Learning and Replication of Periodic Signals in Neural-Like Networks

The paper describes the concepts and background theory for the analysis of a neural-like network for learning and replication of periodic signals containing a finite number of distinct frequency components. The approach is based on the combination of ideas from dynamic neural networks and systems and control theory where concepts of dynamics, adaptive control and tracking of specified time signals are fundamental. The proposed procedure is a two stage process consisting of a learning phase when the network is driven by the required signal followed by a replication phase where the network operates in an autonomous feedback mode whilst continuing to generate the required signal to a desired acccuracy for a specified time. The analysis draws on currently available control theory and, in particular, on concepts from model reference adaptive control

Canonical forms for linear systems

AbstractThis paper considers canonical forms for the similarity action of Gl(n) on ∑n,m={(A,B)∈Cn·n×Cn·m}: Gl(n×∑n,m→∑n,m, (H,(A,B))↦(HAH-1,HB) Those canonical forms are obtained as an application of a more general method to select canonical elements Mc in the orbits OM of a matrix group G acting on a set of matrices M⊂Cl·p. We define a total order (≺) on Cl·p, different from the lexicographic order l≺ [0l≺x ⇔ x <0, but 0≺x≠0 for x∈R] and consider normalized OM-elements with a minimal number of parameters: min{M̌∈OM:M̌ normalized} It is shown that the row and column echelon forms, the Jordan canonical form, and “nice” control canonical forms for reachable (A,B)-pairs have a homogeneous interpretation as such (≺)-minimal orbit elements. Moreover new canonical forms for the general action (≺) are determined via this method

Parameter Influence On The Zeros Of Network­Determinants

To a network N(q) with determinant D(s;q) depending on a parameter vector q Î Rr via identification of some of its vertices, a network N^ (q) is assigned. The paper deals with procedures to find N^ (q), such that its determinant D^ (s;q) admits a factorization in the determinants of appropriate subnetworks, and with the estimation of the deviation of the zeros of D^ from the zeros of D. To solve the estimation problem state space methods are applied

Adaptive Synchronization of Interconnected Linear Systems

In this paper we introduce the concept of an adaptive synchronization controller. Synchronization is modelled as an adaptive tracking problem for families of interconnected linear systems. Stabilization and tracking results are obtained for minimum phase systems

Multiparameter, Polynomial Adaptive Tracking for Minimum Phase Systems

A multiparameter, polynomial feedback strategy is introduced to solve the universal adapative tracking problem for a class of multivariable minimum phase system and reference signals generated by a known linear time-invariant differential equation. For 2-input, 2-output, minimum phase systems (A,B,C) with det(CB)0, a different polynomial tracking controller is given which does not invoke a spectrum unmixing set

Adaptive Tracking for Scalar Minimum Phase Systems

We present the concept of a universal adaptive tracking controller for classes of linear systems. For the class of scalar minimum phase systems of relative degree one, adaptive tracking is shown for arbitrary finite dimensional reference signals. The controller requires no identificaiton of the system parameters. Robustness properties are explored

Sufficient Conditions for Adaptive Stabilization and Tracking

We consider universal adaptive stabilization and tracking controllers for classes of linear systems. Under the technical assumption of linear scaling invariance necessary and sufficient conditions for adaptive stabilization are derived. For scalar systems sufficient conditions for adaptive tracking of finite dimensional reference signals are explored