Controlling large swarms of robotic agents presents many challenges including, but not limited to, computational complexity due to a large number of agents, uncertainty in the functionality of each agent in the swarm, and uncertainty in the swarm's configuration. This work generalizes the swarm state using Random Finite Set (RFS) theory and solves a centralized control problem with a Quasi-Newton optimization through the use of Model Predictive Control (MPC) to overcome the aforementioned challenges. This work uses the RFS formulation to control the distribution of agents assuming an unknown or unspecified number of agents. Computationally efficient solutions are also obtained via the MPC version of the Iterative Linear Quadratic Regulator (ILQR), a variant of Differential Dynamic Programming (DDP). Information divergence is used to define the distance between the swarm RFS and the desired swarm configuration through the use of the modified $L_2^2$ distance. Simulation results using MPC and ILQR show that the swarm intensity converges to the desired intensity. Additionally, the RFS control formulation is shown to be very flexible in terms of the number of agents in the swarm and configuration of the desired Gaussian mixtures. Lastly, the ILQR and the Gaussian Mixture Probability Hypothesis Density filter are used in conjunction to solve a spacecraft relative motion problem with imperfect information to show the viability of centralized RFS control for this real-world scenario.
{"title":"Random Finite Set Theory and Centralized Control of Large Collaborative Swarms","authors":"Bryce Doerr, R. Linares, Pingping Zhu, S. Ferrari","doi":"10.2514/1.g004861","DOIUrl":"https://doi.org/10.2514/1.g004861","url":null,"abstract":"Controlling large swarms of robotic agents presents many challenges including, but not limited to, computational complexity due to a large number of agents, uncertainty in the functionality of each agent in the swarm, and uncertainty in the swarm's configuration. This work generalizes the swarm state using Random Finite Set (RFS) theory and solves a centralized control problem with a Quasi-Newton optimization through the use of Model Predictive Control (MPC) to overcome the aforementioned challenges. This work uses the RFS formulation to control the distribution of agents assuming an unknown or unspecified number of agents. Computationally efficient solutions are also obtained via the MPC version of the Iterative Linear Quadratic Regulator (ILQR), a variant of Differential Dynamic Programming (DDP). Information divergence is used to define the distance between the swarm RFS and the desired swarm configuration through the use of the modified $L_2^2$ distance. Simulation results using MPC and ILQR show that the swarm intensity converges to the desired intensity. Additionally, the RFS control formulation is shown to be very flexible in terms of the number of agents in the swarm and configuration of the desired Gaussian mixtures. Lastly, the ILQR and the Gaussian Mixture Probability Hypothesis Density filter are used in conjunction to solve a spacecraft relative motion problem with imperfect information to show the viability of centralized RFS control for this real-world scenario.","PeriodicalId":265389,"journal":{"name":"arXiv: Systems and Control","volume":"232 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121000296","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 : 2019-09-25DOI: 10.25728/ASSA.2020.20.1.775
D. Dmitrishin, I. Iacob, A. Stokolos
We explore the problem of stabilization of unstable periodic orbits in discrete nonlinear dynamical systems. This work proposes the generalization of predictive control method for resolving the stabilization problem. Our method embodies the development of control method proposed by B.T. Polyak. The control we propose uses a linear (convex) combination of iterated functions. With the proposed method auxiliary, the problem of robust cycle stabilization for various cases of its multipliers localization is solved. An algorithm for finding a given length cycle when its multipliers are known is described as a particular case of our method application. Also, we present numerical simulation results for some well-known mappings and the possibility of further generalization of this method.
{"title":"Average predictive control for nonlinear discrete dynamical systems.","authors":"D. Dmitrishin, I. Iacob, A. Stokolos","doi":"10.25728/ASSA.2020.20.1.775","DOIUrl":"https://doi.org/10.25728/ASSA.2020.20.1.775","url":null,"abstract":"We explore the problem of stabilization of unstable periodic orbits in discrete nonlinear dynamical systems. This work proposes the generalization of predictive control method for resolving the stabilization problem. Our method embodies the development of control method proposed by B.T. Polyak. The control we propose uses a linear (convex) combination of iterated functions. With the proposed method auxiliary, the problem of robust cycle stabilization for various cases of its multipliers localization is solved. An algorithm for finding a given length cycle when its multipliers are known is described as a particular case of our method application. Also, we present numerical simulation results for some well-known mappings and the possibility of further generalization of this method.","PeriodicalId":265389,"journal":{"name":"arXiv: Systems and Control","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116177087","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 : 2016-09-21DOI: 10.14311/nnw.2019.29.020
Katerina Henclova
Proportional integral derivative (PID) controllers are important and widely used tools in system control. Tuning of the controller gains is a laborious task, especially for complex systems such as combustion engines. To minimize the time of an engineer for tuning of the gains in a simulation software, we propose to formulate a part of the problem as a black-box optimization task. In this paper, we summarize the properties and practical limitations of tuning of the gains in this particular application. We investigate the latest methods of black-box optimization and conclude that the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) with bi-population restart strategy, elitist parent selection and active covariance matrix adaptation is best suited for this task. Details of the algorithm's experiment-based calibration are explained as well as derivation of a suitable objective function. The method's performance is compared with that of PSO and SHADE. Finally, its usability is verified on six models of real engines.
