of mathematical modeling of high scale road traffic networks, where a new special hypermatrix structure is intended to be used. The structure describes the inner-inner, inner-outer and outer-outer relations, and laws of a network area. The research examines the nonlinear equation system. The analysed model can be applied to the testing and planning of large-scale road traffic networks and the regulation of traffic systems. The elaborated model is in state space form,...

Modelling and control of an omnidirectional mobile manipulator

Salima Djebrani, Abderraouf Benali, Foudil Abdessemed (2012)

International Journal of Applied Mathematics and Computer Science

A new approach to control an omnidirectional mobile manipulator is developed. The robot is considered to be an individual agent aimed at performing robotic tasks described in terms of a displacement and a force interaction with the environment. A reactive architecture and impedance control are used to ensure reliable task execution in response to environment stimuli. The mechanical structure of our holonomic mobile manipulator is built of two joint manipulators mounted on a holonomic vehicle. The...

Necessary and sufficient Lyapunov-like conditions for robust nonlinear stabilization

Iasson Karafyllis, Zhong-Ping Jiang (2010)

ESAIM: Control, Optimisation and Calculus of Variations

In this work, we propose a methodology for the expression of necessary and sufficient Lyapunov-like conditions for the existence of stabilizing feedback laws. The methodology is an extension of the well-known Control Lyapunov Function (CLF) method and can be applied to very general nonlinear time-varying systems with disturbance and control inputs, including both finite and infinite-dimensional systems. The generality of the proposed methodology is also reflected upon by the fact that partial...

Neural network optimal control for nonlinear system based on zero-sum differential game

Fu Xingjian, Li Zizheng (2021)

Kybernetika

In this paper, for a class of the complex nonlinear system control problems, based on the two-person zero-sum game theory, combined with the idea of approximate dynamic programming(ADP), the constrained optimization control problem is solved for the nonlinear systems with unknown system functions and unknown time-varying disturbances. In order to obtain the approximate optimal solution of the zero-sum game, the multilayer neural network is used to fit the evaluation network, the execution network...

Neural network-based fault diagnosis and fault-tolerant control for nonlinear systems with output measurement noise

Yanjun Shen, Chen Ma, Chenhao Zhao, Zebin Wu (2024)

Kybernetika

In this article, the problems of fault diagnosis (FD) and fault-tolerant control (FTC) are investigated for a class of nonlinear systems with output measurement noise. Due to the influence of measurement noise in the output sensor, the output observation error cannot be accurately obtained, which causes obstacles to the accuracy of FD. To address this issue, an output filter and disturbance estimator are constructed to decrease the negative effects of measurement noise and observer gain disturbances,...

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