Data-driven control for dynamic quantized nonlinear systems with state constraints based on barrier functions

Abstract

In this study, the data-driven control problem is investigated for discrete-time nonlinear systems with state constraints and dynamic quantization. A dynamic quantizer is utilized to encode the control signal to relieve the impact of inherent quantization errors in comparison with traditional uniform quantizers. By employing three sets of neural networks (NNs), a data-based goal representation heuristic dynamic programming algorithm with the concurrent learning technique is offered to achieve the near-optimal control objective without model requirement. Specifically, by introducing the relaxed barrier function into the cost function, a barrier-based control strategy is proposed to generate the repulsive control force when the state moves to the constraint boundary. Subsequently, the recorded historical data is adequately leveraged to build a new weight updating rule, and persistent excitation of weight parameter estimation is hence removed. Furthermore, the Lyapunov method is utilized to demonstrate that the weights estimation errors of NNs are bounded. Finally, numerical simulation and power system examples are employed to demonstrate the validity of the control strategy.