Data-Driven Zero-Sum Neuro-Optimal Control for a Class of Continuous-Time Unknown Nonlinear Systems With Disturbance...

Uncertainty persists regarding how to stabilize nonlinear systems when internal dynamics remain entirely unknown to the controller. Prior research has shown that traditional methods often struggle when external disturbances act as adversarial inputs. That uncertainty drove the need for frameworks that do not rely on precise mathematical models. No prior work had resolved the challenge of integrating data-driven learning with game-theoretic control strategies. This gap motivated the development of techniques capable of handling continuous-time processes without prior system knowledge. Researchers have long sought ways to approximate complex performance indices using neural architectures. Previous studies focused on known models, leaving a void for real-time, data-reliant applications. This paper addresses these limitations by proposing a novel control architecture for unknown environments.

The aim of this study is to develop a new data-driven zero-sum neuro-optimal control framework for continuous-time unknown nonlinear systems subject to external disturbances. The researchers seek to address the challenge of controlling systems where the mathematical model is unavailable. This motivation stems from the need to maintain stability when external factors act as adversarial inputs. The study explores how to utilize input-output data to reconstruct system dynamics effectively. The authors propose using a recurrent neural network to learn these unknown behaviors in real-time. They establish a two-player zero-sum game to formulate the optimal control problem under worst-case disturbance conditions. The work intends to implement adaptive dynamic programming to derive the optimal control law. Finally, the researchers aim to demonstrate the effectiveness of this approach through rigorous simulation results.

Review Approach involves developing a data-driven control framework for continuous-time processes with unknown dynamics. The researchers utilize recurrent neural networks to reconstruct system behavior based on observed input-output data streams. Review Approach incorporates a two-player zero-sum game structure to model the interaction between the controller and external disturbances. The team employs three distinct single-layer neural networks to approximate the performance index and control laws. Review Approach integrates these networks to facilitate the implementation of the adaptive dynamic programming method. The authors design the critic network to evaluate performance while the two action networks determine optimal responses. Review Approach relies on simulation testing to verify the stability and performance of the proposed control architecture. The study evaluates the convergence properties of the system states and the neural network weight matrices through these computational experiments.

Key Findings From the Literature demonstrate that the recurrent neural network successfully reconstructs the dynamics of unknown nonlinear systems using input-output data. The researchers establish that the system state converges to a finite neighborhood of the equilibrium point under the proposed control law. Key Findings From the Literature show that the weight matrices of the critic network and the two action networks converge to finite neighborhoods of their optimal values. The study confirms that the adaptive dynamic programming method effectively obtains the optimal control under the worst-case disturbance scenario. Key Findings From the Literature indicate that the three-network architecture facilitates the implementation of the control strategy. The simulation results provide evidence that the developed data-driven approach maintains stability in the presence of external interference. Key Findings From the Literature reveal that the zero-sum game formulation allows for robust handling of adversarial inputs. The authors report that the effectiveness of the proposed method is validated through these computational simulations.

Synthesis and Implications suggest that the proposed control framework successfully stabilizes unknown nonlinear systems under adversarial conditions. The authors demonstrate that their recurrent neural network architecture effectively reconstructs system dynamics using only input-output observations. Synthesis and Implications indicate that the adaptive dynamic programming approach provides a robust solution for worst-case disturbance scenarios. The researchers confirm that system states reach a finite neighborhood of the equilibrium point through their developed learning process. Synthesis and Implications highlight that the weight matrices for the critic and action networks converge reliably to their optimal values. The study validates that the three-network configuration facilitates the implementation of complex control laws in real-time. Synthesis and Implications show that the simulation results support the theoretical claims regarding system stability and performance. The authors conclude that their data-driven strategy offers a viable path for managing unknown continuous-time processes with external interference.