Learning from neural control of nonlinear systems in normal form |
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Authors: | Tengfei Liu Cong Wang David J Hill |
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Affiliation: | aSchool of Automation and Center for Control and Optimization, South China University of Technology, Guangzhou 510641, China;bResearch School of Information Sciences and Engineering, The Australian National University, Canberra ACT 0200, Australia |
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Abstract: | A deterministic learning theory was recently proposed which states that an appropriately designed adaptive neural controller can learn the system internal dynamics while attempting to control a class of simple nonlinear systems. In this paper, we investigate deterministic learning from adaptive neural control (ANC) of a class of nonlinear systems in normal form with unknown affine terms. The existence of the unknown affine terms makes it difficult to achieve learning by using previous methods. To overcome the difficulties, firstly, an extension of a recent result is presented on stability analysis of linear time-varying (LTV) systems. Then, with a state transformation, the closed-loop control system is transformed into a LTV form for which exponential stability can be guaranteed when a partial persistent excitation (PE) condition is satisfied. Accurate approximation of the closed-loop control system dynamics is achieved in a local region along a recurrent orbit of closed-loop signals. Consequently, learning of control system dynamics (i.e. closed-loop identification) from adaptive neural control of nonlinear systems with unknown affine terms is implemented. |
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Keywords: | Deterministic learning Adaptive neural control Nonlinear systems Normal form Persistent excitation (PE) condition Closed-loop identification |
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