Pub Date : 2025-12-30DOI: 10.1016/j.automatica.2025.112751
Xu Chen , Xiao He , S. Joe Qin
Closed-loop control brings new challenges for process monitoring. Nonlinearities in the correlation structure and the dynamic relations in closed-loop process data further complicate the task. To tackle these issues, a new dynamic latent variable scheme is proposed in this paper for nonlinear closed-loop processes. The nonlinearities of the processes are investigated in detail first, followed by a dynamic latent variable object for latent structure extraction of nonlinear closed-loop processes. An algorithm is then proposed to solve the constructed optimization object which has guaranteed convergency. The relations of the extracted dynamic latent model are revealed in detail afterwards, and the process monitoring strategy is built with comprehensive analysis of variations in closed-loop process data. A numerical simulation and a study on the thruster system of the “Jiaolong” deep-sea submarine are carried on to show the performance of the proposed scheme.
{"title":"Nonlinear bidirectional dynamic latent modeling for closed-loop process monitoring","authors":"Xu Chen , Xiao He , S. Joe Qin","doi":"10.1016/j.automatica.2025.112751","DOIUrl":"10.1016/j.automatica.2025.112751","url":null,"abstract":"<div><div>Closed-loop control brings new challenges for process monitoring. Nonlinearities in the correlation structure and the dynamic relations in closed-loop process data further complicate the task. To tackle these issues, a new dynamic latent variable scheme is proposed in this paper for nonlinear closed-loop processes. The nonlinearities of the processes are investigated in detail first, followed by a dynamic latent variable object for latent structure extraction of nonlinear closed-loop processes. An algorithm is then proposed to solve the constructed optimization object which has guaranteed convergency. The relations of the extracted dynamic latent model are revealed in detail afterwards, and the process monitoring strategy is built with comprehensive analysis of variations in closed-loop process data. A numerical simulation and a study on the thruster system of the “Jiaolong” deep-sea submarine are carried on to show the performance of the proposed scheme.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"185 ","pages":"Article 112751"},"PeriodicalIF":5.9,"publicationDate":"2025-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145884868","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}
Pub Date : 2025-12-30DOI: 10.1016/j.automatica.2025.112814
Xin Xin , Xiaohui Ji , Ziyu Wang , Yannian Liu
In this paper, we investigate strong stabilization for the Acrobot by optimizing its maximal relative stability through selecting an observation point on its second link. Prior work designed a second-order, strongly stabilizing controller that achieves maximal relative stability (the minimum distance from the closed-loop poles to the imaginary axis) for the plant obtained via a fixed observation point, whose transfer function has a nonnegative real zero. We first determine the value of this nonnegative real zero that maximizes maximal relative stability. We prove that maximal relative stability increases monotonically as this real zero moves toward the origin and attains the maximum when the plant has a double zero at the origin. We then extend the existing controller design to plants with conjugate imaginary-axis zeros, proving that maximal relative stability increases monotonically as these zeros move away from the origin within our identified interval. We also prove that all resulting stable second-order controllers are minimum phase.
