In this paper, a stabilizer dedicated for a unicycle-like robot is considered. The proposed smooth control law ensures the global boundedness of position and orientation trajectories to a neighbourhood of the desired point with an arbitrarily selected radius and it is robust to bounded additive measurement noises. The controller consists of a smooth hybrid navigation algorithm and a smooth feedback based on the transverse function approach. The stability proof, simulation and experimental results illustrating properties of the algorithm are discussed
{"title":"A robust smooth controller for a unicycle-like robot","authors":"D. Pazderski","doi":"10.24425/119082","DOIUrl":"https://doi.org/10.24425/119082","url":null,"abstract":"In this paper, a stabilizer dedicated for a unicycle-like robot is considered. The proposed smooth control law ensures the global boundedness of position and orientation trajectories to a neighbourhood of the desired point with an arbitrarily selected radius and it is robust to bounded additive measurement noises. The controller consists of a smooth hybrid navigation algorithm and a smooth feedback based on the transverse function approach. The stability proof, simulation and experimental results illustrating properties of the algorithm are discussed","PeriodicalId":48654,"journal":{"name":"Archives of Control Sciences","volume":"578 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76780802","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 : 2023-07-20DOI: 10.24425/ACS.2018.124711
S. Vaidyanathan, A. Sambas, M. Mamat
In the recent years, chaotic systems with uncountable equilibrium points such as chaotic systems with line equilibrium and curve equilibrium have been studied well in the literature. This reports a new 3-D chaotic system with an axe-shaped curve of equilibrium points. Dynamics of the chaotic system with the axe-shaped equilibrium has been studied by using phase plots, bifurcation diagram, Lyapunov exponents and Lyapunov dimension. Furthermore, an electronic circuit implementation of the new chaotic system with axe-shaped equilibrium has been designed to check its feasibility. As a control application, we report results for the synchronization of the new system possessing an axe-shaped curve of equilibrium points.
{"title":"A new chaotic system with axe-shaped equilibrium, its circuit implementation and adaptive synchronization","authors":"S. Vaidyanathan, A. Sambas, M. Mamat","doi":"10.24425/ACS.2018.124711","DOIUrl":"https://doi.org/10.24425/ACS.2018.124711","url":null,"abstract":"In the recent years, chaotic systems with uncountable equilibrium points such as chaotic systems with line equilibrium and curve equilibrium have been studied well in the literature. This reports a new 3-D chaotic system with an axe-shaped curve of equilibrium points. Dynamics of the chaotic system with the axe-shaped equilibrium has been studied by using phase plots, bifurcation diagram, Lyapunov exponents and Lyapunov dimension. Furthermore, an electronic circuit implementation of the new chaotic system with axe-shaped equilibrium has been designed to check its feasibility. As a control application, we report results for the synchronization of the new system possessing an axe-shaped curve of equilibrium points.","PeriodicalId":48654,"journal":{"name":"Archives of Control Sciences","volume":"42 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81156288","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 : 2023-07-20DOI: 10.24425/ACS.2019.131229
S. Rasappan
J.L. Hindmarsh, R.M. Rose introduced the concept of neuronal burst. In this paper, synchronization is investigated for the construction of a model of neuronal burst using backstepping control with recursive feedback. Synchronization for a model of neuronal bursting system is established using Lyapunov stability theory. The backstepping scheme is a recursive procedure that links the choice of a Lyapunov function with the design of a controller. The backstepping control method is effective and convenient to synchronize identical systems. Numerical simulations are furnished to illustrate and validate the synchronization result derived in this paper.
{"title":"Synchronization of neuronal bursting using backstepping control with recursive feedback","authors":"S. Rasappan","doi":"10.24425/ACS.2019.131229","DOIUrl":"https://doi.org/10.24425/ACS.2019.131229","url":null,"abstract":"J.L. Hindmarsh, R.M. Rose introduced the concept of neuronal burst. In this paper, synchronization is investigated for the construction of a model of neuronal burst using backstepping control with recursive feedback. Synchronization for a model of neuronal bursting system is established using Lyapunov stability theory. The backstepping scheme is a recursive procedure that links the choice of a Lyapunov function with the design of a controller. The backstepping control method is effective and convenient to synchronize identical systems. Numerical simulations are furnished to illustrate and validate the synchronization result derived in this paper.","PeriodicalId":48654,"journal":{"name":"Archives of Control Sciences","volume":"72 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84094601","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 : 2023-07-20DOI: 10.24425/acs.2022.141713
R. Kamocki
In this article we focus on optimal control problems involving a nonlinear fractional control system of different orders with Caputo derivatives, associated to a Lagrange cost functional. Based on a lower closure theorem for orientor fields combined with Filippov’s approach, we derive an existence result for at least one optimal solution for such a problem.
