Pub Date : 2024-06-18DOI: 10.1109/LCSYS.2024.3416071
Francesco De Lellis;Marco Coraggio;Nathan C. Foster;Riccardo Villa;Cristina Becchio;Mario Di Bernardo
We present a data-driven control architecture designed to encode specific information, such as the presence or absence of an emotion, in the movements of an avatar or robot driven by a human operator. Our strategy leverages a set of human-recorded examples as the core for generating information-rich kinematic signals. To ensure successful object grasping, we propose a deep reinforcement learning strategy. We validate our approach using an experimental dataset obtained during the reach-to-grasp phase of a pick-and-place task.
{"title":"Data-Driven Architecture to Encode Information in the Kinematics of Robots and Artificial Avatars","authors":"Francesco De Lellis;Marco Coraggio;Nathan C. Foster;Riccardo Villa;Cristina Becchio;Mario Di Bernardo","doi":"10.1109/LCSYS.2024.3416071","DOIUrl":"https://doi.org/10.1109/LCSYS.2024.3416071","url":null,"abstract":"We present a data-driven control architecture designed to encode specific information, such as the presence or absence of an emotion, in the movements of an avatar or robot driven by a human operator. Our strategy leverages a set of human-recorded examples as the core for generating information-rich kinematic signals. To ensure successful object grasping, we propose a deep reinforcement learning strategy. We validate our approach using an experimental dataset obtained during the reach-to-grasp phase of a pick-and-place task.","PeriodicalId":37235,"journal":{"name":"IEEE Control Systems Letters","volume":null,"pages":null},"PeriodicalIF":2.4,"publicationDate":"2024-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=10559995","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141725566","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-06-18DOI: 10.1109/LCSYS.2024.3416243
Sourav Bhowmick;N. Selvaganesan
In this letter, an epidemic dynamical model driven by perceived disease severity opinion in societies is investigated along with its various dynamical characteristics. More specifically, the epidemic model namely Susceptible-Infected-Recovered-Vaccinated (SIRV) is considered over a transmission network, while the opinion reflecting the perceived disease risk evolves over a social network. In particular, the global and the local stability conditions of the disease-free equilibrium (DFE), i.e., there is no disease in the network, have been investigated, wherein the local stability is revealed to be linked with the basic reproduction rate and the transverse (non-zero) eigenvalues of the Jacobian evaluated at the DFE points. Moreover, the local stability analysis of the endemic equilibrium (EE), i.e., where disease persists in the network, has been investigated. The simulation results verify the theoretical methods.
{"title":"Social Network-Based Epidemic Spread With Opinion-Dependent Vaccination","authors":"Sourav Bhowmick;N. Selvaganesan","doi":"10.1109/LCSYS.2024.3416243","DOIUrl":"https://doi.org/10.1109/LCSYS.2024.3416243","url":null,"abstract":"In this letter, an epidemic dynamical model driven by perceived disease severity opinion in societies is investigated along with its various dynamical characteristics. More specifically, the epidemic model namely Susceptible-Infected-Recovered-Vaccinated (SIRV) is considered over a transmission network, while the opinion reflecting the perceived disease risk evolves over a social network. In particular, the global and the local stability conditions of the disease-free equilibrium (DFE), i.e., there is no disease in the network, have been investigated, wherein the local stability is revealed to be linked with the basic reproduction rate and the transverse (non-zero) eigenvalues of the Jacobian evaluated at the DFE points. Moreover, the local stability analysis of the endemic equilibrium (EE), i.e., where disease persists in the network, has been investigated. The simulation results verify the theoretical methods.","PeriodicalId":37235,"journal":{"name":"IEEE Control Systems Letters","volume":null,"pages":null},"PeriodicalIF":2.4,"publicationDate":"2024-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141583556","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-06-18DOI: 10.1109/LCSYS.2024.3416237
Hamidreza Montazeri Hedesh;Milad Siami
This letter introduces a novel method for the stability analysis of positive feedback systems with a class of fully connected feedforward neural networks (FFNN) controllers. By establishing sector bounds for fully connected FFNNs without biases, we present a stability theorem that demonstrates the global exponential stability of linear systems under fully connected FFNN control. Utilizing principles from positive Lur’e systems and the positive Aizerman conjecture, our approach effectively addresses the challenge of ensuring stability in highly nonlinear systems. The crux of our method lies in maintaining sector bounds that preserve the positivity and Hurwitz property of the overall Lur’e system. We showcase the practical applicability of our methodology through its implementation in a linear system managed by a FFNN trained on output feedback controller data, highlighting its potential for enhancing stability in dynamic systems.
