Exponential stabilization of distributed parameter switched systems under dwell time constraints

The exponential stabilization problem for finite dimensional switched systems is extended to the infinite dimensional distributed parameter systems in the Hilbert space. Based on the semigroup theory, by applying the multiple Lyapunov function method, the exponential stabilization conditions are derived. These conditions are given in the form of linear operator inequalities where the decision variables are operators in the Hilbert space; while the stabilization properties depend on the switching rule. Being applied to the two-dimensional heat switched propagation equations with the Dirichlet boundary conditions, these linear operator inequalities are transformed into standard linear matrix inequalities. Finally, two examples are given to illustrate the effectiveness of the proposed results.

THE EFFECTIVENESS OF GENETIC ALGORITHM IN CAPTURING CONDITIONAL NONLINEAR OPTIMAL PERTURBATION WITH PARAMETERIZATION “ON-OFF” SWITCHES INCLUDED BY A MODEL

In the typhoon adaptive observation based on conditional nonlinear optimal perturbation (CNOP), the ‘on-off’ switch caused by moist physical parameterization in prediction models prevents the conventional adjoint method from providing correct gradient during the optimization process. To address this problem, the capture of CNOP, when the "on-off" switches are included in models, is treated as non-smooth optimization in this study, and the genetic algorithm (GA) is introduced. After detailed algorithm procedures are formulated using an idealized model with parameterization "on-off" switches in the forcing term, the impacts of "on-off" switches on the capture of CNOP are analyzed, and three numerical experiments are conducted to check the effectiveness of GA in capturing CNOP and to analyze the impacts of different initial populations on the optimization result. The result shows that GA is competent for the capture of CNOP in the context of the idealized model with parameterization ‘on-off’ switches in this study. Finally, the advantages and disadvantages of GA in capturing CNOP are analyzed in detail.

Control synthesis of linear distributed parameter switched systems

The control synthesis for switched systems is extended to distributed parameter switched systems in Hilbert space. Based on semigroup and operator theory, by means of multiple Lyapunov method incorporated average dwell time approach, sufficient con- ditions are derived in terms of linear operator inequalities frame- work for distributed parameter switched systems. Being applied to one dimensional heat propagation switched systems, these lin- ear operator inequalities are reduced to linear matrix inequalities subsequently. In particular, the state feedback gain matrices and the switching law are designed, and the state decay estimate is explicitly given whose decay coefficient completely depends on the system＇s parameter and the boundary condition. Finally, two numerical examples are given to illustrate the proposed method.

Stability of multiple fans in mine ventilation networks

In large mines,single fan is usually not enough to ventilate all the working areas.Single mine-fan approach cannot be directly applied to multiple-fan networks because the present of multiple pressures and air quantities associated with each fan in the network.Accordingly,each fan in a multiple-fan system has its own mine characteristic curve,or a subsystem curve.Under some consideration,the conventional concept of a mine characteristic curve of a single-fan system can be directly extended to that of a particular fan within a multiple-fan system.In this paper the mutual effect of the fans on each other and their effect on the stability of the ventilation network were investigated by Hardy Cross algorithm combined with a switching-parameters technique.To show the validity and reliability of this algorithm,the stability of the ventilation system of Abu-Tartur Mine(one of the largest underground mine in Egypt)has been studied.

Tests on the First 500 kV Compact Transmission Line in China

The paper deals with the tests on the first 500 kV compact transmission line. The transmission line stretches from Fangshan Substation to Changping Substation nearby Beijing with a length of 83 km. In order to investigate the characteristics of the transmission line, many tests were performed on the line before and after its operation. The results indicate that all electrical parameters are perfectly identical to the design.

A new piecewise linear Chen system of fractional-order:Numerical approximation of stable attractors

In this paper we present a new version of Chen＇s system： a piecewise linear （PWL） Chert system of fractional-order. Via a sigmoid-like function, the discontinuous system is transformed into a continuous system. By numerical simulations, we reveal chaotic behaviors and also multistability, i.e., the existence of small pararheter windows where, for some fixed bifurcation parameter and depending on initial conditions, coexistence of stable attractors and chaotic attractors is possible. Moreover, we show that by using an algorithm to switch the bifurcation parameter, the stable attractors can be numerically approximated.

Parrondo's paradox for chaos control and anticontrol of fractional-order systems

We present the generalized forms of Parrondo＇s paradox existing in fractional-order nonlinear systems. The gener- alization is implemented by applying a parameter switching （PS） algorithm to the corresponding initial value problems associated with the fractional-order nonlinear systems. The PS algorithm switches a system parameter within a specific set of N 〉 2 values when solving the system with some numerical integration method. It is proven that any attractor of the concerned system can be approximated numerically. By replacing the words ＂winning＂ and ＂loosing＂ in the classical Parrondo＇s paradox with ＂order＂ and ＂chaos＂, respectively, the PS algorithm leads to the generalized Parrondo＇s paradox： chaos1 ＋ chaos2 ＋..- ＋ chaosN = order and order1 ＋ order2 ＋.-. ＋ orderN = chaos. Finally, the concept is well demon- strated with the results based on the fractional-order Chen system.

Non-fragile switched H_∞ control for morphing aircraft with asynchronous switching

This paper deals with the problem of non-fragile linear parameter-varying（LPV） H_∞ control for morphing aircraft with asynchronous switching.The switched LPV model of morphing aircraft is established by Jacobian linearization approach according to the nonlinear model.The data missing is taken into account in the link from sensors to controllers and the link from controllers to actuators,which satisfies Bernoulli distribution.The non-fragile switched LPV controllers are constructed with consideration of the uncertainties of controllers and asynchronous switching phenomenon.The parameter-dependent Lyapunov functional method and mode-dependent average dwell time（MDADT） method are combined to guarantee the stability and prescribed performance of the system.The sufficient conditions on the solvability of the problem are derived in the form of linear matrix inequalities（LMI）.In order to achieve higher efficiency of the designing process,an algorithm is applied to divide the whole set into subsets automatically.Simulation results are provided to verify the effectiveness and superiority of the method in the paper.

Non-fragile switching tracking control for a flexible air-breathing hypersonic vehicle based on polytopic LPV model

This article proposes a linear parameter varying （LPV） switching tracking control scheme for a flexible air-breathing hypersonic vehicle （FAHV）. First, a polytopic LPV model is constructed to represent the complex nonlinear longitudinal model of the FAHV by using Jacobian linearization and tensor-product （T-P） model transformation approach. Second, for less conservative controller design purpose, the flight envelope is divided into four sub-regions and a non-fragile LPV controller is designed for each parameter sub-region. These non-fragile LPV controllers are then switched in order to guarantee the closed-loop FAHV system to be asymptotically stable and satisfy a specified performance criterion. The desired non-fragile LPV switching controller is found by solving a convex constraint problem which can be efficiently solved using available linear matrix inequality （LMI） techniques, and robust stability analysis of the closed-loop FAHV system is verified based on multiple Lypapunov functions （MLFs）. Finally, numerical simulations have demonstrated the effectiveness of the proposed approach.