Improved Adaptive
Controller Synthesis of Piecewise‐Affine Systems |
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| Authors: | Hongwen Zhang Kai Liu Shangmin Zhang Hong Qiao Bobo Qiu |
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| Affiliation: | 1. Beijing Institute of Aerospace Technology, Beijing, China;2. School of Aeronautics and Astronautics, Dalian University of Technology, Dalian, China;3. Department of Automation, Tsinghua University, Beijing, China |
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| Abstract: | This paper considers the adaptive  control problem for piecewise affine systems (PWS), a novel synthesis framework is presented based on the piecewise quadratic Lyapunov function (PQLF) instead of the common quadratic Lyapunov function to achieve the less conservatism. First, by designing the projection‐type piecewise adaptive law, the problem of the adaptive  control of PWS can be reduced to the  control problem of augmented piecewise systems. Then, we construct the piecewise affine control law for augmented piecewise systems in such a way that the PQLF can be employed to establish the stability and  performance. In particular, the Reciprocal Projection Lemma is employed to formulate the synthesis condition as linear matrix inequalities (LMIs), which enables the proposed PQLF approach to be numerically solvable. Finally, an engineering example is shown to illustrate the synthesis results. |
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| Keywords: | Piecewise affine systems
control piecewise quadratic Lyapunov function LMIs |
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control problem for piecewise affine systems (PWS), a novel synthesis framework is presented based on the piecewise quadratic Lyapunov function (PQLF) instead of the common quadratic Lyapunov function to achieve the less conservatism. First, by designing the projection‐type piecewise adaptive law, the problem of the adaptive 
control of PWS can be reduced to the 
control problem of augmented piecewise systems. Then, we construct the piecewise affine control law for augmented piecewise systems in such a way that the PQLF can be employed to establish the stability and 
performance. In particular, the Reciprocal Projection Lemma is employed to formulate the synthesis condition as linear matrix inequalities (LMIs), which enables the proposed PQLF approach to be numerically solvable. Finally, an engineering example is shown to illustrate the synthesis results.