<p>Deterministic learning (DL) enables neural network (NN)-based learning control of single-input single-output (SISO) nonlinear systems and effectively improves control performance through learned knowledge. The focus of this paper is to extend DL to complex multiple-input multiple-output (MIMO) nonlinear systems and, for the first time, to provide a rigorous theoretical analysis for neural learning and control of such systems. The proposed scheme achieves a true NN-based learning and intelligent control framework for complex unknown MIMO systems, enabling them to learn through adaptive control in a manner analogous to human learning, while storing the acquired knowledge for subsequent control tasks. The coupling among multiple subsystems introduces complex and unknown interaction terms at each system level, which creates substantial challenges for both stability analysis and verification of the learning process in MIMO systems. To address this issue, an adaptive neural control strategy is designed to ensure uniform boundedness of all signals and satisfactory tracking performance. Subsequently, to resolve the challenge of establishing learning for MIMO systems, we propose a non-sequential recursive learning proof method. By designing a selection function and leveraging DL theory, we establish the persistent excitation (PE) property of the coupled NN inputs. Furthermore, through state transformations, we construct closed-loop linear time-varying (LTV) systems with coupled interconnections and rigorously prove their exponential stability, enabling accurate approximation of uncertain coupled nonlinear dynamics. Finally, by utilizing the learned knowledge, we construct a knowledge-based learning controller that significantly improves closed-loop control performance. Simulation results validate the effectiveness of the proposed method.</p>

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New results on dynamic modeling and neural control for unknown MIMO nonlinear systems via deterministic learning

  • Qinchen Yang,
  • Fukai Zhang,
  • Cong Wang

摘要

Deterministic learning (DL) enables neural network (NN)-based learning control of single-input single-output (SISO) nonlinear systems and effectively improves control performance through learned knowledge. The focus of this paper is to extend DL to complex multiple-input multiple-output (MIMO) nonlinear systems and, for the first time, to provide a rigorous theoretical analysis for neural learning and control of such systems. The proposed scheme achieves a true NN-based learning and intelligent control framework for complex unknown MIMO systems, enabling them to learn through adaptive control in a manner analogous to human learning, while storing the acquired knowledge for subsequent control tasks. The coupling among multiple subsystems introduces complex and unknown interaction terms at each system level, which creates substantial challenges for both stability analysis and verification of the learning process in MIMO systems. To address this issue, an adaptive neural control strategy is designed to ensure uniform boundedness of all signals and satisfactory tracking performance. Subsequently, to resolve the challenge of establishing learning for MIMO systems, we propose a non-sequential recursive learning proof method. By designing a selection function and leveraging DL theory, we establish the persistent excitation (PE) property of the coupled NN inputs. Furthermore, through state transformations, we construct closed-loop linear time-varying (LTV) systems with coupled interconnections and rigorously prove their exponential stability, enabling accurate approximation of uncertain coupled nonlinear dynamics. Finally, by utilizing the learned knowledge, we construct a knowledge-based learning controller that significantly improves closed-loop control performance. Simulation results validate the effectiveness of the proposed method.