{"title":"Strongly stabilizing the Acrobot by optimizing maximal relative stability via observation point selection","authors":"Xin Xin , Xiaohui Ji , Ziyu Wang , Yannian Liu","doi":"10.1016/j.automatica.2025.112814","DOIUrl":"10.1016/j.automatica.2025.112814","url":null,"abstract":"<div><div>In this paper, we investigate strong stabilization for the Acrobot by optimizing its maximal relative stability through selecting an observation point on its second link. Prior work designed a second-order, strongly stabilizing controller that achieves maximal relative stability (the minimum distance from the closed-loop poles to the imaginary axis) for the plant obtained via a fixed observation point, whose transfer function has a nonnegative real zero. We first determine the value of this nonnegative real zero that maximizes maximal relative stability. We prove that maximal relative stability increases monotonically as this real zero moves toward the origin and attains the maximum when the plant has a double zero at the origin. We then extend the existing controller design to plants with conjugate imaginary-axis zeros, proving that maximal relative stability increases monotonically as these zeros move away from the origin within our identified interval. We also prove that all resulting stable second-order controllers are minimum phase.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"185 ","pages":"Article 112814"},"PeriodicalIF":5.9,"publicationDate":"2025-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145884849","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}
Pub Date : 2025-12-29DOI: 10.1016/j.automatica.2025.112811
Luca Consolini, Mattia Laurini, Marco Locatelli
In this paper we address the speed planning problem for a vehicle along a predefined path. A weighted sum of two conflicting objectives, energy consumption and travel time, is minimized. After deriving a non-convex mathematical model of the problem, we prove that the feasible region of this problem is a lattice. Moreover, we introduce a feasibility-based bound-tightening technique which allows us to derive the minimum and maximum element of the lattice, or establish that the feasible region is empty. We prove the exactness of a convex relaxation of the non-convex problem, obtained by replacing all constraints with the lower and upper bounds for the variables corresponding to the minimum and maximum elements of the lattice, respectively. After proving some properties of optimal solutions of the convex relaxation, we exploit them to develop a dynamic programming approach returning an approximate solution to the convex relaxation, and with time complexity , where is the number of points into which the continuous path is discretized.
{"title":"A convex reformulation for speed planning of a vehicle under the travel time and energy consumption objectives","authors":"Luca Consolini, Mattia Laurini, Marco Locatelli","doi":"10.1016/j.automatica.2025.112811","DOIUrl":"10.1016/j.automatica.2025.112811","url":null,"abstract":"<div><div>In this paper we address the speed planning problem for a vehicle along a predefined path. A weighted sum of two conflicting objectives, energy consumption and travel time, is minimized. After deriving a non-convex mathematical model of the problem, we prove that the feasible region of this problem is a lattice. Moreover, we introduce a feasibility-based bound-tightening technique which allows us to derive the minimum and maximum element of the lattice, or establish that the feasible region is empty. We prove the exactness of a convex relaxation of the non-convex problem, obtained by replacing all constraints with the lower and upper bounds for the variables corresponding to the minimum and maximum elements of the lattice, respectively. After proving some properties of optimal solutions of the convex relaxation, we exploit them to develop a dynamic programming approach returning an approximate solution to the convex relaxation, and with time complexity <span><math><mrow><mi>O</mi><mrow><mo>(</mo><msup><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></mrow></mrow></math></span>, where <span><math><mi>n</mi></math></span> is the number of points into which the continuous path is discretized.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"185 ","pages":"Article 112811"},"PeriodicalIF":5.9,"publicationDate":"2025-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145884851","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}
Pub Date : 2025-12-29DOI: 10.1016/j.automatica.2025.112801
Yu Xiao , Yuan Yuan , Biao Huang , Xiaodong Xu
The constrained output regulation problem has been addressed by the output feedback model predictive control (MPC) algorithm for deterministic system without random disturbances in recent years. This paper further considers the case with the presence of unknown-but-bounded random disturbances in the linear systems performing iterative regulation tasks, which have not been considered. When pursuing infinite-horizon optimization, unknown random disturbances give rise to an infinite horizon policy optimization problem in the MPC controller, and the problem cannot be directly solved. Moreover, the recursive feasibility in dealing with iterative tasks for the deterministic system cannot be guaranteed for uncertain systems, which renders the solution of this paper nontrivial. To this end, we develop a novel robust learning-based MPC algorithm such that the problem of linear iterative output regulation in the presence of unknown-but-bounded random disturbances along with state and input constraints is addressed.