{"title":"Ensuring Both Positivity and Stability Using Sector-Bounded Nonlinearity for Systems With Neural Network Controllers","authors":"Hamidreza Montazeri Hedesh;Milad Siami","doi":"10.1109/LCSYS.2024.3416237","DOIUrl":"https://doi.org/10.1109/LCSYS.2024.3416237","url":null,"abstract":"This letter introduces a novel method for the stability analysis of positive feedback systems with a class of fully connected feedforward neural networks (FFNN) controllers. By establishing sector bounds for fully connected FFNNs without biases, we present a stability theorem that demonstrates the global exponential stability of linear systems under fully connected FFNN control. Utilizing principles from positive Lur’e systems and the positive Aizerman conjecture, our approach effectively addresses the challenge of ensuring stability in highly nonlinear systems. The crux of our method lies in maintaining sector bounds that preserve the positivity and Hurwitz property of the overall Lur’e system. We showcase the practical applicability of our methodology through its implementation in a linear system managed by a FFNN trained on output feedback controller data, highlighting its potential for enhancing stability in dynamic systems.","PeriodicalId":37235,"journal":{"name":"IEEE Control Systems Letters","volume":null,"pages":null},"PeriodicalIF":2.4,"publicationDate":"2024-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141544005","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-06-18DOI: 10.1109/LCSYS.2024.3416240
Yuksel Arslantas;Ege Yuceel;Muhammed O. Sayin
In this letter, we explore the susceptibility of the independent Q-learning algorithms (a classical and widely used multi-agent reinforcement learning method) to strategic manipulation of sophisticated opponents in normal-form games played repeatedly. We quantify how much strategically sophisticated agents can exploit naive Q-learners if they know the opponents’ Q-learning algorithm. To this end, we formulate the strategic actors’ interactions as a stochastic game (whose state encompasses Q-function estimates of the Q-learners) as if the Q-learning algorithms are the underlying dynamical system. We also present a quantization-based approximation scheme to tackle the continuum state space and analyze its performance for two competing strategic actors and a single strategic actor both analytically and numerically.
{"title":"Strategizing Against Q-Learners: A Control-Theoretical Approach","authors":"Yuksel Arslantas;Ege Yuceel;Muhammed O. Sayin","doi":"10.1109/LCSYS.2024.3416240","DOIUrl":"https://doi.org/10.1109/LCSYS.2024.3416240","url":null,"abstract":"In this letter, we explore the susceptibility of the independent Q-learning algorithms (a classical and widely used multi-agent reinforcement learning method) to strategic manipulation of sophisticated opponents in normal-form games played repeatedly. We quantify how much strategically sophisticated agents can exploit naive Q-learners if they know the opponents’ Q-learning algorithm. To this end, we formulate the strategic actors’ interactions as a stochastic game (whose state encompasses Q-function estimates of the Q-learners) as if the Q-learning algorithms are the underlying dynamical system. We also present a quantization-based approximation scheme to tackle the continuum state space and analyze its performance for two competing strategic actors and a single strategic actor both analytically and numerically.","PeriodicalId":37235,"journal":{"name":"IEEE Control Systems Letters","volume":null,"pages":null},"PeriodicalIF":2.4,"publicationDate":"2024-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141602497","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-06-18DOI: 10.1109/LCSYS.2024.3416235
Jiarui Wang;Mahyar Fazlyab
Designing control policies for stabilization tasks with provable guarantees is a long-standing problem in nonlinear control. A crucial performance metric is the size of the resulting region of attraction, which essentially serves as a robustness “margin” of the closed-loop system against uncertainties. In this letter, we propose a new method to train a stabilizing neural network controller along with its corresponding Lyapunov certificate, aiming to maximize the resulting region of attraction while respecting the actuation constraints. Crucial to our approach is the use of Zubov’s Partial Differential Equation (PDE), which precisely characterizes the true region of attraction of a given control policy. Our framework follows an actor-critic pattern where we alternate between improving the control policy (actor) and learning a Zubov function (critic). Finally, we compute the largest certifiable region of attraction by invoking an SMT solver after the training procedure. Our numerical experiments on several design problems show consistent and significant improvements in the size of the resulting region of attraction.
