Machine-Made Synthesis of Stabilization System by Modified Cartesian Genetic Programming
A numerical solution of the problem of the general synthesis of a stabilization system by a symbolic regression method is considered. The goal is to automatically find a feedback control function using a computer so that the control object can reach a given terminal position from anywhere in a given...
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| Published in: | IEEE transactions on cybernetics Vol. 52; no. 7; pp. 1 - 11 |
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| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
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United States
IEEE
01.07.2022
The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
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| ISSN: | 2168-2267, 2168-2275, 2168-2275 |
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| Abstract | A numerical solution of the problem of the general synthesis of a stabilization system by a symbolic regression method is considered. The goal is to automatically find a feedback control function using a computer so that the control object can reach a given terminal position from anywhere in a given region of the initial conditions with an optimal value of the quality criterion. Usually, the control synthesis problem is solved analytically or technically taking into account the specific properties of the mathematical model. We suppose that modern numerical approaches of symbolic regression can be applied to find a solution without reference to specific model equations. It is proposed to use the numerical method of Cartesian genetic programming (CGP). It was developed for automatic writing of programs but has never been used to solve the synthesis problem. In the present work, the method was modified with the principle of small variations in order to reduce the search area and increase the rate of convergence. To apply the general principle of small variations to CGP, we developed special types of variations and coding. The modified CGP searches for the mathematical expression of the feedback control function in the form of a code and, at the same time, the optimal value of the parametric vector which is also a new feature--simultaneous tuning of the parameters inside the search process. This approach enables working with objects and functions of any type, which is not always possible with analytical methods. The need to use the received solution on the onboard processor of the control object imposes certain restrictions on the used basic set of elementary functions. This article proposes the theoretical foundations of the study of these functions, and the concept of the space of machine-made functions is introduced. The capabilities of the approach are demonstrated on the numerical solution of the control system synthesis problems for a mobile robot and a Duffing model. |
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| AbstractList | A numerical solution of the problem of the general synthesis of a stabilization system by a symbolic regression method is considered. The goal is to automatically find a feedback control function using a computer so that the control object can reach a given terminal position from anywhere in a given region of the initial conditions with an optimal value of the quality criterion. Usually, the control synthesis problem is solved analytically or technically taking into account the specific properties of the mathematical model. We suppose that modern numerical approaches of symbolic regression can be applied to find a solution without reference to specific model equations. It is proposed to use the numerical method of Cartesian genetic programming (CGP). It was developed for automatic writing of programs but has never been used to solve the synthesis problem. In the present work, the method was modified with the principle of small variations in order to reduce the search area and increase the rate of convergence. To apply the general principle of small variations to CGP, we developed special types of variations and coding. The modified CGP searches for the mathematical expression of the feedback control function in the form of a code and, at the same time, the optimal value of the parametric vector which is also a new feature--simultaneous tuning of the parameters inside the search process. This approach enables working with objects and functions of any type, which is not always possible with analytical methods. The need to use the received solution on the onboard processor of the control object imposes certain restrictions on the used basic set of elementary functions. This article proposes the theoretical foundations of the study of these functions, and the concept of the space of machine-made functions is introduced. The capabilities of the approach are demonstrated on the numerical solution of the control system synthesis problems for a mobile robot and a Duffing model. A numerical solution of the problem of the general synthesis of a stabilization system by a symbolic regression method is considered. The goal is to automatically find a feedback control function using a computer so that the control object can reach a given terminal position from anywhere in a given region of the initial conditions with an optimal value of the quality criterion. Usually, the control synthesis problem is solved analytically or technically taking into account the specific properties of the mathematical model. We suppose that modern numerical approaches of symbolic regression can be applied to find a solution without reference to specific model equations. It is proposed to use the numerical method of Cartesian genetic programming (CGP). It was developed for automatic writing of programs but has never been used to solve the synthesis problem. In the present work, the method was modified with the principle of small variations in order to reduce the search area and increase the rate of convergence. To apply the general principle of small variations to CGP, we developed special types of variations and coding. The modified CGP searches for the mathematical expression of the feedback control function in the form of a code and, at the same time, the optimal value of the parametric vector which is also a new feature-simultaneous tuning of the parameters inside the search process. This approach enables working with objects and functions of any type, which is not always possible