{"title":"Using CMA-ES for tuning coupled PID controllers within models of combustion engines","authors":"Katerina Henclova","doi":"10.14311/nnw.2019.29.020","DOIUrl":"https://doi.org/10.14311/nnw.2019.29.020","url":null,"abstract":"Proportional integral derivative (PID) controllers are important and widely used tools in system control. Tuning of the controller gains is a laborious task, especially for complex systems such as combustion engines. To minimize the time of an engineer for tuning of the gains in a simulation software, we propose to formulate a part of the problem as a black-box optimization task. In this paper, we summarize the properties and practical limitations of tuning of the gains in this particular application. We investigate the latest methods of black-box optimization and conclude that the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) with bi-population restart strategy, elitist parent selection and active covariance matrix adaptation is best suited for this task. Details of the algorithm's experiment-based calibration are explained as well as derivation of a suitable objective function. The method's performance is compared with that of PSO and SHADE. Finally, its usability is verified on six models of real engines.","PeriodicalId":265389,"journal":{"name":"arXiv: Systems and Control","volume":"255 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114362139","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 : 2016-05-24DOI: 10.1109/AUCC.2016.7868220
Shibdas Roy, I. Petersen
We study robust $H_infty$ coherent-classical estimation for a class of physically realizable linear quantum systems with parameter uncertainties. Such a robust coherent-classical estimator, with or without coherent feedback, can yield better disturbance-to-error performance than the corresponding robust purely-classical estimator for an uncertain plant. Moreover, coherent feedback allows for such a robust coherent-classical estimator to be more robust to uncertainty in comparison to the robust classical-only estimator.
{"title":"Robust $H_infty$ Coherent-Classical Estimation.","authors":"Shibdas Roy, I. Petersen","doi":"10.1109/AUCC.2016.7868220","DOIUrl":"https://doi.org/10.1109/AUCC.2016.7868220","url":null,"abstract":"We study robust $H_infty$ coherent-classical estimation for a class of physically realizable linear quantum systems with parameter uncertainties. Such a robust coherent-classical estimator, with or without coherent feedback, can yield better disturbance-to-error performance than the corresponding robust purely-classical estimator for an uncertain plant. Moreover, coherent feedback allows for such a robust coherent-classical estimator to be more robust to uncertainty in comparison to the robust classical-only estimator.","PeriodicalId":265389,"journal":{"name":"arXiv: Systems and Control","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116795338","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 : 2016-04-23DOI: 10.1016/J.IFACOL.2017.08.1481
Insoon Yang
{"title":"Online Combinatorial Optimization for Interconnected Refrigeration Systems: Linear Approximation and Submodularity","authors":"Insoon Yang","doi":"10.1016/J.IFACOL.2017.08.1481","DOIUrl":"https://doi.org/10.1016/J.IFACOL.2017.08.1481","url":null,"abstract":"","PeriodicalId":265389,"journal":{"name":"arXiv: Systems and Control","volume":"60 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123023460","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 : 2015-06-11DOI: 10.6084/M9.FIGSHARE.1445954.V1
Journals Iosr, O.Zakary, M.Rachik
Discrete-time linear systems with perturbed initial state are considered. A disturbance that infects the initial state is said to be $epsilon$-tolerable if the corresponding output signal is relatively insensitive to their effects. In this paper, we will define a new set that characterize each gain matrix K and the associated feedback control law ui=Kxi, this set will be called the $epsilon$-capacity of the gain matrix K. The set of all possible gain matrix that makes the system insensitive to all disturbances is noted $Phicdot$. The characterization of $Phicdot$ is investigated, and we propose an algorithmic approach that allows to determine if a control law is belongs to $Phicdot$ or not. Numerical simulations are given.
