Hamid Kalantari, Mohsen Mojiri, Javad Askari, Najmeh Zamani
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It is proved that the computational complexity of SA-QMPC is <span></span><math>\n <semantics>\n <mrow>\n <mi>O</mi>\n <mo>(</mo>\n <mi>N</mi>\n <msup>\n <mi>n</mi>\n <mn>2</mn>\n </msup>\n <mo>)</mo>\n </mrow>\n <annotation>$O(Nn^2)$</annotation>\n </semantics></math> for a region of the initial conditions and <span></span><math>\n <semantics>\n <mrow>\n <mi>O</mi>\n <mo>(</mo>\n <msup>\n <mi>N</mi>\n <mn>2</mn>\n </msup>\n <msup>\n <mi>n</mi>\n <mn>2</mn>\n </msup>\n <mo>)</mo>\n </mrow>\n <annotation>$O(N^2n^2)$</annotation>\n </semantics></math> for sufficiently small sampling time and all initial conditions, where <span></span><math>\n <semantics>\n <mi>N</mi>\n <annotation>$N$</annotation>\n </semantics></math> and <span></span><math>\n <semantics>\n <mi>n</mi>\n <annotation>$n$</annotation>\n </semantics></math> are the horizon time and dimension of the state vector, respectively. Numerical results indicate the potential and properties of the proposed algorithm.</p>","PeriodicalId":50382,"journal":{"name":"IET Control Theory and Applications","volume":null,"pages":null},"PeriodicalIF":2.2000,"publicationDate":"2024-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1049/cth2.12642","citationCount":"0","resultStr":"{\"title\":\"Fast quadratic model predictive control based on sensitivity analysis and Wolfe method\",\"authors\":\"Hamid Kalantari, Mohsen Mojiri, Javad Askari, Najmeh Zamani\",\"doi\":\"10.1049/cth2.12642\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>This paper proposes a new algorithm based on sensitivity analysis and the Wolfe method to solve a sequence of parametric quadratic programming (QP) problems such as those that arise in quadratic model predictive control (QMPC). The Wolfe method, based on Karush–Kuhn–Tucker conditions, has been used to convert parametric QP problems to parametric linear programming (LP) problems, and then the sensitivity analysis is applied to solve the sequence of the parametric LP problems. This strategy obtains sensitivity analysis-based QMPC (SA-QMPC) algorithm. It is proved that the computational complexity of SA-QMPC is <span></span><math>\\n <semantics>\\n <mrow>\\n <mi>O</mi>\\n <mo>(</mo>\\n <mi>N</mi>\\n <msup>\\n <mi>n</mi>\\n <mn>2</mn>\\n </msup>\\n <mo>)</mo>\\n </mrow>\\n <annotation>$O(Nn^2)$</annotation>\\n </semantics></math> for a region of the initial conditions and <span></span><math>\\n <semantics>\\n <mrow>\\n <mi>O</mi>\\n <mo>(</mo>\\n <msup>\\n <mi>N</mi>\\n <mn>2</mn>\\n </msup>\\n <msup>\\n <mi>n</mi>\\n <mn>2</mn>\\n </msup>\\n <mo>)</mo>\\n </mrow>\\n <annotation>$O(N^2n^2)$</annotation>\\n </semantics></math> for sufficiently small sampling time and all initial conditions, where <span></span><math>\\n <semantics>\\n <mi>N</mi>\\n <annotation>$N$</annotation>\\n </semantics></math> and <span></span><math>\\n <semantics>\\n <mi>n</mi>\\n <annotation>$n$</annotation>\\n </semantics></math> are the horizon time and dimension of the state vector, respectively. 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Fast quadratic model predictive control based on sensitivity analysis and Wolfe method
This paper proposes a new algorithm based on sensitivity analysis and the Wolfe method to solve a sequence of parametric quadratic programming (QP) problems such as those that arise in quadratic model predictive control (QMPC). The Wolfe method, based on Karush–Kuhn–Tucker conditions, has been used to convert parametric QP problems to parametric linear programming (LP) problems, and then the sensitivity analysis is applied to solve the sequence of the parametric LP problems. This strategy obtains sensitivity analysis-based QMPC (SA-QMPC) algorithm. It is proved that the computational complexity of SA-QMPC is for a region of the initial conditions and for sufficiently small sampling time and all initial conditions, where and are the horizon time and dimension of the state vector, respectively. Numerical results indicate the potential and properties of the proposed algorithm.
期刊介绍：
IET Control Theory & Applications is devoted to control systems in the broadest sense, covering new theoretical results and the applications of new and established control methods. Among the topics of interest are system modelling, identification and simulation, the analysis and design of control systems (including computer-aided design), and practical implementation. The scope encompasses technological, economic, physiological (biomedical) and other systems, including man-machine interfaces.
Most of the papers published deal with original work from industrial and government laboratories and universities, but subject reviews and tutorial expositions of current methods are welcomed. Correspondence discussing published papers is also welcomed.
Applications papers need not necessarily involve new theory. Papers which describe new realisations of established methods, or control techniques applied in a novel situation, or practical studies which compare various designs, would be of interest. Of particular value are theoretical papers which discuss the applicability of new work or applications which engender new theoretical applications.
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