Reinforcement learning controller design for affine nonlinear discrete-time systems using online approximators.

No prior work had resolved the challenge of controlling unknown nonlinear discrete-time systems using adaptive critic structures. Traditional control methods often struggle when system dynamics remain entirely unidentified or subject to external perturbations. Researchers previously relied on precise mathematical models that are frequently unavailable in real-world engineering scenarios. That uncertainty drove the development of adaptive strategies capable of learning in real time. Prior research has shown that neural networks can approximate complex functions effectively within closed-loop architectures. However, integrating these approximators into multi-input multi-output frameworks while maintaining stability remains a significant hurdle. This gap motivated the exploration of reinforcement learning as a robust alternative for managing such intricate control tasks. The current study addresses these limitations by proposing a flexible framework for state and output feedback control.

The aim of this study is to develop reinforcement learning-based adaptive critic controllers for unknown affine nonlinear discrete-time systems. These systems often present significant challenges due to their multi-input multi-output nature and the presence of bounded disturbances. The researchers seek to create a flexible control framework that does not rely on precise mathematical models of the plant. By utilizing online approximators, the authors intend to enable real-time learning and adaptation to changing system conditions. The motivation stems from the need for robust control strategies in environments where system dynamics are partially or entirely unidentified. Furthermore, the study addresses the difficulty of state estimation by incorporating observer networks for output-feedback scenarios. This design choice aims to eliminate the restrictive requirement of the separation principle in complex control architectures. Ultimately, the work strives to provide a theoretically sound and practically effective method for stabilizing intricate mechanical systems.

The review approach involves designing adaptive critic controllers for multi-input multi-output discrete-time systems. Researchers utilize online approximators to manage unknown dynamics and bounded disturbances within the control loop. The design incorporates two distinct entities: an action network for signal generation and a critic network for performance assessment. Tuning of the critic occurs through recursive equations derived from heuristic dynamic programming principles. Neural networks function as the primary approximators for both the action and critic modules. For output-feedback scenarios, the team designates an additional observer network to estimate missing state variables. Stability analysis relies on Lyapunov theory to ensure uniform ultimate boundedness of the closed-loop system. Finally, the team validates these control schemes using numerical simulations on pendulum and robotic arm models.

The researchers report that their adaptive critic controllers successfully stabilize affine nonlinear systems under the influence of bounded disturbances. The findings indicate that the action network produces optimal signals while the critic network accurately evaluates performance. Simulation results confirm that both state-feedback and output-feedback designs maintain uniform ultimate boundedness throughout the operation. The study shows that the observer network effectively estimates unavailable states, removing the requirement for a separation principle. The authors observe that the neural network weight tuning laws remain stable during the entire simulation process. Testing on a pendulum balancing system demonstrates the practical utility of the proposed control architecture. Similarly, the two-link robotic arm simulation verifies the effectiveness of the controllers in complex multi-input multi-output environments. These results highlight the capability of the proposed methods to handle unknown system dynamics through online learning.

The authors demonstrate that their adaptive critic framework successfully stabilizes affine nonlinear systems despite the presence of bounded disturbances. Their synthesis suggests that utilizing online approximators allows for effective control without requiring a separation principle. The researchers conclude that neural networks provide a versatile mechanism for both action and critic components within the proposed architecture. This work implies that heuristic dynamic programming offers a viable pathway for tuning cost-to-go functions in real time. The study confirms that uniform ultimate boundedness is maintained for the closed-loop system under the derived weight tuning laws. These findings indicate that the proposed controllers perform reliably across different mechanical applications like pendulum balancing and robotic arms. The authors highlight that their approach bypasses the need for exact system models by learning performance evaluations online. Ultimately, this research provides a robust foundation for applying reinforcement learning to complex, unknown discrete-time dynamics.