Shaohui Yang

Shaohui Yang, Colin N. Jones

The Brunovsky canonical form provides sparse structural representations that are beneficial for computational optimal control, yet existing methods fail to compute it reliably. We propose a technique that produces Brunovsky transformations with substantially lower construction errors and improved conditioning. A controllable linear system is first reduced to the staircase form via an orthogonal similarity transformation. We then derive a simple linear parametrization of the transformations yielding the unique Brunovsky form. Numerical stability is further enhanced by applying a deadbeat gain before computing system matrix powers and by optimizing the linear parameters to minimize condition numbers.

Yuan Zhang, Shaohui Yang, Toshiyuki Ohtsuka et al.

Model predictive control (MPC) has played a more crucial role in various robotic control tasks, but its high computational requirements are concerning, especially for nonlinear dynamical models. This paper presents a $\textbf{la}$tent $\textbf{l}$inear $\textbf{q}$uadratic $\textbf{r}$egulator (LaLQR) that maps the state space into a latent space, on which the dynamical model is linear and the cost function is quadratic, allowing the efficient application of LQR. We jointly learn this alternative system by imitating the original MPC. Experiments show LaLQR's superior efficiency and generalization compared to other baselines.

Junqi Zhao, Zhijin Fang, Shu Li et al.

Large language models (LLMs) are essential in natural language processing but often struggle with inference speed and computational efficiency, limiting real-time deployment. The key-value (KV) cache mechanism reduces computational overhead in transformer models, but challenges in maintaining contextual understanding remain. In this paper, we propose BUZZ, a novel KV caching algorithm that leverages structured contextual information to minimize cache memory usage while enhancing inference speed. BUZZ employs a beehive-structured sparse cache, incorporating a sliding window to capture recent information and dynamically segmenting historical tokens into chunks to prioritize important tokens in local neighborhoods. We evaluate BUZZ on four real-world datasets: CNN/Daily Mail, XSUM, Wikitext, and 10-QA. Our results demonstrate that BUZZ (1) reduces cache memory usage by $\textbf{2.5}\times$ in LLM inference while maintaining over 99% accuracy in long-text summarization, and (2) surpasses state-of-the-art performance in multi-document question answering by $\textbf{7.69%}$ under the same memory limit, where full cache methods encounter out-of-memory issues. Additionally, BUZZ achieves significant inference speedup with a $\log{n}$ time complexity. The code is available at https://github.com/JunqiZhao888/buzz-llm.