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Probabilistic reachable sets of stochastic nonlinear systems with contextual uncertainties

IF 4.8 2区计算机科学 Q1 AUTOMATION & CONTROL SYSTEMS

Automatica

Pub Date : 2025-03-06 DOI: 10.1016/j.automatica.2025.112237

Xun Shen , Ye Wang , Kazumune Hashimoto , Yuhu Wu , Sebastien Gros

Validating and controlling safety-critical systems in uncertain environments necessitates probabilistic reachable sets of future state evolutions. The existing methods of computing probabilistic reachable sets normally assume that stochastic uncertainties are independent of system states, inputs, and other environment variables. However, this assumption falls short in many real-world applications, where the probability distribution governing uncertainties depends on these variables, referred to as contextual uncertainties. This paper addresses the challenge of computing probabilistic reachable sets of stochastic nonlinear states with contextual uncertainties by seeking minimum-volume polynomial sublevel sets with contextual chance constraints. The formulated problem cannot be solved by the existing sample-based approximation method since the existing methods do not consider conditional probability densities. To address this, we propose a consistent sample approximation of the original problem by leveraging conditional density estimation and resampling. The obtained approximate problem is a tractable optimization problem. Additionally, we prove the proposed sample-based approximation’s almost uniform convergence, showing that it gives the optimal solution almost consistently with the original ones. Through a numerical example, we evaluate the effectiveness of the proposed method against existing approaches, highlighting its capability to significantly reduce the bias inherent in sample-based approximation without considering a conditional probability density.

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引用次数: 0

Maximizing the smallest eigenvalue of grounded Laplacian matrices via edge addition

IF 4.8 2区计算机科学 Q1 AUTOMATION & CONTROL SYSTEMS

Automatica

Pub Date : 2025-03-06 DOI: 10.1016/j.automatica.2025.112238

Xinfeng Ru , Weiguo Xia , Ming Cao

The smallest eigenvalue of the grounded Laplacian matrix holds pivotal significance across various practical scenarios, particularly in characterizing the convergence rate of leader–follower networks in multi-agent systems, with a larger smallest eigenvalue indicating a faster convergence rate. This paper focuses on maximizing the smallest eigenvalue of the grounded Laplacian matrix via adding edges for both undirected and directed networks. For undirected networks, under intuitive conditions, we prove that adding one edge between two vertices that correspond to the smallest and largest eigenvector components for the smallest eigenvalue will maximize the smallest eigenvalue of the grounded Laplacian matrix. In addition, the discussion is extended to the case of multiple edge addition, where a suboptimal algorithm is proposed to maximize the eigenvalue with a low time complexity. For directed networks, when fixing a vertex

i

and adding an edge pointing to it, choosing the vertex, if there is any, that has the smallest eigenvector component than that of

i

leads to the maximal increase of the smallest eigenvalue. We apply the derived results to the distributed neighbor selection for directed networks.

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引用次数: 0

Properties of immersions for systems with multiple limit sets with implications to learning Koopman embeddings

IF 4.8 2区计算机科学 Q1 AUTOMATION & CONTROL SYSTEMS

Automatica

Pub Date : 2025-03-05 DOI: 10.1016/j.automatica.2025.112226

Zexiang Liu , Necmiye Ozay , Eduardo D. Sontag

Linear immersions (such as Koopman eigenfunctions) of a nonlinear system have wide applications in prediction and control. In this work, we study the properties of linear immersions for nonlinear systems with multiple omega-limit sets. While previous research has indicated the possibility of discontinuous one-to-one linear immersions for such systems, it has been unclear whether continuous one-to-one linear immersions are attainable. Under mild conditions, we prove that any continuous immersion to a class of systems including finite-dimensional linear systems collapses all the omega-limit sets, and thus cannot be one-to-one. Furthermore, we show that this property is also shared by approximate linear immersions learned from data as sample size increases and sampling interval decreases. Multiple examples are studied to illustrate our results.

引用次数: 0

Generic diagonalizability, structural functional observability and output controllability

IF 4.8 2区计算机科学 Q1 AUTOMATION & CONTROL SYSTEMS

Automatica

Pub Date : 2025-03-03 DOI: 10.1016/j.automatica.2025.112232

Yuan Zhang , Tyrone Fernando , Mohamed Darouach

This paper investigates the structural functional observability (SFO) and structural output controllability (SOC) of a class of systems and explores the associated minimal sensor and actuator placement problems. The verification of SOC and the corresponding sensor and actuator placement problems, i.e., the problems of determining the minimum number of outputs and inputs required to achieve SFO and SOC, respectively, are yet open for general systems. This motivates our focus on a large class of systems enabling polynomial-time solutions. In this line, we first define and characterize generically diagonalizable systems, referring to structured systems for which almost all realizations of the state matrices are diagonalizable. We then develop computationally efficient criteria for SFO and SOC within the context of generically diagonalizable systems. Our work expands the class of systems amenable to polynomial-time SOC verification. Thanks to the simplicity of the obtained criteria, we derive closed-form solutions for determining the minimal sensor placement to achieve SFO and the minimal actuator deployment to achieve SOC in such systems, along with efficient weighted maximum matching-based and weighted maximum flow-based algorithms. For more general systems to achieve SFO, we establish an upper bound on the number of required sensors by identifying a non-decreasing property of SFO with respect to a specific class of edge additions, which is proven to be optimal under certain conditions.

