arXiv subjects

Erfan Shakhesi

Publications and source records attributed to Erfan Shakhesi.

6 recordsLinked to original sources

arXiv2026

Model Predictive Control for Dynamic Hydraulic Balancing in Building Radiator Heating Systems: Modeling, Design, and Experimental Validation

Hydronic radiator systems are among the most widely used heating systems in buildings. In the literature, radiator heat outputs are often assumed to be independent of one another and arbitrarily adjustable in time when designing controllers. However, in practice, radiators are supplied by one or multiple common heat sources and are hydraulically coupled through the water circulation system. Maintaining occupant comfort in multi-zone buildings therefore requires not only an appropriate supply temperature but also proper hydraulic balancing to distribute the available water flow according to the heating demand of each zone. To this end, we develop a grey-box thermal model that captures the hydraulic interactions among radiators and the effects of radiator valves, circulation pumps, and heat sources. In a real building, we show that accounting for hydraulic interactions reduces the root mean square error (RMSE) between the measured and modeled zone temperatures by approximately 11% compared with a model that neglects these interactions. Additionally, we integrate the developed model into a model predictive control (MPC) framework for dynamic hydraulic balancing that jointly optimizes valve openings and the supply temperature to maintain thermal comfort in each zone while reducing energy consumption. Through both real-world experiments and numerical case studies, we demonstrate that, compared with existing MPC formulations that neglect hydraulic interactions or do not control radiator valves, the proposed MPC reduces comfort-range violations by at least 27% while requiring a similar or even lower cumulative supply temperature.

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arXiv2025

Verification and Synthesis of Discrete-Time Control Barrier Functions

Discrete-time Control Barrier Functions (DTCBFs) have recently attracted interest for guaranteeing safety and synthesizing safe controllers for discrete-time dynamical systems. This paper addresses the open challenges of verifying candidate DTCBFs and synthesizing DTCBFs for general nonlinear discrete-time systems with input constraints and arbitrary safe sets. In particular, we propose a branch-and-bound method, inspired by the $α$BB algorithm, for the verification of candidate DTCBFs in both cases, whether a corresponding control policy is known or unknown. We prove that this method, in a finite number of iterations, either verifies a given candidate function as a valid DTCBF or falsifies it by providing a counterexample (within predefined tolerances). As a second main contribution, we propose a novel bilevel optimization approach to synthesize a DTCBF and a corresponding control policy in finite time. This involves determining the unknown coefficients of a parameterized DTCBF and a parameterized control policy. Furthermore, we introduce various strategies to reduce the computational burden of the bilevel approach. We also demonstrate our methods using numerical case studies.

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arXiv2025

Counterexample-Guided Synthesis of Robust Discrete-Time Control Barrier Functions

Learning-based methods have gained popularity for training candidate Control Barrier Functions (CBFs) to satisfy the CBF conditions on a finite set of sampled states. However, since the CBF is unknown a priori, it is unclear which sampled states belong to its zero-superlevel set and must satisfy the CBF conditions, and which ones lie outside it. Existing approaches define a set in which all sampled states are required to satisfy the CBF conditions, thus introducing conservatism. In this paper, we address this issue for robust discrete-time CBFs (R-DTCBFs). Furthermore, we propose a class of R-DTCBFs that can be used in an online optimization problem to synthesize safe controllers for general discrete-time systems with input constraints and bounded disturbances. To train such an R-DTCBF that is valid not only on sampled states but also across the entire region, we employ a verification algorithm iteratively in a counterexample-guided approach. We apply the proposed method to numerical case studies.

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arXiv2025

Synthesis of Discrete-time Control Barrier Functions for Polynomial Systems Based on Sum-of-Squares Programming

Discrete-time Control Barrier Functions (DTCBFs) are commonly utilized in the literature as a powerful tool for synthesizing control policies that guarantee safety of discrete-time dynamical systems. However, the systematic synthesis of DTCBFs in a computationally efficient way is at present an important open problem. This article first proposes a novel alternating-descent approach based on Sum-of-Squares programming to synthesize quadratic DTCBFs and corresponding polynomial control policies for discrete-time control-affine polynomial systems with input constraints and semi-algebraic safe sets. Subsequently, two distinct approaches are introduced to extend the proposed method to the synthesis of higher-degree polynomial DTCBFs. To demonstrate its efficacy, we apply the proposed method to numerical case studies.

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arXiv2024

Optimization-based Verification of Discrete-time Control Barrier Functions: A Branch-and-Bound Approach

Discrete-time Control Barrier Functions (DTCBFs) form a powerful control theoretic tool to guarantee safety and synthesize safe controllers for discrete-time dynamical systems. In this paper, we provide an optimization-based algorithm, inspired by the $α$BB algorithm, for the verification of a candidate DTCBF, i.e., either verifying a given candidate function as a valid DTCBF or falsifying it by providing a counterexample for a general nonlinear discrete-time system with input constraints. This method is applicable whether a corresponding control policy is known or unknown. We apply our method to a numerical case study to illustrate its efficacy.

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arXiv2023

Discrete-time Control Barrier Functions for Guaranteed Recursive Feasibility in Nonlinear MPC: An Application to Lane Merging

In this paper, we present conditions under which the terminal ingredients, defined by discrete-time control barrier function (DTCBF) certificates, guarantee recursive feasibility in nonlinear MPC. Further, we introduce the notion of quasi-DTCBF (qDTCBF) certificates. Compared to DTCBFs, qDTCBF conditions can be satisfied with tighter control input bounds, which is highly advantageous if only limited actuation is possible. Both certificates encourage an earlier reaction of the control system and result in a lower cumulative MPC cost. The methodology is applied to a lane merging problem in automated driving, in which DTCBF and qDTCBF certificates subject to input constraints form the terminal ingredients to guarantee recursive feasibility of the nonlinear MPC scheme. A simulation study demonstrates the efficacy of the concept.

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