{"title":"Actor–Critic Physics-Informed Neural Lyapunov Control","authors":"Jiarui Wang;Mahyar Fazlyab","doi":"10.1109/LCSYS.2024.3416235","DOIUrl":"https://doi.org/10.1109/LCSYS.2024.3416235","url":null,"abstract":"Designing control policies for stabilization tasks with provable guarantees is a long-standing problem in nonlinear control. A crucial performance metric is the size of the resulting region of attraction, which essentially serves as a robustness “margin” of the closed-loop system against uncertainties. In this letter, we propose a new method to train a stabilizing neural network controller along with its corresponding Lyapunov certificate, aiming to maximize the resulting region of attraction while respecting the actuation constraints. Crucial to our approach is the use of Zubov’s Partial Differential Equation (PDE), which precisely characterizes the true region of attraction of a given control policy. Our framework follows an actor-critic pattern where we alternate between improving the control policy (actor) and learning a Zubov function (critic). Finally, we compute the largest certifiable region of attraction by invoking an SMT solver after the training procedure. Our numerical experiments on several design problems show consistent and significant improvements in the size of the resulting region of attraction.","PeriodicalId":37235,"journal":{"name":"IEEE Control Systems Letters","volume":null,"pages":null},"PeriodicalIF":2.4,"publicationDate":"2024-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141602550","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-06-18DOI: 10.1109/LCSYS.2024.3416069
Shuang Zhang;Sara Ifqir;Vicenç Puig
This letter proposes a zonotopic approach for the state feedback control problem of a class of uncertain switched systems subject to unknown but bounded disturbances and measurement noises. The proposed approach is the zonotopic analogous case of the switched Linear Quadratic Gaussian (LQG) control, in which the feedback loop is closed using the optimal estimates of a Switched Zonotopic Kalman Filter (SZKF) leading to a Switched Linear Quadratic Zonotopic (SLQZ) control scheme. In this context, first, a SZKF with offline filter gains design is proposed so that the unmeasurable system states can be estimated. Then, to tackle the synthesis of the SZKF and the state feedback controller, separation principle is proved so that the computation of the optimal controller and estimator can be done separately by finding the solutions to a finite set of Linear Matrix Inequalities (LMIs). At last, a reference path tracking controller of the vehicle lateral dynamics is designed to demonstrate the validity and performance of the proposed method.
{"title":"Linear Quadratic Zonotopic Control of Switched Systems: Application to Autonomous Vehicle Path-Tracking","authors":"Shuang Zhang;Sara Ifqir;Vicenç Puig","doi":"10.1109/LCSYS.2024.3416069","DOIUrl":"https://doi.org/10.1109/LCSYS.2024.3416069","url":null,"abstract":"This letter proposes a zonotopic approach for the state feedback control problem of a class of uncertain switched systems subject to unknown but bounded disturbances and measurement noises. The proposed approach is the zonotopic analogous case of the switched Linear Quadratic Gaussian (LQG) control, in which the feedback loop is closed using the optimal estimates of a Switched Zonotopic Kalman Filter (SZKF) leading to a Switched Linear Quadratic Zonotopic (SLQZ) control scheme. In this context, first, a SZKF with offline filter gains design is proposed so that the unmeasurable system states can be estimated. Then, to tackle the synthesis of the SZKF and the state feedback controller, separation principle is proved so that the computation of the optimal controller and estimator can be done separately by finding the solutions to a finite set of Linear Matrix Inequalities (LMIs). At last, a reference path tracking controller of the vehicle lateral dynamics is designed to demonstrate the validity and performance of the proposed method.","PeriodicalId":37235,"journal":{"name":"IEEE Control Systems Letters","volume":null,"pages":null},"PeriodicalIF":2.4,"publicationDate":"2024-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141602548","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-06-18DOI: 10.1109/LCSYS.2024.3416405
M. Di Ferdinando;G. Pola;S. Di Gennaro;P. Pepe
In this letter, the sampled-data stabilization problem of nonlinear asynchronous switched systems is studied. In particular, a new methodology for the design of sampled-data controllers is provided for fully nonlinear asynchronous switched systems (i.e. not necessarily affine in the control inputs) described by locally Lipschitz functions. Firstly, the new notion of Steepest Descent Switching Feedback (SDSF) is introduced. Then, it is proved the existence of a suitably fast sampling such that the digital implementation of SDSFs (continuous or not) ensures the semi-global practical stability property with arbitrarily small final target ball of the related sampled-data closed-loop system under any kind of switching with arbitrarily pre-fixed dwell time. The stabilization in the sample-and-hold sense theory is used as a tool to prove the results. Possible discontinuities in the function describing the controller at hand are also managed. The case of aperiodic sampling is included in the theory here developed. The proposed theoretical results are validated through a numerical example.
