Application of the Lyapunov Algorithm to Optimize the Control Strategy of Low-Voltage and High-Current Synchronous DC Generator Systems

In the present study, a novel multiple three-phase low-voltage and high-current permanent magnet synchronous generation system is proposed, which has only half-turn coils per phase. The proposed system is composed of a generator and two confluence plates with 108 rectifier modules. The output can reach up to 10,000 A continuous DC power supply, which is suitable for the outdoors and non-commercial power supply. The application of the Lyapunov algorithm in the synchronous rectification control was optimized. A current sharing loop control was added to the closed-loop control to ensure a stable output voltage and the output current sharing of each rectifier module. Since the two control variables solved by the Lyapunov algorithm were coupled and the negative definite function of the Lyapunov algorithm could not be guaranteed in this system, a simple decoupling method was used to decouple the control variables. Compared to the conventional control, the proposed strategy highly improved the dynamic performance of the system. The effectiveness of the proposed strategy was verified by the simulation. The 5 V/10,000 A hardware experiment platform was built, which proved the feasibility and validity of the proposed strategy for a high-power generation system.

A New Approach to Stable Optimal Control of Complex Nonlinear Dynamical Systems

This paper gives a simple approach to designing a controller that minimizes a user-specified control cost for a mechanical system while ensuring that the control is stable. For a user-given Lyapunov function, the method ensures that its time rate of change is negative and equals a user specified negative definite function. Thus a closed-form, optimal, nonlinear controller is obtained that minimizes a desired control cost at each instant of time and is guaranteed to be Lyapunov stable. The complete nonlinear dynamical system is handled with no approximations/linearizations, and no a priori structure is imposed on the nature of the controller. The methodology is developed here for systems modeled by second-order, nonautonomous, nonlinear, differential equations. The approach relies on some recent fundamental results in analytical dynamics and uses ideas from the theory of constrained motion.

Stability Criterion of Discrete Hopfield Neural Networks with Weighted Function Matrix and one-Delay

In this paper, discrete Hopfield neural networks with weight function matrix(WFM) and delay(DHNNWFMD) are presented. And we obtain an important result that if the WFM is a symmetric function matrix(SFM) and delayed function matrix(DFM) is a diagonally dominant function matrix(DDFM), DHNNWFMD will converge to a state in serial mode and if the WFM is a SFM and non-negative definite function matrix(NFM) and DFM is a DDFM, DHNNWFMD will converge to a state in parallel mode. It provides some theory basis for the application of DHNNWFMD.

On the geodesic distance and group actions on trees

The natural distance function on the vertices of a tree is a kernel of negative type. As a corollary, for any group G acting on a tree X, the length function |g| = d(υ, gυ) is a negative definite function on G for any given vertex υ of X.

Non-symmetric translation invariant Dirichlet forms on hypergroups

In this note translation-invariant Dirichlet forms on a commutative hypergroup are studied. The main theorem gives a characterisation of an invariant Dirichlet form in terms of the negative definite function associated with it. As an illustration constructions of potentials arising from invariant Dirichlet forms are given. The examples of one- and two-dimensional Jacobi hypergroups yield specifications of invariant Dirichlet forms, particularly in the case of Gelfand pairs of compact type.

Remarks on the paper “Transient Markov convolution semi-groups and the associated negative definite functions”

Let X be a locally compact and σ-compact abelian group and let denote the dual group of X. We denote by ξ a fixed Haar measure on X and by the Haar measure associated with ξ. In [2], we show the followingTheorem. Let (αt)t≧0 be a sub-Markov convolution semi-group on X and let ψ be the negative definite function associated with (αt)t≧0. Then (αt)t≧0 is transient if and only if Re (1/ψ) is locally -summable.

Unbounded Negative Definite Functions

Negative definite functions (all definitions are given in § 1 below) on a locally compact, σ-compact group G have been used in several different contexts recently [2, 5, 7, 11]. In this paper we show how such functions relate to other properties such a group may have. Here are six properties which G might have. They are grouped into three pairs with one property of each pair involving negative definite functions. We show that the paired properties are equivalent and, where possible, give counter-examples to other equivalences. We assume throughout that G is not compact.(1A) G does not have property T.(IB) There is a continuous, negative definite function on G which is unbounded.(2A) G has the (weak and/or strong) dual R-L property.(2B) For every closed, non-compact set Q ⊂ G there is a continuous, negative definite function on G which is unbounded on Q.