{"title":"Generic diagonalizability, structural functional observability and output controllability","authors":"Yuan Zhang , Tyrone Fernando , Mohamed Darouach","doi":"10.1016/j.automatica.2025.112232","DOIUrl":"10.1016/j.automatica.2025.112232","url":null,"abstract":"<div><div>This paper investigates the structural functional observability (SFO) and structural output controllability (SOC) of a class of systems and explores the associated minimal sensor and actuator placement problems. The verification of SOC and the corresponding sensor and actuator placement problems, i.e., the problems of determining the minimum number of outputs and inputs required to achieve SFO and SOC, respectively, are yet open for general systems. This motivates our focus on a large class of systems enabling polynomial-time solutions. In this line, we first define and characterize generically diagonalizable systems, referring to structured systems for which almost all realizations of the state matrices are diagonalizable. We then develop computationally efficient criteria for SFO and SOC within the context of generically diagonalizable systems. Our work expands the class of systems amenable to polynomial-time SOC verification. Thanks to the simplicity of the obtained criteria, we derive closed-form solutions for determining the minimal sensor placement to achieve SFO and the minimal actuator deployment to achieve SOC in such systems, along with efficient weighted maximum matching-based and weighted maximum flow-based algorithms. For more general systems to achieve SFO, we establish an upper bound on the number of required sensors by identifying a non-decreasing property of SFO with respect to a specific class of edge additions, which is proven to be optimal under certain conditions.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"176 ","pages":"Article 112232"},"PeriodicalIF":4.8,"publicationDate":"2025-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143551407","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Robust fault detection method based on interval neural networks optimized by ellipsoid bundles

IF 4.8 2区计算机科学 Q1 AUTOMATION & CONTROL SYSTEMS

Automatica

Pub Date : 2025-03-03 DOI: 10.1016/j.automatica.2025.112233

Meng Zhou , Yinyue Zhang , Jing Wang , Tarek Raïssi , Vicenç Puig

In this paper, a novel framework for interval prediction neural network model optimized by ellipsoid bundles is designed for data-driven systems with unknown but bounded noise and disturbances. Firstly, a point prediction neural network model is constructed with input and output data, the prediction error is assumed to be unknown but bounded. Then, a feasible set related to the output weights of the neural network model is described by ellipsoid bundles, which allows decreasing conservatism compared to other types of sets such as zonotopes or ellipsoids. To obtain a more precise description shape of the feasible set, an optimal iterative formula is theoretically derived by minimizing the Frobenius norm of ellipsoid bundles. Next, an outer bounding box is established to obtain the maximum and minimum weights that satisfy the feasible set, thereby providing the output prediction interval. This interval characterizes the systems’ disturbance and can be used as the threshold when dealing with fault diagnosis applications. Finally, the effectiveness of the proposed interval neural network model is demonstrated by using faulty data from a wastewater treatment process. Simulation results verify that the proposed method can achieve accurate prediction outputs and fault diagnosis performance.

{"title":"Robust fault detection method based on interval neural networks optimized by ellipsoid bundles","authors":"Meng Zhou , Yinyue Zhang , Jing Wang , Tarek Raïssi , Vicenç Puig","doi":"10.1016/j.automatica.2025.112233","DOIUrl":"10.1016/j.automatica.2025.112233","url":null,"abstract":"<div><div>In this paper, a novel framework for interval prediction neural network model optimized by ellipsoid bundles is designed for data-driven systems with unknown but bounded noise and disturbances. Firstly, a point prediction neural network model is constructed with input and output data, the prediction error is assumed to be unknown but bounded. Then, a feasible set related to the output weights of the neural network model is described by ellipsoid bundles, which allows decreasing conservatism compared to other types of sets such as zonotopes or ellipsoids. To obtain a more precise description shape of the feasible set, an optimal iterative formula is theoretically derived by minimizing the Frobenius norm of ellipsoid bundles. Next, an outer bounding box is established to obtain the maximum and minimum weights that satisfy the feasible set, thereby providing the output prediction interval. This interval characterizes the systems’ disturbance and can be used as the threshold when dealing with fault diagnosis applications. Finally, the effectiveness of the proposed interval neural network model is demonstrated by using faulty data from a wastewater treatment process. Simulation results verify that the proposed method can achieve accurate prediction outputs and fault diagnosis performance.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"176 ","pages":"Article 112233"},"PeriodicalIF":4.8,"publicationDate":"2025-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143551412","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Event-triggered learning-based control for output tracking with unknown cost functions

