H_∞-Based Minimal Energy Adaptive Control With Preset Convergence Rate

Area of Science:

• Control Theory
• Systems Engineering
• Applied Mathematics

Background:

• Linear time-invariant continuous-time systems are susceptible to external disturbances.
• Existing H-infinity control methods may not directly address minimal control energy or preset convergence rates.
• Actuator saturation poses a significant challenge in practical control system design.

Purpose of the Study:

• To design an H-infinity controller for disturbed linear systems that minimizes control input energy.
• To ensure closed-loop system asymptotic stability with a preset convergence rate (PCR).
• To address actuator magnitude saturation in the presence of unknown system dynamics.

Main Methods:

• Development of a modified game algebraic Riccati equation (MGARE) by omitting the state cost.
• Theoretical analysis of the existence and uniqueness of positive-definite solutions for the MGARE.
• Proposal of a model-free policy iteration approach to solve the control problem without exact system dynamics knowledge.

Main Results:

• A novel control strategy is formulated based on the MGARE, enabling minimal energy control with PCR.
• The proposed approach effectively handles actuator magnitude saturation.
• The model-free policy iteration method provides a viable solution when system dynamics are not precisely known.

Conclusions:

• The MGARE-based approach successfully achieves H-infinity minimal energy control with preset convergence rates for disturbed systems.
• The developed methods are effective in mitigating actuator saturation issues.
• Simulation examples validate the practical applicability and effectiveness of the proposed control strategies.