Eduard Petlenkov | Searcharxiv

arXiv2026

Regularized Model Predictive Control

In model predictive control (MPC), the choice of cost-weighting matrices and designing the Hessian matrix directly affects the trade-off between rapid state regulation and minimizing the control effort. However, traditional MPC in quadratic programming relies on fixed design matrices across the entire horizon, which can lead to suboptimal performance. This study presents a Riccati equation-based method for adjusting the design matrix within the MPC framework, which enhances real-time performance. We employ a penalized least-squares (PLS) approach to derive a quadratic cost function for a discrete-time linear system over a finite prediction horizon. Using the method of weighting and enforcing the equality constraint by introducing a large penalty parameter, we solve the constrained optimization problem and generate control inputs for forward-shifted horizons. This process yields a recursive PLS-based Riccati equation that updates the design matrix as a regularization term in each shift, forming the foundation of the regularized MPC (Re-MPC) algorithm. To accomplish this, we provide a convergence and stability analysis of the developed algorithm. Numerical analysis demonstrates its superiority over traditional methods by allowing Riccati equation-based adjustments.

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arXiv2026

When control meets large language models: From words to dynamics

While large language models (LLMs) are transforming engineering and technology through enhanced control capabilities and decision support, they are simultaneously evolving into complex dynamical systems whose behavior must be regulated. This duality highlights a reciprocal connection in which prompts support control system design while control theory helps shape prompts to achieve specific goals efficiently. In this study, we frame this emerging interconnection of LLM and control as a bidirectional continuum, from prompt design to system dynamics. First, we investigate how LLMs can advance the field of control in two distinct capacities: directly, by assisting in the design and synthesis of controllers, and indirectly, by augmenting research workflows. Second, we examine how control concepts help LLMs steer their trajectories away from undesired meanings, improving reachability and alignment via input optimization, parameter editing, and activation-level interventions. Third, we look into deeper integrations by treating LLMs as dynamic systems within a state-space framework, where their internal representations are closely linked to external control loops. Finally, we identify key challenges and outline future research directions to understand LLM behavior and develop interpretable and controllable LLMs that are as trustworthy and robust as their electromechanical counterparts, thereby ensuring they continue to support and safeguard society.

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