{"title":"On Sampled-Data Control of Nonlinear Asynchronous Switched Systems","authors":"M. Di Ferdinando;G. Pola;S. Di Gennaro;P. Pepe","doi":"10.1109/LCSYS.2024.3416405","DOIUrl":"https://doi.org/10.1109/LCSYS.2024.3416405","url":null,"abstract":"In this letter, the sampled-data stabilization problem of nonlinear asynchronous switched systems is studied. In particular, a new methodology for the design of sampled-data controllers is provided for fully nonlinear asynchronous switched systems (i.e. not necessarily affine in the control inputs) described by locally Lipschitz functions. Firstly, the new notion of Steepest Descent Switching Feedback (SDSF) is introduced. Then, it is proved the existence of a suitably fast sampling such that the digital implementation of SDSFs (continuous or not) ensures the semi-global practical stability property with arbitrarily small final target ball of the related sampled-data closed-loop system under any kind of switching with arbitrarily pre-fixed dwell time. The stabilization in the sample-and-hold sense theory is used as a tool to prove the results. Possible discontinuities in the function describing the controller at hand are also managed. The case of aperiodic sampling is included in the theory here developed. The proposed theoretical results are validated through a numerical example.","PeriodicalId":37235,"journal":{"name":"IEEE Control Systems Letters","volume":null,"pages":null},"PeriodicalIF":2.4,"publicationDate":"2024-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141543992","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-06-18DOI: 10.1109/LCSYS.2024.3416072
László Gerencsér;György Michaletzky;József Bokor;Péter Polcz
We show that a class of optimal input design problems have only discrete spectral measures as solutions. If we fix any finite set of possible frequencies then a randomized version of the resulting convex problem has a unique (sparse) solution with probability 1. We also propose a data-driven approach to optimal input design via virtual off-line estimators that coincide with the optimized PE estimator modulo a negligible error, both for open loop and closed loop systems.
我们证明，一类优化输入设计问题的解只有离散谱量。如果我们固定任何可能频率的有限集合，那么由此产生的凸问题的随机版本就有一个概率为 1 的唯一（稀疏）解。我们还提出了一种数据驱动的优化输入设计方法，即通过虚拟离线估计器进行优化设计，该估计器与优化的 PE 估计器在可忽略的误差范围内重合，适用于开环和闭环系统。
{"title":"Notes on Input Design: From Multi-Sine Design to Data-Driven Procedures","authors":"László Gerencsér;György Michaletzky;József Bokor;Péter Polcz","doi":"10.1109/LCSYS.2024.3416072","DOIUrl":"https://doi.org/10.1109/LCSYS.2024.3416072","url":null,"abstract":"We show that a class of optimal input design problems have only discrete spectral measures as solutions. If we fix any finite set of possible frequencies then a randomized version of the resulting convex problem has a unique (sparse) solution with probability 1. We also propose a data-driven approach to optimal input design via virtual off-line estimators that coincide with the optimized PE estimator modulo a negligible error, both for open loop and closed loop systems.","PeriodicalId":37235,"journal":{"name":"IEEE Control Systems Letters","volume":null,"pages":null},"PeriodicalIF":2.4,"publicationDate":"2024-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=10559978","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141725591","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-06-17DOI: 10.1109/LCSYS.2024.3415473
T. J. Meijer;K. J. A. Scheres;S. van den Eijnden;T. Holicki;C. W. Scherer;W. P. M. H. Heemels
In this letter, we present a unified general non-strict Finsler lemma. This result is general in the sense that it does not impose any restrictions on the involved matrices and, thereby, it encompasses all existing non-strict versions of Finsler’s lemma that do impose such restrictions. To further illustrate its usefulness, we showcase applications of the non-strict Finsler’s lemma in deriving a structured solution to a special case of the non-strict projection lemma, and we use the unified non-strict Finsler’s lemma to prove a more general version of the matrix Finsler’s lemma.