IF 4.8 2区计算机科学 Q1 AUTOMATION & CONTROL SYSTEMS

Automatica

Pub Date : 2025-03-03 DOI: 10.1016/j.automatica.2025.112235

Jiliang Song , Dawei Shi , Shu-Xia Tang , Hao Yu , Yang Shi

In this paper, a two-layer event-triggered learning-based control framework is proposed to address extremum seeking problem in networked control systems with limited communication resources and unknown cost function. In this framework, the lower layer is an event-triggered controller to drive the output to track the given setpoints generated from the upper layer, where a learning-based optimizer is developed to approach the extremum of the unknown cost function. Specifically, in the lower layer, an event-triggered output controller, based on a high-gain extended state observer, is designed to tackle uncertainties and disturbances. In the upper layer, a nonparametric gradient model is established, and then the gradient descent method is applied to generate setpoints for the tracking control. The update of the learning and optimization process is determined by the tracking performance of the lower layer. The stability and Zeno-freeness of the proposed event-triggered controller is proved. Furthermore, the dependence of the convergence rate of the proposed learning-based extremum seeking algorithm on the designed parameters is also explicitly characterized. Finally, the effectiveness of the proposed framework is validated by numerical examples.

{"title":"Event-triggered learning-based control for output tracking with unknown cost functions","authors":"Jiliang Song , Dawei Shi , Shu-Xia Tang , Hao Yu , Yang Shi","doi":"10.1016/j.automatica.2025.112235","DOIUrl":"10.1016/j.automatica.2025.112235","url":null,"abstract":"<div><div>In this paper, a two-layer event-triggered learning-based control framework is proposed to address extremum seeking problem in networked control systems with limited communication resources and unknown cost function. In this framework, the lower layer is an event-triggered controller to drive the output to track the given setpoints generated from the upper layer, where a learning-based optimizer is developed to approach the extremum of the unknown cost function. Specifically, in the lower layer, an event-triggered output controller, based on a high-gain extended state observer, is designed to tackle uncertainties and disturbances. In the upper layer, a nonparametric gradient model is established, and then the gradient descent method is applied to generate setpoints for the tracking control. The update of the learning and optimization process is determined by the tracking performance of the lower layer. The stability and Zeno-freeness of the proposed event-triggered controller is proved. Furthermore, the dependence of the convergence rate of the proposed learning-based extremum seeking algorithm on the designed parameters is also explicitly characterized. Finally, the effectiveness of the proposed framework is validated by numerical examples.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"176 ","pages":"Article 112235"},"PeriodicalIF":4.8,"publicationDate":"2025-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143551411","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Emergent homeomorphic curves in swarms

IF 4.8 2区计算机科学 Q1 AUTOMATION & CONTROL SYSTEMS

Automatica

Pub Date : 2025-02-28 DOI: 10.1016/j.automatica.2025.112221

Peter Travis Jardine, Sidney Givigi

We propose a new decentralized approach for producing emergent curve trajectories in swarms of agents. The central innovation lies in use of a quaternion-based stabilizing embedding, which permits the application of linear control policies to produce globally-stable behaviour from local observations. Agents are modelled as particles in free space using double integrator dynamics. We stabilize an arbitrary number of agents indirectly, through virtual representations bijected onto a circle, and then produce elaborate curve trajectories through a family of topological homeomorphisms. We formulate these virtual agents as embeddings, through a combination of state feedback, rotations, and variable changes. The result is evenly-spaced swarms along the desired trajectories, with each agent only requiring information about the state of its neighbours. Simulations demonstrate the emergent qualities of the swarm as it converges to the desired geometry. The agents maintain separation and automatically compensate for loss or addition of agents in the swarm. We provide mathematical proofs of stability for the embedding, trajectories, and controller.

引用次数: 0

Stochastically constrained best arm identification with Thompson sampling

IF 4.8 2区计算机科学 Q1 AUTOMATION & CONTROL SYSTEMS

Automatica

Pub Date : 2025-02-28 DOI: 10.1016/j.automatica.2025.112223

Le Yang , Siyang Gao , Cheng Li , Yi Wang

We consider the problem of the best arm identification in the presence of stochastic constraints, where there is a finite number of arms associated with multiple performance measures. The goal is to identify the arm that optimizes the objective measure subject to constraints on the remaining measures. We will explore the popular idea of Thompson sampling (TS) as a means to solve it. To the best of our knowledge, it is the first attempt to extend TS to this problem. We will design a TS-based sampling algorithm, establish its asymptotic optimality in the rate of posterior convergence, and demonstrate its superior performance using numerical examples.

