Complex dynamic regimes connected with the noise-induced mixed-mode oscillations in the thermochemical model of flow reactor are studied. It is revealed that the underlying reason of such excitability is in the high stochastic sensitivity of the equilibrium. The problem of stabilization of the excitable equilibrium regimes is investigated. We develop the control approach using feedback regulators which reduce the stochastic sensitivity and keep the randomly forced system near the stable equilibrium. We consider also a case when the information about system state is incomplete. Our new mathematical technique is applied to the stabilization of operating modes in the flow chemical reactors forced by random disturbances.
A new class of controlled time-varying complex dynamical networks with similarity is investigated and a decentralized holographic-structure controller is designed to stabilize the network asymptotically at its equilibrium states. The control design is based on the similarity assumption for isolated node dynamics and the topological structure of the overall network. Network synchronization problems, both locally and globally, are considered on the ground of decentralized control approach. Each sub-controller makes use of the information on the corresponding node's dynamics and the resulting overall controller is composed of those sub-controllers. The overall controller can be obtained by means of a combination of typical control designs and appropriate parametric tuning for each isolated node. Several numerical simulation examples are given to illustrate the feasibility and the efficiency of the proposed control design.
In this paper, we discuss some generalized stability of solutions to a class of nonlinear impulsive evolution equations in the certain piecewise essentially bounded functions space. Firstly, stabilization of solutions to nonlinear impulsive evolution equations are studied by means of fixed point methods at an appropriate decay rate. Secondly, stable manifolds for the associated singular perturbation problems with impulses are compared with each other. Finally, an example on initial boundary value problem for impulsive parabolic equations is illustrated to our theory results.
We consider the local projection finite element method for the discretization of a scalar convection-diffusion equation with a divergence-free convection field. We introduce a new fluctuation operator which is defined using an orthogonal L2 projection with respect to a weighted L2 inner product. We prove that the bilinear form corresponding to the discrete problem satisfies an inf-sup condition with respect to the SUPG norm and derive an error estimate for the discrete solution.
A cascade scheme for passivity-based stabilization of a wide class of nonlinear systems is proposed in this paper. Starting from the definitions and basic concepts of passivity-based stabilization via feedback (which are applicable to minimum phase nonlinear systems expressed in their normal forms) a cascade stabilization scheme is proposed for minimum and non-minimum phase nonlinear systems where the constraint of stable zero dynamics imposed by previous stabilization approaches is abandoned. Simulation results of the proposed algorithm are presented to demonstrate its performance.
In this paper, an intermittent control approach with multiple switched periods is proposed for the robust exponential stabilization of uncertain complex-variable delayed nonlinear systems with parameters perturbation, in which the considered complex systems have bounded parametric uncertainties. Based on the Lyapunov stability theory and comparison theorem of differential equations, some stability criteria are established for a class of uncertain complex delayed nonlinear systems with parameters perturbation. Finally, some numerical simulations are given to show the effectiveness and the benefits of the theoretical results.
In this paper, we study the problem of stabilization via homogeneous feedback of single-input homogeneous polynomial systems in the plane. We give a complete classification of systems for which there exists a homogeneous stabilizing feedback that is smooth on R2∖{(0,0)} and preserve the homogeneity of the closed loop system. Our results are essentially based on Theorem of Hahn in which the author gives necessary and sufficient conditions of stability of homogeneous systems in the plane.