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In this paper, we propose a class of super-schemes for efficiently solving nonlinear unconstrained optimization problems. The proposed approach introduces two novel choices of step-size parameters, leading to efficient descent directions…
We study the problem of optimal state-feedback tracking control for unknown discrete-time deterministic systems with input constraints. To handle input constraints, state-of-art methods utilize a certain nonquadratic stage cost function,…
Nonlinear contraction theory is a comparatively recent dynamic control system design tool based on an exact differential analysis of convergence, in essence converting a nonlinear stability problem into a linear time-varying stability…
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…
The single-step explicit time integration methods have long been valuable for solving large-scale nonlinear structural dynamic problems, classified into single-solve and multi-sub-step approaches. However, no existing explicit single-solve…
This paper presents three main contributions to the field of multi-step system identification. First, drawing inspiration from Neural Network (NN) training, it introduces a tool for solving identification problems by leveraging first-order…
How can one quickly answer the most and top popular objects at any time, given a large log stream in a system of billions of users? It is equivalent to find the mode and top-frequent elements in a dynamic array corresponding to the log…
We propose an efficient fine-tuning method for time series foundation models, termed TRACE: Time Series Parameter Efficient Fine-tuning. While pretrained time series foundation models are gaining popularity, they face the following…
This paper proposes a dynamic quantum-assisted co-design framework for nonlinear closed-loop systems in which controller parameters and Lyapunov-certificate parameters are redesigned jointly at successive decision epochs. Unlike…
Sequential algorithms for the Stable Matching Problem are often too slow in the context of some large scale applications like switch scheduling. Parallel architectures can offer a notable decrease in runtime complexity. We propose a stable…
Parameter-efficient fine-tuning aims to achieve performance comparable to fine-tuning, using fewer trainable parameters. Several strategies (e.g., Adapters, prefix tuning, BitFit, and LoRA) have been proposed. However, their designs are…
Projection-based model reduction has become a popular approach to reduce the cost associated with integrating large-scale dynamical systems so they can be used in many-query settings such as optimization and uncertainty quantification. For…
Multiscale is a hallmark feature of complex nonlinear systems. While the simulation using the classical numerical methods is restricted by the local \textit{Taylor} series constraints, the multiscale techniques are often limited by finding…
Parallel scaling has emerged as a powerful paradigm to enhance reasoning capabilities in large language models (LLMs) by generating multiple Chain-of-Thought (CoT) traces simultaneously. However, this approach introduces significant…
In this work, we establish different control design approaches for discrete-time systems, which build upon the notion of finite-step control Lyapunov functions (fs-CLFs). The design approaches are formulated as optimization problems and…
We propose semidefinite trajectory optimization (STROM), a framework that computes fast and certifiably optimal solutions for nonconvex trajectory optimization problems defined by polynomial objectives and constraints. STROM employs sparse…
Massively parallel hardware (GPUs) and long sequence data have made parallel algorithms essential for machine learning at scale. Yet dynamical systems, like recurrent neural networks and Markov chain Monte Carlo, were thought to suffer from…
Nonlinear differential equations rarely admit closed-form solutions, thus requiring numerical time-stepping algorithms to approximate solutions. Further, many systems characterized by multiscale physics exhibit dynamics over a vast range of…
We propose a sequential homotopy method for the solution of mathematical programming problems formulated in abstract Hilbert spaces under the Guignard constraint qualification. The method is equivalent to performing projected backward Euler…
Signal Temporal Logic (STL) has gained popularity in recent years as a specification language for cyber-physical systems, especially in robotics. Beyond being expressive and easy to understand, STL is appealing because the synthesis…