{"title":"A Unified Non-Strict Finsler Lemma","authors":"T. J. Meijer;K. J. A. Scheres;S. van den Eijnden;T. Holicki;C. W. Scherer;W. P. M. H. Heemels","doi":"10.1109/LCSYS.2024.3415473","DOIUrl":"https://doi.org/10.1109/LCSYS.2024.3415473","url":null,"abstract":"In this letter, we present a unified general non-strict Finsler lemma. This result is general in the sense that it does not impose any restrictions on the involved matrices and, thereby, it encompasses all existing non-strict versions of Finsler’s lemma that do impose such restrictions. To further illustrate its usefulness, we showcase applications of the non-strict Finsler’s lemma in deriving a structured solution to a special case of the non-strict projection lemma, and we use the unified non-strict Finsler’s lemma to prove a more general version of the matrix Finsler’s lemma.","PeriodicalId":37235,"journal":{"name":"IEEE Control Systems Letters","volume":null,"pages":null},"PeriodicalIF":2.4,"publicationDate":"2024-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141965242","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-06-17DOI: 10.1109/LCSYS.2024.3415457
Xue Lin;Qiang Jiao
Epidemic models have been used to analyze various spreading phenomena in the population, and usually consider that the spreading object does not change in the spreading process. Yet generally, the virus may evolve due to the influence of environments and medical interventions, or the information may be modified by individuals in networks. In this letter, we investigate the spread of two competing viruses in a network, where one of the viruses can mutate into the other one with a certain probability. Based on the multi-group susceptible-infected-susceptible (SIS) model, a mathematical model is proposed to describe the spread of viruses with mutations. We provide a necessary and sufficient condition for the uniqueness of the zero equilibrium, and the conditions for the existence, uniqueness, and local exponential stability of the coexisting equilibrium. Our results demonstrate that the mutation can affect the spreading ability of the virus and the coexistence of viruses. Moreover, we show the effect of mutation on the proportion of infected individuals by comparing it with the model without mutation.
{"title":"The Equilibrium Analysis for Competitive Spreading Over Networks With Mutations","authors":"Xue Lin;Qiang Jiao","doi":"10.1109/LCSYS.2024.3415457","DOIUrl":"https://doi.org/10.1109/LCSYS.2024.3415457","url":null,"abstract":"Epidemic models have been used to analyze various spreading phenomena in the population, and usually consider that the spreading object does not change in the spreading process. Yet generally, the virus may evolve due to the influence of environments and medical interventions, or the information may be modified by individuals in networks. In this letter, we investigate the spread of two competing viruses in a network, where one of the viruses can mutate into the other one with a certain probability. Based on the multi-group susceptible-infected-susceptible (SIS) model, a mathematical model is proposed to describe the spread of viruses with mutations. We provide a necessary and sufficient condition for the uniqueness of the zero equilibrium, and the conditions for the existence, uniqueness, and local exponential stability of the coexisting equilibrium. Our results demonstrate that the mutation can affect the spreading ability of the virus and the coexistence of viruses. Moreover, we show the effect of mutation on the proportion of infected individuals by comparing it with the model without mutation.","PeriodicalId":37235,"journal":{"name":"IEEE Control Systems Letters","volume":null,"pages":null},"PeriodicalIF":2.4,"publicationDate":"2024-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141544087","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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