{"title":"Existence of optimal control for multi-order fractional optimal control problems","authors":"R. Kamocki","doi":"10.24425/acs.2022.141713","DOIUrl":"https://doi.org/10.24425/acs.2022.141713","url":null,"abstract":"In this article we focus on optimal control problems involving a nonlinear fractional control system of different orders with Caputo derivatives, associated to a Lagrange cost functional. Based on a lower closure theorem for orientor fields combined with Filippov’s approach, we derive an existence result for at least one optimal solution for such a problem.","PeriodicalId":48654,"journal":{"name":"Archives of Control Sciences","volume":"7 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74719022","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 : 2023-07-20DOI: 10.24425/acs.2020.134678
S. Vaidyanathan, I. Moroz
A new 4-D dynamical system with hyperchaos is reported in this work. It is shown that the proposed nonlinear dynamical system with hyperchaos has no equilibrium point. Hence, the new dynamical system exhibits hidden hyperchaotic attractor. An in-depth dynamic analysis of the new hyperchaotic system is carried out with bifurcation transition diagrams, multistability analysis, period-doubling bubbles and offset boosting analysis. Using Integral Sliding Mode Control (ISMC), global hyperchaos synchronization results of the new hyperchaotic system are described in detail. Furthermore, an electronic circuit realization of the new hyperchaotic system has been simulated in MultiSim software version 13.0 and the results of which are in good agreement with the numerical simulations using MATLAB.
{"title":"A new 4-D hyperchaotic system with no equilibrium, its multistability, offset boosting and circuit simulation","authors":"S. Vaidyanathan, I. Moroz","doi":"10.24425/acs.2020.134678","DOIUrl":"https://doi.org/10.24425/acs.2020.134678","url":null,"abstract":"A new 4-D dynamical system with hyperchaos is reported in this work. It is shown that the proposed nonlinear dynamical system with hyperchaos has no equilibrium point. Hence, the new dynamical system exhibits hidden hyperchaotic attractor. An in-depth dynamic analysis of the new hyperchaotic system is carried out with bifurcation transition diagrams, multistability analysis, period-doubling bubbles and offset boosting analysis. Using Integral Sliding Mode Control (ISMC), global hyperchaos synchronization results of the new hyperchaotic system are described in detail. Furthermore, an electronic circuit realization of the new hyperchaotic system has been simulated in MultiSim software version 13.0 and the results of which are in good agreement with the numerical simulations using MATLAB.","PeriodicalId":48654,"journal":{"name":"Archives of Control Sciences","volume":"1 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75229255","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 : 2023-07-20DOI: 10.24425/ACS.2018.124706
A. Khurshudyan
{"title":"Exact and approximate controllability conditions for the micro-swimmers deflection governed by electric field on a plane: The Green’s function approach","authors":"A. Khurshudyan","doi":"10.24425/ACS.2018.124706","DOIUrl":"https://doi.org/10.24425/ACS.2018.124706","url":null,"abstract":"","PeriodicalId":48654,"journal":{"name":"Archives of Control Sciences","volume":"36 6 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82808760","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 : 2023-07-20DOI: 10.24425/acs.2021.138694
S. Kazhikenova, S. Shaltakov, B. Nussupbekov
The basic objective of the research is to construct a differencemodel of the melt motion. The existence of a solution to the problem is proven in the paper. It is also proven the convergence of the difference problem solution to the original problem solution of the melt motion. The Rothe method is implemented to study the Navier–Stokes equations, which provides the study of the boundary value problems correctness for a viscous incompressible flow both numerically and analytically.
{"title":"Difference melt model","authors":"S. Kazhikenova, S. Shaltakov, B. Nussupbekov","doi":"10.24425/acs.2021.138694","DOIUrl":"https://doi.org/10.24425/acs.2021.138694","url":null,"abstract":"The basic objective of the research is to construct a differencemodel of the melt motion. The existence of a solution to the problem is proven in the paper. It is also proven the convergence of the difference problem solution to the original problem solution of the melt motion. The Rothe method is implemented to study the Navier–Stokes equations, which provides the study of the boundary value problems correctness for a viscous incompressible flow both numerically and analytically.","PeriodicalId":48654,"journal":{"name":"Archives of Control Sciences","volume":"26 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91172293","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 : 2023-07-20DOI: 10.24425/acs.2021.137421
A. Ouannas, Fatiha Mesdoui, S. Momani, I. Batiha, G. Grassi
The Fitzhugh-Nagumo model (FN model), which is successfully employed in modeling the function of the so-called membrane potential, exhibits various formations in neuronal networks and rich complex dynamics. This work deals with the problem of control and synchronization of the FN reaction-diffusion model. The proposed control law in this study is designed to be uni-dimensional and linear law for the purpose of reducing the cost of implementation. In order to analytically prove this assertion, Lyapunov’s second method is utilized and illustrated numerically in one-and/or two-spatial dimensions.
