The Synthesis of Arbitrary Stable Dynamics in Non-linear Neural Networks II: Feedback and Universality

We wish to construct a realization theory of stable neural networks and use this theory to model the variety of stable dynamics apparent in natural data. Such a theory should have numerous applications to constructing specific artificial neural networks with desired dynamical behavior. The networks used in this theory should have well understood dynamics yet be as diverse as possible to capture natural diversity. In this article, I describe a parameterized family of higher order, gradient-like neural networks which have known arbitrary equilibria with unstable manifolds of known specified dimension. Moreover, any system with hyperbolic dynamics is conjugate to one of these systems in a neighborhood of the equilibrium points. Prior work on how to synthesize attractors using dynamical systems theory, optimization, or direct parametric. fits to known stable systems, is either non-constructive, lacks generality, or has unspecified attracting equilibria. More specifically, We construct a parameterized family of gradient-like neural networks with a simple feedback rule which will generate equilibrium points with a set of unstable manifolds of specified dimension. Strict Lyapunov functions and nested periodic orbits are obtained for these systems and used as a method of synthesis to generate a large family of systems with the same local dynamics. This work is applied to show how one can interpolate finite sets of data, on nested periodic orbits.Air Force Office of Scientific Research (90-0128

Accurate Settling-Time Modeling and Design Procedures for Two-Stage Miller-Compensated Amplifiers for Switched-Capacitor Circuits

We present modeling techniques for accurate estimation of settling errors in switched-capacitor (SC) circuits built with Miller-compensated operational transconductance amplifiers (OTAs). One distinctive feature of the proposal is the computation of the impact of signal levels (on both the model parameters and the model structure) as they change during transient evolution. This is achieved by using an event-driven behavioral approach that combines small- and large-signal behavioral descriptions and keeps track of the amplifier state after each clock phase. Also, SC circuits are modeled under closed-loop conditions to guarantee that the results remain close to those obtained by electrical simulation of the actual circuits. Based on these models, which can be regarded as intermediate between the more established small-signal approach and full-fledged simulations, design procedures for dimensioning SC building blocks are presented whose targets are system-level specifications (such as ENOB and SNDR) instead of OTA specifications. The proposed techniques allow to complete top-down model-based designs with 0.3-b accuracy.Ministerio de Educación y Ciencia TEC2006-03022Junta de Andalucía TIC-0281

An autocrine role for pituitary GABA: Activation of GABA-B receptors and regulation of growth hormone levels

There is increasing evidence suggesting that the neurotransmitter gamma-aminobutyric acid (GABA) is a local factor involved in the regulation of endocrine organs. Examples of such functions are documented in the pancreas, but recent results suggest that GABA may act in a similar way in the pituitary, in which GABA receptors are expressed and pituitary growth hormone (GH) cells provide a source of GABA. We hypothesised that GABA secreted in somatotropes may act as an autoregulatory signaling molecule. To test this hypothesis we first examined the nature of GABA receptors expressed by GH cells. RT-PCR analysis demonstrated that GABA-B receptor subunits R1 and R2 are present in the whole rat pituitary. Laser microdissection of immunostained GH cells, followed by RT-PCR as well as immunoelectron microscopy, showed that GABA-B receptors are expressed on somatotropes. To investigate GABA-B receptor function in somatotropes, we used rat GH3 adenoma cells, which, like pituitary GH cells, express GABA-B R1 and R2 (as assessed by RT-PCR and immunoelectron microscopy) and produce GABA (checked by high performance liquid chromatography). After inhibition of endogenous GABA synthesis, GH production was stimulated by baclofen, a chromatography). After inhibition of endogenous GABA synthesis, GH production was stimulated by bactofen, a GABA-B receptor agonist. By contrast, blocking GABA-B receptors by an antagonist, phaclofen, decreased GH levels. We conclude that in GH-producing cells, GABA acts as an autocrine factor via GABA-B receptors to control GH levels. Copyright (C) 2002 S. KargerAG, Basel

Localized LQR Optimal Control

This paper introduces a receding horizon like control scheme for localizable distributed systems, in which the effect of each local disturbance is limited spatially and temporally. We characterize such systems by a set of linear equality constraints, and show that the resulting feasibility test can be solved in a localized and distributed way. We also show that the solution of the local feasibility tests can be used to synthesize a receding horizon like controller that achieves the desired closed loop response in a localized manner as well. Finally, we formulate the Localized LQR (LLQR) optimal control problem and derive an analytic solution for the optimal controller. Through a numerical example, we show that the LLQR optimal controller, with its constraints on locality, settling time, and communication delay, can achieve similar performance as an unconstrained H2 optimal controller, but can be designed and implemented in a localized and distributed way.Comment: Extended version for 2014 CDC submissio

Sequential Synthesis of Distributed Controllers for Cascade Interconnected Systems

We consider the problem of designing distributed controllers to ensure passivity of a large-scale interconnection of linear subsystems connected in a cascade topology. The control design process needs to be carried out at the subsystem-level with no direct knowledge of the dynamics of other subsystems in the interconnection. We present a distributed approach to solve this problem, where subsystem-level controllers are locally designed in a sequence starting at one end of the cascade using only the dynamics of the particular subsystem, coupling with the immediately preceding subsystem and limited information from the preceding subsystem in the cascade to ensure passivity of the interconnected system up to that point. We demonstrate that this design framework also allows for new subsystems to be compositionally added to the interconnection without requiring redesign of the pre-existing controllers.Comment: Accepted to appear in the proceedings of the American Control Conference (ACC) 201