引用次数: 0

Robust optimal density control of robotic swarms

IF 4.8 2区计算机科学 Q1 AUTOMATION & CONTROL SYSTEMS

Automatica

Pub Date : 2025-02-28 DOI: 10.1016/j.automatica.2025.112218

Carlo Sinigaglia , Andrea Manzoni , Francesco Braghin , Spring Berman

In this paper we propose a computationally efficient, robust density control strategy for the mean-field model of a robotic swarm. We formulate a static optimal control problem (OCP) that computes a robot velocity field which drives the swarm to a target equilibrium density, and we prove the stability of the controlled system in the presence of transient perturbations and uncertainties in the initial conditions. The density dynamics are described by a linear elliptic advection–diffusion equation in which the control enters bilinearly into the advection term. The well-posedness of the state problem is ensured by an integral constraint. We prove the existence of optimal controls by embedding the state constraint into the weak formulation of the state dynamics. The resulting control field is space-dependent and does not require any communication between robots or costly density estimation algorithms. Based on the properties of the primal and dual systems, we first propose a method to accommodate the state constraint. Exploiting the properties of the state dynamics and associated controls, we then construct a modified dynamic OCP to speed up the convergence to the target equilibrium density of the associated static problem. We show that the finite-element discretization of the static and dynamic OCPs inherits the structure and several useful properties of their infinite-dimensional formulations. Finally, we demonstrate the effectiveness of our control approach through numerical simulations of scenarios with obstacles and an external velocity field.

{"title":"Robust optimal density control of robotic swarms","authors":"Carlo Sinigaglia , Andrea Manzoni , Francesco Braghin , Spring Berman","doi":"10.1016/j.automatica.2025.112218","DOIUrl":"10.1016/j.automatica.2025.112218","url":null,"abstract":"<div><div>In this paper we propose a computationally efficient, robust density control strategy for the mean-field model of a robotic swarm. We formulate a static optimal control problem (OCP) that computes a robot velocity field which drives the swarm to a target equilibrium density, and we prove the stability of the controlled system in the presence of transient perturbations and uncertainties in the initial conditions. The density dynamics are described by a linear elliptic advection–diffusion equation in which the control enters bilinearly into the advection term. The well-posedness of the state problem is ensured by an integral constraint. We prove the existence of optimal controls by embedding the state constraint into the weak formulation of the state dynamics. The resulting control field is space-dependent and does not require any communication between robots or costly density estimation algorithms. Based on the properties of the primal and dual systems, we first propose a method to accommodate the state constraint. Exploiting the properties of the state dynamics and associated controls, we then construct a modified dynamic OCP to speed up the convergence to the target equilibrium density of the associated static problem. We show that the finite-element discretization of the static and dynamic OCPs inherits the structure and several useful properties of their infinite-dimensional formulations. Finally, we demonstrate the effectiveness of our control approach through numerical simulations of scenarios with obstacles and an external velocity field.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"176 ","pages":"Article 112218"},"PeriodicalIF":4.8,"publicationDate":"2025-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143511938","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Distributed parameter estimation with Gaussian observation noises in time-varying digraphs

IF 4.8 2区计算机科学 Q1 AUTOMATION & CONTROL SYSTEMS

Automatica

Pub Date : 2025-02-27 DOI: 10.1016/j.automatica.2025.112209

Jiaqi Yan , Hideaki Ishii

In this paper, we consider the problem of distributed parameter estimation in sensor networks. Each sensor makes successive observations of an unknown

d

-dimensional parameter, which might be subject to Gaussian random noises. The sensors aim to infer the true value of the unknown parameter by cooperating with each other. To this end, we first generalize the so-called dynamic regressor extension and mixing (DREM) algorithm to stochastic systems, with which the problem of estimating a

d

-dimensional vector parameter is transformed to that of

d

scalar ones: one for each of the unknown parameters. For each of the scalar problem, both combine-then-adapt (CTA) and adapt-then-combine (ATC) diffusion-based estimation algorithms are given, where each sensor performs a combination step to fuse the local estimates in its in-neighborhood, alongside an adaptation step to process its streaming observations. Under weak conditions on network topology and excitation of regressors, we show that the proposed estimators guarantee that each sensor infers the true parameter, even if any individual of them cannot by itself. Specifically, it is required that the union of topologies over an interval with fixed length is strongly connected. Moreover, the sensors must collectively satisfy a cooperative persistent excitation (PE) condition, which relaxes the traditional PE condition. Numerical examples are finally provided to illustrate the established results.

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引用次数: 0

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