{"title":"Constrained output regulation for linear systems performing iterative tasks via robust learning MPC","authors":"Yu Xiao , Yuan Yuan , Biao Huang , Xiaodong Xu","doi":"10.1016/j.automatica.2025.112801","DOIUrl":"10.1016/j.automatica.2025.112801","url":null,"abstract":"<div><div>The constrained output regulation problem has been addressed by the output feedback model predictive control (MPC) algorithm for deterministic system without random disturbances in recent years. This paper further considers the case with the presence of unknown-but-bounded random disturbances in the linear systems performing iterative regulation tasks, which have not been considered. When pursuing infinite-horizon optimization, unknown random disturbances give rise to an infinite horizon policy optimization problem in the MPC controller, and the problem cannot be directly solved. Moreover, the recursive feasibility in dealing with iterative tasks for the deterministic system cannot be guaranteed for uncertain systems, which renders the solution of this paper nontrivial. To this end, we develop a novel robust learning-based MPC algorithm such that the problem of linear iterative output regulation in the presence of unknown-but-bounded random disturbances along with state and input constraints is addressed.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"185 ","pages":"Article 112801"},"PeriodicalIF":5.9,"publicationDate":"2025-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145884872","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}
Pub Date : 2025-12-29DOI: 10.1016/j.automatica.2025.112813
Zhijian Hu , Renjie Ma
This paper considers adaptive event-triggered tracking control problem in the presence of uncertainties, including unmodeled dynamics and external disturbances. A novel switching function is introduced, and the compensated tracking error dynamics is constructed via a command filter. Based on the backstepping methodology, virtual controllers are designed together with an adaptive law that estimates the supremum of uncertainty effects, leading to an event-triggered control strategy, such that uniform finite-time stability is established for different switching function scenarios. Finally, a simulation study on a soft robot illustrates the effectiveness of the proposed approach.
{"title":"Adaptive event-triggered tracking control via switching functions","authors":"Zhijian Hu , Renjie Ma","doi":"10.1016/j.automatica.2025.112813","DOIUrl":"10.1016/j.automatica.2025.112813","url":null,"abstract":"<div><div>This paper considers adaptive event-triggered tracking control problem in the presence of uncertainties, including unmodeled dynamics and external disturbances. A novel switching function is introduced, and the compensated tracking error dynamics is constructed via a command filter. Based on the backstepping methodology, virtual controllers are designed together with an adaptive law that estimates the supremum of uncertainty effects, leading to an event-triggered control strategy, such that uniform finite-time stability is established for different switching function scenarios. Finally, a simulation study on a soft robot illustrates the effectiveness of the proposed approach.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"185 ","pages":"Article 112813"},"PeriodicalIF":5.9,"publicationDate":"2025-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145884870","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}
Given a network of agents, we say that the agents achieve a -agreement when their state variables converge to a point that corresponds to the projection of the agents’ states onto a -dimensional linear subspace. The -agreement problem generalizes the classical consensus problem; unlike in consensus, where the agents’ states must asymptotically coincide, in -agreement the agents reach an agreement in a generalized sense (within a linear subspace, where the states do not necessarily coincide). In this paper, we investigate which interaction topologies enable a network of agents to reach an agreement on a prescribed -dimensional subspace through local coordination algorithms. We show that achieving -agreement requires communication over highly connected graphs; specifically, the number of edges in the interaction graph must grow linearly with the dimension of the agreement subspace. Our characterization reveals that the presence of cycles in the communication graph (particularly, independent families of cycles) constitutes the fundamental structural feature enabling the agents to achieve -agreement. We also investigate the use of common graph topologies, such as path and circulant graphs, for -agreement, deriving insights into the relationship between the subspace dimension and the required network connectivity. The effectiveness of the proposed framework is demonstrated through simulations in robotic formation control problems.
