60 research outputs found
A New Recursive Least-Squares Method with Multiple Forgetting Schemes
We propose a recursive least-squares method with multiple forgetting schemes
to track time-varying model parameters which change with different rates. Our
approach hinges on the reformulation of the classic recursive least-squares
with forgetting scheme as a regularized least squares problem. A simulation
study shows the effectiveness of the proposed method
Automated and Sound Synthesis of Lyapunov Functions with SMT Solvers
In this paper we employ SMT solvers to soundly synthesise Lyapunov functions
that assert the stability of a given dynamical model. The search for a Lyapunov
function is framed as the satisfiability of a second-order logical formula,
asking whether there exists a function satisfying a desired specification
(stability) for all possible initial conditions of the model. We synthesise
Lyapunov functions for linear, non-linear (polynomial), and for parametric
models. For non-linear models, the algorithm also determines a region of
validity for the Lyapunov function. We exploit an inductive framework to
synthesise Lyapunov functions, starting from parametric templates. The
inductive framework comprises two elements: a learner proposes a Lyapunov
function, and a verifier checks its validity - its lack is expressed via a
counterexample (a point over the state space), for further use by the learner.
Whilst the verifier uses the SMT solver Z3, thus ensuring the overall soundness
of the procedure, we examine two alternatives for the learner: a numerical
approach based on the optimisation tool Gurobi, and a sound approach based
again on Z3. The overall technique is evaluated over a broad set of benchmarks,
which shows that this methodology not only scales to 10-dimensional models
within reasonable computational time, but also offers a novel soundness proof
for the generated Lyapunov functions and their domains of validity
Data-driven Abstractions for Verification of Deterministic Systems
A common technique to verify complex logic specifications for dynamical
systems is the construction of symbolic abstractions: simpler, finite-state
models whose behaviour mimics the one of the systems of interest. Typically,
abstractions are constructed exploiting an accurate knowledge of the underlying
model: in real-life applications, this may be a costly assumption. By sampling
random -step trajectories of an unknown system, we build an abstraction
based on the notion of -completeness. We newly define the notion of
probabilistic behavioural inclusion, and provide probably approximately correct
(PAC) guarantees that this abstraction includes all behaviours of the concrete
system, for finite and infinite time horizon, leveraging the scenario theory
for non convex problems. Our method is then tested on several numerical
benchmarks
Augmented Neural Lyapunov Control
Machine learning-based methodologies have recently been adapted to solve control problems. The Neural Lyapunov Control (NLC) method is one such example. This approach combines Artificial Neural Networks (ANNs) with Satisfiability Modulo Theories (SMT) solvers to synthesise stabilising control laws and to prove their formal correctness. The ANNs are trained over a dataset of state-space samples to generate candidate control and Lyapunov functions, while the SMT solvers are tasked with certifying the correctness of the Lyapunov function over a continuous domain or by returning a counterexample. Despite the approach’s attractiveness, issues can occur due to subsequent calls of the SMT module at times returning similar counterexamples, which can turn out to be uninformative and may lead to dataset overfitting. Additionally, the control network weights are usually initialised with pre-computed gains from state-feedback controllers, e.g. Linear-Quadratic Regulators. To properly perform the initialisation requires user time and control expertise. In this work, we present an Augmented NLC method that mitigates these drawbacks, removes the need for the control initialisation and further improves counterexample generation. As a result, the proposed method allows the synthesis of nonlinear (as well as linear) control laws with the sole requirement being the knowledge of the system dynamics. The ANLC is tested over challenging benchmarks such as the Lorenz attractor and outperformed existing methods in terms of successful synthesis rate. The developed framework is released open-source at: https://github.com/grande-dev/Augmented-Neural-Lyapunov-Control
Formal Synthesis of Lyapunov Neural Networks
We propose an automatic and formally sound method for synthesising Lyapunov
functions for the asymptotic stability of autonomous non-linear systems.
