Stability Of Recurrent Neural Networks Research Articles

Global exponential stability of recurrent neural networks for synthesizing linear feedback control systems via pole assignment

Global exponential stability is the most desirable stability property of recurrent neural networks. The paper presents new results for recurrent neural networks applied to online computation of feedback gains of linear time-invariant multivariable systems via pole assignment. The theoretical analysis focuses on the global exponential stability, convergence rates, and selection of design parameters. The theoretical results are further substantiated by simulation results conducted for synthesizing linear feedback control systems with different specifications and design requirements.

Global exponential stability of recurrent neural networks for solving optimization and related problems

Global exponential stability is a desirable property for dynamic systems. This paper studies the global exponential stability of several existing recurrent neural networks for solving linear programming problems, convex programming problems with interval constraints, convex programming problems with nonlinear constraints, and monotone variational inequalities. In contrast to the existing results on global exponential stability, the present results do not require additional conditions on the weight matrices of recurrent neural networks and improve some existing conditions for global exponential stability. Therefore, the stability results in this paper further demonstrate the superior convergence properties of the existing neural networks for optimization.

NL/sub q/ theory: checking and imposing stability of recurrent neural networks for nonlinear modeling

It is known that many discrete-time recurrent neural networks, such as e.g., neural state space models, multilayer Hopfield networks, and locally recurrent globally feedforward neural networks, can be represented as NL/sub q/ systems. Sufficient conditions for global asymptotic stability and input/output stability of NL/sub q/ systems are available, including three types of criteria: (1) diagonal scaling; (2) criteria depending on diagonal dominance; (3) condition number factors of certain matrices. The paper discusses how Narendra's (1990, 1991) dynamic backpropagation procedure, which is used for identifying recurrent neural networks from I/O measurements, can be modified with an NL/sub q/ stability constraint in order to ensure globally asymptotically stable identified models. An example illustrates how system identification of an internally stable model corrupted by process noise may lead to unwanted limit cycle behavior and how this problem can be avoided by adding the stability constraint.

A learning scheme for dynamic neural networks: Equilibrium manifold and connective stability

Stability of recurrent neural network N: x ̇ i=x i+ ∑ j=1 n e ijw ij8 j(x i)+I i, i=1,2,…,n y i=g i(x i) with learning rule L: e ̇ ij=uh ij(e,y,y ∗), i,j=1,2,…,n is analyzed using the concept of equilibrium manifold. We shall show that the concept provides an ideal setting for the formulation of a learning rule L that adaptively teaches network N to acquire a desired pattern y ∗ as one of its asymptotically stable equilibria. Connective stability of a moving equilibrium in the composite two-time-scale system N & L is established for bounded interconnection weights e ij w ij and a sufficiently small learning rate μ. The conditions for connective stability, which are derived using the M-matrices and the concept of vector Liapunov functions, are suitable for studying the design trade-offs between the bounds on the nominal weights w ij, the shape of the sigmoid function g i(x i), the learning rule h (e, y, y ∗), and rate μ, as well as the size of the stability region containing y ∗.

ON THE ASYMPTOTIC PROPERTIES OF RECURRENT NEURAL NETWORKS FOR OPTIMIZATION

Asymptotic properties of recurrent neural networks for optimization are analyzed. Specifically, asymptotic stability of recurrent neural networks with monotonically time-varying penalty parameters for optimization is proven; sufficient conditions of feasibility and optimality of solutions generated by the recurrent neural networks are characterized. Design methodology of the recurrent neural networks for solving optimization problems is discussed. Operating characteristics of the recurrent neural networks are also presented using illustrative examples.