Adaptive Sampling Artificial-Actual Control for Non-Zero-Sum Games of Constrained Systems

Background

In modern industrial and scientific research fields, the rapid development of intelligent technology and control systems makes traditional control methods difficult to meet the strict requirements of ensuring system stability and minimizing energy consumption. Actual systems are usually very complex, at least involving two control units, with intricate competition and cooperation relationships between components. In this case, the designed control scheme not only needs to maximize the benefit for individual controllers but also achieve global optimization. Such problems are usually regarded as Non-Zero-Sum Games (NZSG), and handling system-coupled dynamics under multi-physical input constraints is an important research challenge.

Paper Source

The paper titled “Adaptive Sampling Artificial-Actual Control for Non-Zero-Sum Games of Constrained Systems” was completed by Lu Liu and Ruizhuo Song, both from the Industrial Spectrum Imaging Engineering Research Center, School of Automation and Electronic Engineering, University of Science and Technology Beijing. This paper will be published in the journal “Neural Networks” in 2024. The acceptance and revision dates of the paper were November 7, 2023, and April 21, 2024, respectively, and it was finally accepted on May 27, 2024.

Research Content

This paper proposes an Adaptive Dynamic Programming (ADP) scheme that optimizes control strategies through interaction between artificial and actual systems to address non-zero-sum game problems under constrained inputs. The core of this research is to handle the efficient control of multi-input nonlinear systems through cost function design and the approximation of the Nash equilibrium solution of NZSG.

Artificial-Actual Control and ADP

The study constructs an artificial system using an improved Elman Dynamic Neural Network (EDNNs), which gradually approximates the dynamic behavior of the real system by adaptively adjusting parameters, achieving more effective control. This artificial system continuously learns and adjusts parameters, interacting with the physical system in an artificial-actual manner to predict the system state.

Specific steps are as follows: 1. Constructing the artificial system: Use improved Elman neural networks for training, including input layer, hidden layer, sustain layer, and output layer. Dropout regularization is used to prevent overfitting, where a certain proportion of activation values of each hidden neuron are randomly discarded to improve network performance. 2. Constructing critic-actor structure: Use polynomial parameterization to approximate the value function and control strategy. By using gradient descent, constantly update the weight parameters to minimize errors. 3. Introducing three triggering mechanisms: Event-triggered Mechanism (ETM), Dynamic Event-triggered Mechanism (DETM), and Self-triggered Mechanism (STM). These mechanisms optimize communication efficiency and system stability in different ways.

Experiments and Results

To verify the designed control scheme, the research conducted simulation experiments on a two-link robotic manipulator system with constrained inputs. The system control process is divided into the following steps:

1. System State Modeling: Define the system state model including position and velocity.
2. Control Strategy Simulation: Compare control strategies under ETM, DETM, and STM mechanisms and impose specific constraints on controller input signals.
3. Data Analysis: Record trigger times, trigger rates, and system state changes by setting different trigger thresholds.

Specific Results

1. Event-triggered Mechanism (ETM):

   • Saves communication resources and reduces unnecessary updates, showing high efficiency.
   • The system shows stepwise changes, and the control strategy effectively converges the system state to the equilibrium point.
   • Avoids Zeno phenomena, maintaining system stability.

2. Dynamic Event-triggered Mechanism (DETM):

   • Introduces dynamic variables to further reduce communication volume and improve sampling efficiency.
   • Dynamically adjust the triggering interval in the control strategy to improve system learning efficiency.
   • Experiments show that DETM maintains system stability and has higher resource utilization.

3. Self-triggered Mechanism (STM):

   • Has active response capability without relying on external monitoring hardware.
   • Predicts the next trigger point through internal calculation, enhancing system prediction capabilities and proactivity.
   • Experimental results show that STM effectively manages communication resources and avoids trigger delays.

Conclusion and Significance

This study constructs an ADP scheme using artificial-actual interaction to optimize systems, successfully solving the non-zero-sum game control problem under multi-input constraints. Optimizing data communication reduces the computational and communication pressure of the system, enhancing the overall control efficiency and stability of the system. The research results of this paper not only enrich theoretical research methods in the field of automatic control but also provide highly feasible solutions for practical engineering applications.

Highlights

1. Innovative Artificial-Actual Interaction Control Mechanism: Achieves high-precision system state prediction through EDNNs, improving control effects.
2. Three Adaptive Trigger Mechanisms: Effectively reduce data transmission volume, optimize system performance, and have high engineering practicality.
3. Application Prospects: The research results have important application value in multiple fields such as robotic systems and intelligent control systems, especially suitable for complex systems with limited resources and high reliability requirements.

The above is a comprehensive report and interpretation of the paper “Adaptive Sampling Artificial-Actual Control for Non-Zero-Sum Games of Constrained Systems”. This study provides an innovative solution for complex multi-input control systems through adaptive dynamic programming and multiple triggering mechanism design.