{"title":"The $ε$-capacity of a gain matrix and tolerable disturbances: Discrete-time perturbed linear systems.","authors":"Journals Iosr, O.Zakary, M.Rachik","doi":"10.6084/M9.FIGSHARE.1445954.V1","DOIUrl":"https://doi.org/10.6084/M9.FIGSHARE.1445954.V1","url":null,"abstract":"Discrete-time linear systems with perturbed initial state are considered. A disturbance that infects the initial state is said to be $epsilon$-tolerable if the corresponding output signal is relatively insensitive to their effects. In this paper, we will define a new set that characterize each gain matrix K and the associated feedback control law ui=Kxi, this set will be called the $epsilon$-capacity of the gain matrix K. The set of all possible gain matrix that makes the system insensitive to all disturbances is noted $Phicdot$. The characterization of $Phicdot$ is investigated, and we propose an algorithmic approach that allows to determine if a control law is belongs to $Phicdot$ or not. Numerical simulations are given.","PeriodicalId":265389,"journal":{"name":"arXiv: Systems and Control","volume":"335 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115878176","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}
The interest on autonomous systems is increasing both in industry and academia. Such systems must operate with limited human intervention in a changing environment and must be able to compensate for significant system failures without external intervention. The most appropriate models of autonomous systems can be found in the class of hybrid systems (which study continuous-state dynamic processes via discrete-state controllers) that interact with their environment. This workshop brings together researchers interested in all aspects of autonomy and resilience of hybrid systems.
{"title":"Proceedings Third International Workshop on Hybrid Autonomous Systems","authors":"L. Bortolussi, Manuela L. Bujorianu, G. Pola","doi":"10.4204/EPTCS.124","DOIUrl":"https://doi.org/10.4204/EPTCS.124","url":null,"abstract":"The interest on autonomous systems is increasing both in industry and academia. Such systems must operate with limited human intervention in a changing environment and must be able to compensate for significant system failures without external intervention. The most appropriate models of autonomous systems can be found in the class of hybrid systems (which study continuous-state dynamic processes via discrete-state controllers) that interact with their environment. This workshop brings together researchers interested in all aspects of autonomy and resilience of hybrid systems.","PeriodicalId":265389,"journal":{"name":"arXiv: Systems and Control","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114985089","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}
We study the stability of a Markovian model of electricity production and consumption that incorporates production volatility due to renewables and uncertainty about actual demand versus planned production. We assume that the energy producer targets a fixed energy reserve, subject to ramp-up and ramp-down constraints, and that appliances are subject to demand-response signals and adjust their consumption to the available production by delaying their demand. When a constant fraction of the delayed demand vanishes over time, we show that the general state Markov chain characterizing the system is positive Harris and ergodic (i.e., delayed demand is bounded with high probability). However, when delayed demand increases by a constant fraction over time, we show that the Markov chain is non-positive (i.e., there exists a non-zero probability that delayed demand becomes unbounded). We exhibit Lyapunov functions to prove our claims. In addition, we provide examples of heating appliances that, when delayed, have energy requirements corresponding to the two considered cases.
{"title":"Stability of a Stochastic Model for Demand-Response","authors":"J. Boudec, Dan-Cristian Tomozei","doi":"10.1214/11-SSY048","DOIUrl":"https://doi.org/10.1214/11-SSY048","url":null,"abstract":"We study the stability of a Markovian model of electricity production and consumption that incorporates production volatility due to renewables and uncertainty about actual demand versus planned production. We assume that the energy producer targets a fixed energy reserve, subject to ramp-up and ramp-down constraints, and that appliances are subject to demand-response signals and adjust their consumption to the available production by delaying their demand. When a constant fraction of the delayed demand vanishes over time, we show that the general state Markov chain characterizing the system is positive Harris and ergodic (i.e., delayed demand is bounded with high probability). However, when delayed demand increases by a constant fraction over time, we show that the Markov chain is non-positive (i.e., there exists a non-zero probability that delayed demand becomes unbounded). We exhibit Lyapunov functions to prove our claims. In addition, we provide examples of heating appliances that, when delayed, have energy requirements corresponding to the two considered cases.","PeriodicalId":265389,"journal":{"name":"arXiv: Systems and Control","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116846343","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 : 1900-01-01DOI: 10.1007/978-3-642-30096-7_24
Christian Dirscherl, C. Hackl, Korbinian Schechner
{"title":"Modellierung und Regelung von modernen Windkraftanlagen: Eine Einführung","authors":"Christian Dirscherl, C. Hackl, Korbinian Schechner","doi":"10.1007/978-3-642-30096-7_24","DOIUrl":"https://doi.org/10.1007/978-3-642-30096-7_24","url":null,"abstract":"","PeriodicalId":265389,"journal":{"name":"arXiv: Systems and Control","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124859275","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 : 1900-01-01DOI: 10.1007/978-1-4939-7822-9_10
M. Chertkov, Sidhant Misra, Marc Vuffray, Dvijotham Krishnamurthy, Pascal Van Hentenryck
{"title":"Graphical Models and Belief Propagation Hierarchy for Physics-Constrained Network Flows","authors":"M. Chertkov, Sidhant Misra, Marc Vuffray, Dvijotham Krishnamurthy, Pascal Van Hentenryck","doi":"10.1007/978-1-4939-7822-9_10","DOIUrl":"https://doi.org/10.1007/978-1-4939-7822-9_10","url":null,"abstract":"","PeriodicalId":265389,"journal":{"name":"arXiv: Systems and Control","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114984432","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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