Optimal Control Algorithm for Stochastic Systems with Parameter Drift.

Area of Science:

• Control Systems Engineering
• Stochastic Systems Analysis
• Optimization Theory

Background:

• Multiple input multiple output (MIMO) stochastic systems face challenges with parameter drift, external disturbances, and observation noise.
• Existing control strategies often struggle to simultaneously address control objectives and parameter estimation due to inherent conflicts.

Purpose of the Study:

• To develop a novel optimal control strategy for MIMO stochastic systems with mixed parameter drift.
• To address the conflict between control and estimation for improved system performance and parameter identification.

Main Methods:

• A dual control algorithm integrating a weight factor and innovation is proposed.
• Kalman filtering is employed to estimate and track transformed drift parameters.
• A modified optimization problem is solved to derive the analytic control law.

Main Results:

• The proposed controller can track and identify drift parameters in finite time.
• The algorithm achieves a balance between control and estimation, optimizing system performance.
• An analytic solution for the control law is obtained, offering optimality through integrated parameter estimation.

Conclusions:

• The dual control algorithm effectively manages the trade-off between control and estimation in MIMO stochastic systems.
• Numerical experiments confirm the algorithm's effectiveness in diverse scenarios.
• This approach provides an optimal control law by incorporating parameter estimation directly into the objective function.