with analytical methods. The need to use the received solution on the onboard processor of the control object imposes certain restrictions on the used basic set of elementary functions. This article proposes the theoretical foundations of the study of these functions, and the concept of the space of machine-made functions is introduced. The capabilities of the approach are demonstrated on the numerical solution of the control system synthesis problems for a mobile robot and a Duffing model.A numerical solution of the problem of the general synthesis of a stabilization system by a symbolic regression method is considered. The goal is to automatically find a feedback control function using a computer so that the control object can reach a given terminal position from anywhere in a given region of the initial conditions with an optimal value of the quality criterion. Usually, the control synthesis problem is solved analytically or technically taking into account the specific properties of the mathematical model. We suppose that modern numerical approaches of symbolic regression can be applied to find a solution without reference to specific model equations. It is proposed to use the numerical method of Cartesian genetic programming (CGP). It was developed for automatic writing of programs but has never been used to solve the synthesis problem. In the present work, the method was modified with the principle of small variations in order to reduce the search area and increase the rate of convergence. To apply the general principle of small variations to CGP, we developed special types of variations and coding. The modified CGP searches for the mathematical expression of the feedback control function in the form of a code and, at the same time, the optimal value of the parametric vector which is also a new feature-simultaneous tuning of the parameters inside the search process. This approach enables working with objects and functions of any type, which is not always possible with analytical methods. The need to use the received solution on the onboard processor of the control object imposes certain restrictions on the used basic set of elementary functions. This article proposes the theoretical foundations of the study of these functions, and the concept of the space of machine-made functions is introduced. The capabilities of the approach are demonstrated on the numerical solution of the control system synthesis problems for a mobile robot and a Duffing model. |
| Author | Diveev, Askhat I. Shmalko, Elizaveta Y. |
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| References | åström (ref1) 1995 ref12 ref15 ref14 ref31 diveev (ref32) 2017 ref30 ref33 ref11 ref10 ref2 lee (ref35) 1967 ref19 ref18 garg (ref4) 2013 ashkan parsa (ref16) 2018 hasseni (ref13) 2018 zelinka (ref23) 2002 ref24 ref26 ref20 ref22 ref21 šuster (ref34) 2011; 11 koza (ref17) 1992 ref28 ref27 ref29 ref8 ref7 ref9 ref3 ref6 ref5 nikolaev (ref25) 2006 |
| References_xml | – ident: ref19 doi: 10.1109/TCYB.2020.2963849 – ident: ref7 doi: 10.1109/TCYB.2016.2581220 – ident: ref5 doi: 10.1137/0301003 – ident: ref24 doi: 10.1007/978-3-540-46239-2_9 – ident: ref22 doi: 10.1109/4235.942529 – ident: ref14 doi: 10.1109/JAS.2016.7510019 – ident: ref2 doi: 10.3182/20090706-3-FR-2004.00256 – start-page: 23 year: 2018 ident: ref16 article-title: Backstepping control based on sliding mode for station-keeping of stratospheric airship publication-title: Proc 6th RSI Int Conf Robot Mechatronics (IcRoM) – ident: ref11 doi: 10.1016/0167-6911(92)90111-5 – year: 1992 ident: ref17 publication-title: Genetic Programming On the Programming of Computers by Means of Natural Selection – ident: ref29 doi: 10.1109/CDC.2016.7798684 – year: 1995 ident: ref1 publication-title: PID Controllers Theory Design and Tuning – start-page: 158 year: 2017 ident: ref32 article-title: Evolutionary computations for synthesis of control system of group of robots and the optimum choice of trajectories for their movement publication-title: Proc CEUR Workshop 8th Int Conf Optim Appl (OPTIMA) – ident: ref18 doi: 10.1109/TCYB.2015.2509863 – start-page: 25 year: 2006 ident: ref25 article-title: Inductive genetic programming publication-title: Adaptive Learning of Polynomial Networks – ident: ref31 doi: 10.1109/FSKD.2017.8393051 – volume: 11 start-page: 38 year: 2011 ident: ref34 article-title: Tracking trajectory of the mobile robot khepera II using approaches of artificial intelligence publication-title: Acta Electrotechnica et Informatica doi: 10.2478/v10198-011-0006-y – ident: ref9 doi: 10.17587/mau.17.435-445 – ident: ref21 doi: 10.1109/TCYB.2018.2799683 – ident: ref15 doi: 10.23919/ChiCC.2017.8028320 – ident: ref26 doi: 10.1134/S1064230712010066 – start-page: 586 year: 1967 ident: ref35 publication-title: Foundations of Optimal Control Theory – ident: ref10 doi: 10.1155/2018/4868791 – start-page: 816 year: 2013 ident: ref4 article-title: Potential function based formation control of mobile multiple-agent systems publication-title: Proc 1st Int 16th Nat Conf Mach Mechanisms – ident: ref27 doi: 10.1016/j.engappai.2012.05.015 – ident: ref20 doi: 10.1109/TCYB.2015.2411285 – ident: ref28 doi: 10.1016/j.asoc.2020.106432 – start-page: 348 year: 2018 ident: ref13 article-title: Integral backstepping/LFT-LPV H? control for the trajectory tracking of a quadcopter publication-title: Proc 7th Int Conf Syst Control (ICSC) – ident: ref6 doi: 10.1109/TAC.2005.863496 – ident: ref33 doi: 10.1016/j.ifacol.2015.11.054 – ident: ref30 doi: 10.1109/IROS.2018.8593881 – ident: ref3 doi: 10.17587/mau.16.530-535 – ident: ref12 doi: 10.1109/JAS.2019.1911798 – ident: ref8 doi: 10.1007/s10957-013-0403-8 – start-page: 93 year: 2002 ident: ref23 article-title: Analytic programming by means of soma algorithm publication-title: Proc 8th Int Conf Soft Comput |
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| SubjectTerms | Aerospace electronics Cartesian coordinates Cartesian genetic programming (CGP) control synthesis Control systems Differential equations Feedback control Genetic algorithms Genetic programming Initial conditions machine-made functions Mathematical model Mathematical models Microprocessors mobile robot Neural networks Numerical methods Principles Process control Process parameters Search problems Search process Stabilization Synthesis |
| Title | Machine-Made Synthesis of Stabilization System by Modified Cartesian Genetic Programming |
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