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Every system of any significant size is created by composition from smaller sub-systems or components. It is thus fruitful to analyze the fault-tolerance of a system as a function of its composition. In this paper, two basic types of system…
Feed-forward neural networks consist of a sequence of layers, in which each layer performs some processing on the information from the previous layer. A downside to this approach is that each layer (or module, as multiple modules can…
Robust control design is mainly devoted to guarantee closed-loop stability of a model-based control law in presence of parametric and structural uncertainties. The control law is usually a complex feedback law which is derived from a…
A control design approach is developed for a general class of uncertain strict-feedback-like nonlinear systems with dynamic uncertain input nonlinearities with time delays. The system structure considered in this paper includes a nominal…
A control system $\dot{q} = f(q,u)$ is said to be trivializable if there exists local coordinates in which the system is feedback equivalent to a control system of the form $\dot{q} = f(u)$. In this paper we characterize trivializable…
Recurrent neural networks have been extensively studied in the context of neuroscience and machine learning due to their ability to implement complex computations. While substantial progress in designing effective learning algorithms has…
In this paper, we propose a deep unfolding-based framework for the output feedback control of systems with input saturation. Although saturation commonly arises in several practical control systems, there is still a scarce of effective…
An approach to stabilization of control systems with ultimately wide ranges of uncertainly disturbed parameters is offered. The method relies on using of nonlinear structurally stable functions from catastrophe theory as controllers.…
Graded monads refine traditional monads using effect annotations in order to describe quantitatively the computational effects that a program can generate. They have been successfully applied to a variety of formal systems for reasoning…
The present paper studies a feedback regulation problem, which may be interpreted as an adaptive control problem, but has not yet been studied in the control literature. The problem, which arises in at least two different biological…
Here we show that, given a finite homological system $({\cal P},\leq,\{\Delta_u\}_{u\in {\cal P}})$ for a finite-dimensional algebra $\Lambda$ over an algebraically closed field, the category ${\cal F}(\Delta)$ of $\Delta$-filtered modules…
In this work, we generalize several topological results and concepts from ring theory to the setting of monoids.
Many current challenges involve understanding the complex dynamical interplay between the constituents of systems. Typically, the number of such constituents is high, but only limited data sources on them are available. Conventional…
Human feedback is increasingly used across diverse applications like training AI models, developing recommender systems, and measuring public opinion -- with granular feedback often being preferred over binary feedback for its greater…
There is increasing acknowledgement - including from the UK government - of the benefit of employing deliberative processes (deliberative fora, citizens' juries, etc.). Evidence suggests that the qualitative reporting of deliberative fora…
We consider moduli spaces of dynamical systems of correspondences over the projective line as a generalization of moduli spaces of dynamical systems of endomorphisms on the projective line. We obtain the rationality of the moduli spaces.…
Compositional generalization is a basic and essential intellective capability of human beings, which allows us to recombine known parts readily. However, existing neural network based models have been proven to be extremely deficient in…
Transformer-based models excel in various tasks but their generalization capabilities, especially in arithmetic reasoning, remain incompletely understood. Arithmetic tasks provide a controlled framework to explore these capabilities, yet…
We present a new approach to termination analysis of logic programs. The essence of the approach is that we make use of general orderings (instead of level mappings), like it is done in transformational approaches to logic program…
We develop a predictor-feedback control design for multi-input nonlinear systems with distinct input delays, of arbitrary length, in each individual input channel. Due to the fact that different input signals reach the plant at different…