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In the article$^a$, the authors introduced a time-varying Lyapunov function for the stability analysis of nonlinear systems whose motion is governed by standard Newton-Euler equations. The authors established asymptotic stability with the…
As a first approach to the study of systems coupling finite and infinite dimensional natures, this article addresses the stability of a system of ordinary differential equations coupled with a classic heat equation using a Lyapunov…
Recently, there has been great interest in connections between continuous-time dynamical systems and optimization methods, notably in the context of accelerated methods for smooth and unconstrained problems. In this paper we extend this…
As a popular meta-learning approach, the model-agnostic meta-learning (MAML) algorithm has been widely used due to its simplicity and effectiveness. However, the convergence of the general multi-step MAML still remains unexplored. In this…
While distributed parameter estimation has been extensively studied in the literature, little has been achieved in terms of robust analysis and tuning methods in the presence of disturbances. However, disturbances such as measurement noise…
We study systems on time scales that are generalizations of classical differential or difference equations. In this paper we consider linear systems and their small nonlinear perturbations. In terms of time scales and of eigenvalues of…
This paper considers a cross-layer optimization problem driven by multi-timescale stochastic exogenous processes in wireless communication networks. Due to the hierarchical information structure in a wireless network, a mixed timescale…
Bayesian modelling allows for the quantification of predictive uncertainty which is crucial in safety-critical applications. Yet for many machine learning (ML) algorithms, it is difficult to construct or implement their Bayesian…
This brief gives a set of unified Lyapunov stability conditions to guarantee the predefined-time/finite-time stability of a dynamical systems. The derived Lyapunov theorem for autonomous systems establishes equivalence with existing…
We present a novel way of generating Lyapunov functions for proving linear convergence rates of first-order optimization methods. Our approach provably obtains the fastest linear convergence rate that can be verified by a quadratic Lyapunov…
We consider the problem of estimating the maximum posterior probability (MAP) state sequence for a finite state and finite emission alphabet hidden Markov model (HMM) in the Bayesian setup, where both emission and transition matrices have…
There are much recent interests in solving noncovnex min-max optimization problems due to its broad applications in many areas including machine learning, networked resource allocations, and distributed optimization. Perhaps, the most…
Reversibility is a key concept in Markov models and Master-equation models of molecular kinetics. The analysis and interpretation of the transition matrix encoding the kinetic properties of the model relies heavily on the reversibility…
In contexts where data samples represent a physically stable state, it is often assumed that the data points represent the local minima of an energy landscape. In control theory, it is well-known that energy can serve as an effective…
In this paper, we develop and analyze an integral fixed-time sliding mode control method for a scenario in which the system model is only partially known, utilizing Gaussian processes. We present two theorems on fixed-time convergence. The…
In this paper, synchronization of identical switched chaotic systems is explored based on Lyapunov theory of guaranteed stability. Concepts from robust control principles and switched linear systems are merged together to derive a…
This paper deals with the robust stability analysis of linear systems, subject to time-varying parameters. The Parameter Dependent Lyapunov Function are considered, assuming that the temporal derivative of the parameters are bounded. Some…
This paper studies the stability of sampled and networked control systems with sampling and communication times governed by probabilistic clocks. The clock models have few restrictions, and can be used to model numerous phenomena such as…
A dynamic method to solve the Non-linear Programming (NLP) problem with Equality Constraints (ECs) and Inequality Constraints (IECs) is proposed. Inspired by the Lyapunov continuous-time dynamics stability theory in the control field, the…
Modern control systems must operate in increasingly complex environments subject to safety constraints and input limits, and are often implemented in a hierarchical fashion with different controllers running at multiple time scales. Yet…