Traditional methods are either analytical and require manual effort or are
numerical but lack of formal soundness. Symbolic computational methods for
Lyapunov functions, which are in between, give formal guarantees but are
typically semi-automatic because they rely on the user to provide appropriate
function templates. We propose a method that finds Lyapunov functions fully
automaticallyusing machine learningwhile also providing formal
guaranteesusing satisfiability modulo theories (SMT). We employ a
counterexample-guided approach where a numerical learner and a symbolic
verifier interact to construct provably correct Lyapunov neural networks
(LNNs). The learner trains a neural network that satisfies the Lyapunov
criteria for asymptotic stability over a samples set; the verifier proves via
SMT solving that the criteria are satisfied over the whole domain or augments
the samples set with counterexamples. Our method supports neural networks with
polynomial activation functions and multiple depth and width, which display
wide learning capabilities. We demonstrate our method over several non-trivial
benchmarks and compare it favourably against a numerical optimisation-based
approach, a symbolic template-based approach, and a cognate LNN-based approach.
Our method synthesises Lyapunov functions faster and over wider spatial domains
than the alternatives, yet providing stronger or equal guarantees
Augmented Neural Lyapunov Control
Machine learning-based methodologies have recently been adapted to solve control problems. The Neural Lyapunov Control (NLC) method is one such example. This approach combines Artificial Neural Networks (ANNs) with Satisfiability Modulo Theories (SMT) solvers to synthesise stabilising control laws and to prove their formal correctness. The ANNs are trained over a dataset of state-space samples to generate candidate control and Lyapunov functions, while the SMT solvers are tasked with certifying the correctness of the Lyapunov function over a continuous domain or by returning a counterexample. Despite the approach’s attractiveness, issues can occur due to subsequent calls of the SMT module at times returning similar counterexamples, which can turn out to be uninformative and may lead to dataset overfitting. Additionally, the control network weights are usually initialised with pre-computed gains from state-feedback controllers, e.g. Linear-Quadratic Regulators. To properly perform the initialisation requires user time and control expertise. In this work, we present an Augmented NLC method that mitigates these drawbacks, removes the need for the control initialisation and further improves counterexample generation. As a result, the proposed method allows the synthesis of nonlinear (as well as linear) control laws with the sole requirement being the knowledge of the system dynamics. The ANLC is tested over challenging benchmarks such as the Lorenz attractor and outperformed existing methods in terms of successful synthesis rate. The developed framework is released open-source at: https://github.com/grande-dev/Augmented-Neural-Lyapunov-Control
Expression of calcium-binding proteins and selected neuropeptides in the human, chimpanzee, and crab-eating macaque claustrum
The claustrum is present in all mammalian species examined so far and its morphology, chemoarchitecture, physiology, phylogenesis and ontogenesis are still a matter of debate. Several morphologically distinct types of immunostained cells were described in different mammalian species. To date, a comparative study on the neurochemical organization of the human and non-human primates claustrum has not been fully described yet, partially due to technical reasons linked to the postmortem sampling interval. The present study analyze the localization and morphology of neurons expressing parvalbumin (PV), calretinin (CR), NPY, and somatostatin (SOM) in the claustrum of man (# 5), chimpanzee (# 1) and crab-eating monkey (# 3). Immunoreactivity for the used markers was observed in neuronal cell bodies and processes distributed throughout the anterior-posterior extent of human, chimpanzee and macaque claustrum. Both CR- and PV-immunoreactive (ir) neurons were mostly localized in the central and ventral region of the claustrum of the three species while SOM- and NPY-ir neurons seemed to be equally distributed throughout the ventral-dorsal extent. In the chimpanzee claustrum SOM-ir elements were not observed. No co-localization of PV with CR was found, thus suggesting the existence of two non-overlapping populations of PV and CR-ir interneurons. The expression of most proteins (CR, PV, NPY), was similar in all species. The only exception was the absence of SOM-ir elements in the claustrum of the chimpanzee, likely due to species specific variability. Our data suggest a possible common structural organization shared with the adjacent insular region, a further element that emphasizes a possible common ontogeny of the claustrum and the neocortex
Una prospettiva sulla spintronica. An outlook on spintronics
La spintronica è un nuovo campo di ricerca dell’elettronica, con grandissime potenzialità di creare dispositivi a basso consumo di potenza e maggiori performance. Nella tesi sono trattati effetti come la IEC, la GMR, la TMR, l’accoppiamento spin-orbita, la spin torque, l’effetto hall di spin. Notevoli sono le applicazioni, già presenti nel mercato, come gli hard disk, le valvole spin, o le MRAM, o in via di sviluppo, come i semiconduttori ferromagnetici, lo spin-led o lo spin-transistor. In meno di vent’anni la spintronica ha cambiato il volto dell’immagazzinamento dei dati, aprono le porte al mondo dei video digitali e di interne
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