Conditions for Guaranteeing Non-Overshooting Control of Nonlinear Systems with Full-State Constraints
In this paper, the problem of non-overshooting tracking control (NOTC) for a class of nonlinear systems with full-state constraints (FSCs) is studied. Firstly, this paper introduces the mapping constraint function to solve the FSC control problem and transform the controlled system into a new nonlin...
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| author | Xiang-Qin Xiang Chi Zhang |
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| description | In this paper, the problem of non-overshooting tracking control (NOTC) for a class of nonlinear systems with full-state constraints (FSCs) is studied. Firstly, this paper introduces the mapping constraint function to solve the FSC control problem and transform the controlled system into a new nonlinear system. Then, to obtain a closed-loop system that can solve the expression of tracking error, this paper transforms the <i>n</i>-order system into a system in which only the <i>n</i>-th subsystem is nonlinear by coordinate transformation, that is, subsystem 1 to subsystem <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></semantics></math></inline-formula> are linear. Finally, according to the closed-loop system (CLS), the expressions of the first state of CLSs with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>n</mi><mo>=</mo><mn>2</mn></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>n</mi><mo>=</mo><mn>3</mn></mrow></semantics></math></inline-formula>, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>n</mi><mo>≥</mo><mn>4</mn></mrow></semantics></math></inline-formula> are solved, respectively. By analyzing these expressions, a wider range of conditions with NOTC are obtained. This algorithm obtains more conditions with non-overshooting. Compared with the existing results, the algorithm in this paper reduces the conservatism. Finally, the algorithm is applied to the single-link robot system, and the effectiveness of the algorithm is verified. That is, the algorithm in this paper not only makes all signals of the CLS bounded, but also makes the overshoot of the system zero. |
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| spelling | doaj-art-370f5c49204b452cafaef980ff8e05f12025-08-20T02:32:50ZengMDPI AGApplied Sciences2076-34172025-05-011511581610.3390/app15115816Conditions for Guaranteeing Non-Overshooting Control of Nonlinear Systems with Full-State ConstraintsXiang-Qin Xiang0Chi Zhang1School of Artificial Intelligence and Big Data, Hefei University, Hefei 230601, ChinaSchool of Artificial Intelligence and Big Data, Hefei University, Hefei 230601, ChinaIn this paper, the problem of non-overshooting tracking control (NOTC) for a class of nonlinear systems with full-state constraints (FSCs) is studied. Firstly, this paper introduces the mapping constraint function to solve the FSC control problem and transform the controlled system into a new nonlinear system. Then, to obtain a closed-loop system that can solve the expression of tracking error, this paper transforms the <i>n</i>-order system into a system in which only the <i>n</i>-th subsystem is nonlinear by coordinate transformation, that is, subsystem 1 to subsystem <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></semantics></math></inline-formula> are linear. Finally, according to the closed-loop system (CLS), the expressions of the first state of CLSs with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>n</mi><mo>=</mo><mn>2</mn></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>n</mi><mo>=</mo><mn>3</mn></mrow></semantics></math></inline-formula>, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>n</mi><mo>≥</mo><mn>4</mn></mrow></semantics></math></inline-formula> are solved, respectively. By analyzing these expressions, a wider range of conditions with NOTC are obtained. This algorithm obtains more conditions with non-overshooting. Compared with the existing results, the algorithm in this paper reduces the conservatism. Finally, the algorithm is applied to the single-link robot system, and the effectiveness of the algorithm is verified. That is, the algorithm in this paper not only makes all signals of the CLS bounded, but also makes the overshoot of the system zero.https://www.mdpi.com/2076-3417/15/11/5816nonlinear systemsnon-overshooting controlbacksteppingfull-state constraints |
| spellingShingle | Xiang-Qin Xiang Chi Zhang Conditions for Guaranteeing Non-Overshooting Control of Nonlinear Systems with Full-State Constraints Applied Sciences nonlinear systems non-overshooting control backstepping full-state constraints |
| title | Conditions for Guaranteeing Non-Overshooting Control of Nonlinear Systems with Full-State Constraints |
| title_full | Conditions for Guaranteeing Non-Overshooting Control of Nonlinear Systems with Full-State Constraints |
| title_fullStr | Conditions for Guaranteeing Non-Overshooting Control of Nonlinear Systems with Full-State Constraints |
| title_full_unstemmed | Conditions for Guaranteeing Non-Overshooting Control of Nonlinear Systems with Full-State Constraints |
| title_short | Conditions for Guaranteeing Non-Overshooting Control of Nonlinear Systems with Full-State Constraints |
| title_sort | conditions for guaranteeing non overshooting control of nonlinear systems with full state constraints |
| topic | nonlinear systems non-overshooting control backstepping full-state constraints |
| url | https://www.mdpi.com/2076-3417/15/11/5816 |
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