Evolving and Incremental Value Iteration Schemes for Nonlinear Discrete-Time Zero-Sum Games.

Area of Science:

• Control Theory
• Game Theory
• Optimization

Background:

• Discrete-time zero-sum games present challenges in control and optimization.
• Existing value iteration (VI) methods may not fully address evolving or nonlinear systems.

Purpose of the Study:

• To develop novel evolving and incremental value iteration (VI) frameworks for discrete-time zero-sum games.
• To ensure system stability and enhance the convergence of control policies.
• To solve regulation and tracking problems in nonlinear zero-sum games.

Main Methods:

• Construction of evolving value iteration (VI) frameworks with stability criteria for policy pairs.
• Development of an incremental VI algorithm incorporating historical iterative data.
• Introduction of incremental factors to modulate the convergence rate of cost function sequences.

Main Results:

• Demonstrated the effectiveness of evolving policy pairs in regulating closed-loop systems.
• Showcased the ability of the incremental VI algorithm to solve nonlinear zero-sum game problems.
• Validated the performance and stability of the proposed VI schemes through simulations on linear and nonlinear systems.

Conclusions:

• The proposed evolving and incremental VI frameworks effectively address discrete-time zero-sum games.
• Stability criteria guarantee the availability of evolving policy pairs.
• The incremental VI approach offers adjustable convergence rates for improved efficiency.