Huashu Qin

Optimal impulsive control in periodic ecosystem

Abstract In this paper, the impulsive exploitation of single species modelled by periodic Logistic equation is considered. First, it is shown that the generally periodic Kolmogorov system with impulsive harvest has a unique positive solution which is globally asymptotically stable for the positive solution. Further, choosing the maximum annual biomass yield as the management objective, we investigate the optimal harvesting policies for periodic logistic equation with impulsive harvest. When the optimal harvesting effort maximizes the annual biomass yield, the corresponding optimal population level, and the maximum annual biomass yield are obtained. Their explicit expressions are obtained in terms of the intrinsic growth rate, the carrying capacity, and the impulsive moments. In particular, it is proved that the maximum biomass yield is in fact the maximum sustainable yield (MSY). The results extend and generalize the classical results of Clark [Mathematical Bioeconomics: The Optimal Management of Renewable Resources, Wiley, New York, 1976] and Fan [Optimal harvesting policy for single population with periodic coefficients, Math. Biosci. 152 (1998) 165–177] for a population described by autonomous or nonautonomous logistic model with continuous harvest in renewable resources.

Energy-Based Stabilization of Forced Hamiltonian Systems with its Application to Power Systems

Abstract The purpose of this paper is twofold. First of all, the stabilization of excitation control of power systems is considered. The system has been formulated as a forced Hamiltonian system with dissipation. Then the energy-based Lyapunov function is constructed to investigate the stability of the forced system. Secondly, the model of the generalized Hamiltonian systems is proposed, which consists of externally supplied energy, dissipation and internal energy source. The state space is described as a manifold equipped with a quadratic tensor field. Global coordinate free model of the generalized Hamiltonian systems is obtained.

Controllability of linear systems in Banach spaces

The problem of controllability of linear systems in Banach spaces is considered. First, some properties of dual semigroups with respect to Lebesgue measure is presented. Then, based on the properties, the criteria for controllability in reflexive Banach spaces are extended to general Banach spaces and some new criteria for controllability are established. An example is presented to show that the scope of controllable systems can be enlarged if the non-traditional space of control functions is used.

Stabilization of minimum phase nonlinear systems by dynamic output feedback

In this paper, the stabilization problem of minimum phase nonlinear systems by dynamic output feedback is investigated. It is shown that if the zero dynamics of an affine nonlinear system is asymptotically stable according to the kth approximation, then the system is stabilizable by dynamic output feedback. The proof is constructive, which provides a method to design the stabilizer. The result is applied to investigating the stabilization problem of the rotating stall in axial flow compressors.

Finite-time stabilizing excitation control of a synchronous generator

Using finite-time control approach, this paper proposes a new design method of non-linear robust excitation controllers of the third-order model in power systems. The finite-time excitation controller obtained here can improve the systems behaviour in several aspects, such as quick convergence and robustness for bounded uncertainties. Simulations show that the finite-time excitation controller is more effective than some other excitation controllers.

A new approach to excitation control of power systems

Using finite-time control approach, this paper proposes a new design method of nonlinear robust excitation controller of the 3rd-order model in power systems. The finite-time excitation controller obtained can improve the system behaviors in several aspects such as quick convergence and robustness for bounded uncertainties. Simulations show that the finite-time excitation controller is more effective than some other excitation controllers.

Nonlinear H∞ Excitation Control Based on Regulation Linearization

Abstract With the help of regulation linearization and H∞ approach, this work presents a design method to lay emphasis on nonlinear H∞ theory for nonlinear robust optimal excitation control of multimachine system. The controller constructed is implemented via purely local measurement. Moreover, it is independent of the parameters of power networks. In addition, this paper has verified that the H ∞ control for the regulation linearization system is equivalent to a nonlinear H ∞ control for the primitive nonlinear control system in the sense of differential game theory.

Bifurcation stabilization of nonlinear systems by dynamic output feedback with application to rotating stall control

The paper deals with the problem of stabilization of stationary bifurcation solutions of nonlinear systems via dynamic output feedback. It is emphasized that the parameter of the system is not directly available. We introduce the concepts of uniform observability of the inverse of a function of state and input and N-orderinput-to-state bifurcation stability. Based on the concepts, we propose a new method for designing dynamic compensators that guarantee bifurcation stability for the closed-loop system. As an example, we apply the general theory to active control of rotating stall in axial flow compressors by designing a stabilizing dynamic compensator for the three-state Moore-Greitzer model with a class of cubic compressor characteristics.

Bifurcation control of rotating stall in axial flow compressors via dynamic output feedback

This paper deals with the problem of bifurcation control of rotating stall in axial flow compressors via output feedback. The pressure rise of the compressor is the only measurable output. For some classes of the compressor cubic characteristic curves, the problem of output feedback control of rotating stall had been solved. Based on the theory of center manifolds, we present a method of designing dynamic compensators for the compressors with a general cubic characteristic curve. The dynamic compensators can guarantee that the closed loop systems have bifurcation stability.

Dynamic output feedback stabilization of partially linear composite systems

Abstract The problem of stabilization by dynamic output feedback is investigated for partially linear composite systems. The main result is that if the linear subsystem has no unstable zero points and the nonlinear subsystem is homogeneously asymptotically stable, then the system is stabilizable by dynamic output feedback. A corollary of the result is that a minimum phase nonlinear system with the homogeneously asymptotically stable zero dynamics is stabilizable by dynamic output feedback. The controller is linear and can be constructed explicitly.