{"title":"The role of network connectivity in distributed k-agreement protocols","authors":"Gianluca Bianchin , Miguel Vaquero , Jorge Cortés , Emiliano Dall’Anese","doi":"10.1016/j.automatica.2025.112753","DOIUrl":"10.1016/j.automatica.2025.112753","url":null,"abstract":"<div><div>Given a network of agents, we say that the agents achieve a <span><math><mi>k</mi></math></span>-<em>agreement</em> when their state variables converge to a point that corresponds to the projection of the agents’ states onto a <span><math><mi>k</mi></math></span>-dimensional linear subspace. The <span><math><mi>k</mi></math></span>-agreement problem generalizes the classical consensus problem; unlike in consensus, where the agents’ states must asymptotically coincide, in <span><math><mi>k</mi></math></span>-agreement the agents reach an agreement in a generalized sense (within a linear subspace, where the states do not necessarily coincide). In this paper, we investigate which interaction topologies enable a network of agents to reach an agreement on a prescribed <span><math><mi>k</mi></math></span>-dimensional subspace through local coordination algorithms. We show that achieving <span><math><mi>k</mi></math></span>-agreement requires communication over highly connected graphs; specifically, the number of edges in the interaction graph must grow linearly with the dimension <span><math><mi>k</mi></math></span> of the agreement subspace. Our characterization reveals that the presence of cycles in the communication graph (particularly, independent families of cycles) constitutes the fundamental structural feature enabling the agents to achieve <span><math><mi>k</mi></math></span>-agreement. We also investigate the use of common graph topologies, such as path and circulant graphs, for <span><math><mi>k</mi></math></span>-agreement, deriving insights into the relationship between the subspace dimension <span><math><mi>k</mi></math></span> and the required network connectivity. The effectiveness of the proposed framework is demonstrated through simulations in robotic formation control problems.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"185 ","pages":"Article 112753"},"PeriodicalIF":5.9,"publicationDate":"2025-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145884874","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}
Pub Date : 2025-12-29DOI: 10.1016/j.automatica.2025.112799
Sebin Gracy , Brian D.O. Anderson , Mengbin Ye , César A. Uribe
The paper studies the simultaneous spread of two competing viruses over a network of population nodes with higher-order interactions (HOI), using a continuous-time time-invariant competitive bivirus networked susceptible–infected–susceptible (SIS) system. In this paper, by HOI, we mean interactions among group sizes of no more than three nodes. The first key contribution is to establish several important general properties for generic systems. Namely, there are a finite number of equilibria, each equilibrium is nondegenerate, and the system is a strongly monotone dynamical system. Put together, we establish that for almost all initial conditions, the system will converge to a stable equilibrium (of which there may be many). We then turn our focus to characterizing the existence and stability of the equilibria of this system, which are (i) the disease-free equilibrium (DFE), (ii) single-virus endemic equilibria, and (iii) coexistence equilibria (where both viruses are present). We present a range of conditions on the existence or nonexistence of various equilibria. Two key features underpin our results: First, we substantially relax the connectivity conditions of the network relative to existing literature. More specifically, for securing several important general properties for generic systems, we do not require strong connectivity of the standard pairwise interaction graph. Second, we identify dynamical phenomena, including multiple stable equilibria, which are known to be impossible without HOI. The latter illustrates the novel insights that are obtained by including HOI into models of epidemic spread. Finally, we illustrate our results using a real-world large-scale network.