{"title":"Synchronization of FitzHugh-Nagumo reaction-diffusion systems via one-dimensional linear control law","authors":"A. Ouannas, Fatiha Mesdoui, S. Momani, I. Batiha, G. Grassi","doi":"10.24425/acs.2021.137421","DOIUrl":"https://doi.org/10.24425/acs.2021.137421","url":null,"abstract":"The Fitzhugh-Nagumo model (FN model), which is successfully employed in modeling the function of the so-called membrane potential, exhibits various formations in neuronal networks and rich complex dynamics. This work deals with the problem of control and synchronization of the FN reaction-diffusion model. The proposed control law in this study is designed to be uni-dimensional and linear law for the purpose of reducing the cost of implementation. In order to analytically prove this assertion, Lyapunov’s second method is utilized and illustrated numerically in one-and/or two-spatial dimensions.","PeriodicalId":48654,"journal":{"name":"Archives of Control Sciences","volume":"39 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77897158","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 : 2023-07-20DOI: 10.24425/acs.2021.137425
S. Jilavyan
The Green’s function approach is applied for studying the exact and approximate null-controllability of a finite rod in finite time by means of a source moving along the rod with controllable trajectory. The intensity of the source remains constant. Applying the recently developed Green’s function approach, the analysis of the exact null-controllability is reduced to an infinite system of nonlinear constraints with respect to the control function. A sufficient condition for the approximate null-controllability of the rod is obtained. Since the exact solution of the system of constraints is a long-standing open problem, some heuristic solutions are used instead. The efficiency of these solutions is shown on particular cases of approximate controllability.
{"title":"Heating control of a finite rod with a mobile source","authors":"S. Jilavyan","doi":"10.24425/acs.2021.137425","DOIUrl":"https://doi.org/10.24425/acs.2021.137425","url":null,"abstract":"The Green’s function approach is applied for studying the exact and approximate null-controllability of a finite rod in finite time by means of a source moving along the rod with controllable trajectory. The intensity of the source remains constant. Applying the recently developed Green’s function approach, the analysis of the exact null-controllability is reduced to an infinite system of nonlinear constraints with respect to the control function. A sufficient condition for the approximate null-controllability of the rod is obtained. Since the exact solution of the system of constraints is a long-standing open problem, some heuristic solutions are used instead. The efficiency of these solutions is shown on particular cases of approximate controllability.","PeriodicalId":48654,"journal":{"name":"Archives of Control Sciences","volume":"174 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74134317","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 : 2023-07-20DOI: 10.24425/ACS.2020.133502
Robert Nebeluk, P. Marusak
Model predictive control (MPC) algorithms brought increase of the control system performance in many applications thanks to relatively easily solving issues that are hard to solve without these algorithms. The paper is focused on investigating how to further improve the control system performance using a trajectory of parameters weighting predicted control errors in the performance function of the optimization problem. Different shapes of trajectories are proposed and their influence on control systems is tested. Additionally, experiments checking the influence of disturbances and of modeling uncertainty on control system performance are conducted. The case studies were done in control systems of three control plants: a linear nonminimumphase plant, a nonlinear polymerization reactor and a nonlinear thin film evaporator. Three types of MPC algorithms were used during research: linear DMC, nonlinear DMC with successive linearization (NDMC–SL), nonlinear DMC with nonlinear prediction and linearization (NDMC–NPL). Results of conducted experiments are presented in greater detail for the control system of the polymerization reactor, whereas for the other two control systems only the most interesting results are presented, for the sake of brevity. The experiments in the control system of the linear plant were done as preliminary experiments with the modified optimization problem. In the case of control system of the thin film evaporator the researched mechanisms were used in the control system of a MIMO plant showing possibilities of improving the control system performance.
{"title":"Efficient MPC algorithms with variable trajectories of parameters weighting predicted control errors","authors":"Robert Nebeluk, P. Marusak","doi":"10.24425/ACS.2020.133502","DOIUrl":"https://doi.org/10.24425/ACS.2020.133502","url":null,"abstract":"Model predictive control (MPC) algorithms brought increase of the control system performance in many applications thanks to relatively easily solving issues that are hard to solve without these algorithms. The paper is focused on investigating how to further improve the control system performance using a trajectory of parameters weighting predicted control errors in the performance function of the optimization problem. Different shapes of trajectories are proposed and their influence on control systems is tested. Additionally, experiments checking the influence of disturbances and of modeling uncertainty on control system performance are conducted. The case studies were done in control systems of three control plants: a linear nonminimumphase plant, a nonlinear polymerization reactor and a nonlinear thin film evaporator. Three types of MPC algorithms were used during research: linear DMC, nonlinear DMC with successive linearization (NDMC–SL), nonlinear DMC with nonlinear prediction and linearization (NDMC–NPL). Results of conducted experiments are presented in greater detail for the control system of the polymerization reactor, whereas for the other two control systems only the most interesting results are presented, for the sake of brevity. The experiments in the control system of the linear plant were done as preliminary experiments with the modified optimization problem. In the case of control system of the thin film evaporator the researched mechanisms were used in the control system of a MIMO plant showing possibilities of improving the control system performance.","PeriodicalId":48654,"journal":{"name":"Archives of Control Sciences","volume":"15 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81659435","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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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