{"title":"Networked competitive bivirus SIS spread with higher order interactions","authors":"Sebin Gracy , Brian D.O. Anderson , Mengbin Ye , César A. Uribe","doi":"10.1016/j.automatica.2025.112799","DOIUrl":"10.1016/j.automatica.2025.112799","url":null,"abstract":"<div><div>The paper studies the simultaneous spread of two competing viruses over a network of population nodes with higher-order interactions (HOI), using a continuous-time time-invariant competitive bivirus networked susceptible–infected–susceptible (SIS) system. In this paper, by HOI, we mean interactions among group sizes of no more than three nodes. The first key contribution is to establish several important general properties for generic systems. Namely, there are a finite number of equilibria, each equilibrium is nondegenerate, and the system is a strongly monotone dynamical system. Put together, we establish that for almost all initial conditions, the system will converge to a stable equilibrium (of which there may be many). We then turn our focus to characterizing the existence and stability of the equilibria of this system, which are (i) the disease-free equilibrium (DFE), (ii) single-virus endemic equilibria, and (iii) coexistence equilibria (where both viruses are present). We present a range of conditions on the existence or nonexistence of various equilibria. Two key features underpin our results: First, we substantially relax the connectivity conditions of the network relative to existing literature. More specifically, for securing several important general properties for generic systems, we do <em>not</em> require strong connectivity of the standard pairwise interaction graph. Second, we identify dynamical phenomena, including multiple stable equilibria, which are known to be impossible without HOI. The latter illustrates the novel insights that are obtained by including HOI into models of epidemic spread. Finally, we illustrate our results using a real-world large-scale network.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"185 ","pages":"Article 112799"},"PeriodicalIF":5.9,"publicationDate":"2025-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145884867","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}
Pub Date : 2025-12-26DOI: 10.1016/j.automatica.2025.112808
Hai-Tao Zhang , Jiayu Zou , Xingjian Liu
It has long been a challenging task for optimal coverage control of multi-agent systems (MASs) in non-convex surface environments often encountered in real coordinated detection applications. To this end, this paper develops a surface cooperative control scheme for MASs to perform coverage operations. First, a coverage surface partition protocol is devised to divide a non-convex surface into multiple sectorial sub-surfaces. Accordingly, a performance index in surface coverage is established considering the curvature spatial evolution of the surface environments. Thereby, a random-initial-point algorithm is designed to minimize the performance index, and a surface-constrained optimal control law is developed to deploy MASs at niche positions. Significantly, sufficient conditions are derived to guarantee the asymptotical stability of the present scheme. Finally, numerical simulations are conducted to verify the effectiveness of the present surface coverage design.
{"title":"Cooperative optimal surface coverage control of multi-agent systems in non-convex surface environments","authors":"Hai-Tao Zhang , Jiayu Zou , Xingjian Liu","doi":"10.1016/j.automatica.2025.112808","DOIUrl":"10.1016/j.automatica.2025.112808","url":null,"abstract":"<div><div>It has long been a challenging task for optimal coverage control of multi-agent systems (MASs) in non-convex surface environments often encountered in real coordinated detection applications. To this end, this paper develops a surface cooperative control scheme for MASs to perform coverage operations. First, a coverage surface partition protocol is devised to divide a non-convex surface into multiple sectorial sub-surfaces. Accordingly, a performance index in surface coverage is established considering the curvature spatial evolution of the surface environments. Thereby, a random-initial-point algorithm is designed to minimize the performance index, and a surface-constrained optimal control law is developed to deploy MASs at niche positions. Significantly, sufficient conditions are derived to guarantee the asymptotical stability of the present scheme. Finally, numerical simulations are conducted to verify the effectiveness of the present surface coverage design.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"185 ","pages":"Article 112808"},"PeriodicalIF":5.9,"publicationDate":"2025-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145841799","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}
Pub Date : 2025-12-24DOI: 10.1016/j.automatica.2025.112761
Licheng Wang , Zidong Wang
This paper investigates the event-based probability guaranteed tracking control problem for a class of discrete-time systems with a relay-aided communication scheme. The uncertainties of the system matrices are taken into account, which is described by mutually independent uniformly distributed random variables. An adaptive event-triggering scheme is introduced during the signal exchange from the sensor to the relay where the triggering threshold is dynamically regulated. Moreover, an amplify-to-forward relay is employed to improve the communication quality between the sensor and the controller. With the help of the Lyapunov stability theory, sufficient conditions are established to guarantee that the tracking error dynamics achieves the asymptotical stability and the performance with probability constraints. The desired controller parameters are derived by means of the solution to certain optimization problem subject to matrix inequality constraints. Finally, a numerical example is provided to show the effectiveness of the developed tracking control scheme.
{"title":"Event-based probability-guaranteed tracking control with amplify-and-forward relay schemes","authors":"Licheng Wang , Zidong Wang","doi":"10.1016/j.automatica.2025.112761","DOIUrl":"10.1016/j.automatica.2025.112761","url":null,"abstract":"<div><div>This paper investigates the event-based probability guaranteed <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>∞</mi></mrow></msub></math></span> tracking control problem for a class of discrete-time systems with a relay-aided communication scheme. The uncertainties of the system matrices are taken into account, which is described by mutually independent uniformly distributed random variables. An adaptive event-triggering scheme is introduced during the signal exchange from the sensor to the relay where the triggering threshold is dynamically regulated. Moreover, an amplify-to-forward relay is employed to improve the communication quality between the sensor and the controller. With the help of the Lyapunov stability theory, sufficient conditions are established to guarantee that the tracking error dynamics achieves the asymptotical stability and the <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>∞</mi></mrow></msub></math></span> performance with probability constraints. The desired controller parameters are derived by means of the solution to certain optimization problem subject to matrix inequality constraints. Finally, a numerical example is provided to show the effectiveness of the developed tracking control scheme.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"185 ","pages":"Article 112761"},"PeriodicalIF":5.9,"publicationDate":"2025-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145822795","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}
This paper introduces novel companion form realizations for quasi-Linear Parameter Varying (qLPV) state space models obtained from input–output models, which are identified using neural networks (NN). The data for training the NN is generated from a multi-input, multi-output (MIMO) dynamic system. The method, at first, trains a (possibly deep) neural network to minimize one-step or multi-step prediction errors. If the layer activation functions of the NN satisfy a certain property, labeled as Lipschitz factorability, then the NN can be cast into a quasi-linear difference equation that describe the input–output dynamics of the nonlinear MIMO system. Such a NN consisting of Lipschitz factorable activation layers is termed as a Lipschitz factorable NN. Next, the input–output, qLPV difference equation is then realized into qLPV MIMO state space model in companion form via suitable state definitions. To demonstrate the effectiveness of the proposed method, such a realized qLPV state space model, identified from a trained NN, is used as the prediction model in a simulated sub-optimal nonlinear Model Predictive Control (MPC) example for a benchmark quadruple tank system, wherein voltages of two pumps are manipulated to control levels of two tanks.
{"title":"qLPV state space models in companion form via realization of factorable neural networks","authors":"Deepti Khimani , Machhindranath Patil , Sharad Bhartiya","doi":"10.1016/j.automatica.2025.112812","DOIUrl":"10.1016/j.automatica.2025.112812","url":null,"abstract":"<div><div>This paper introduces novel companion form realizations for quasi-Linear Parameter Varying (qLPV) state space models obtained from input–output models, which are identified using neural networks (NN). The data for training the NN is generated from a multi-input, multi-output (MIMO) dynamic system. The method, at first, trains a (possibly deep) neural network to minimize one-step or multi-step prediction errors. If the layer activation functions of the NN satisfy a certain property, labeled as Lipschitz factorability, then the NN can be cast into a quasi-linear difference equation that describe the input–output dynamics of the nonlinear MIMO system. Such a NN consisting of Lipschitz factorable activation layers is termed as a Lipschitz factorable NN. Next, the input–output, qLPV difference equation is then realized into qLPV MIMO state space model in companion form via suitable state definitions. To demonstrate the effectiveness of the proposed method, such a realized qLPV state space model, identified from a trained NN, is used as the prediction model in a simulated sub-optimal nonlinear Model Predictive Control (MPC) example for a benchmark quadruple tank system, wherein voltages of two pumps are manipulated to control levels of two tanks.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"185 ","pages":"Article 112812"},"PeriodicalIF":5.9,"publicationDate":"2025-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145822794","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}
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