Distributed stochastic model predictive control for systems with stochastic multiplicative uncertainty and chance...

Area of Science:

• Control Engineering
• Systems Science
• Applied Mathematics

Background:

• Complex systems with multiple interacting subsystems are prevalent in modern technology.
• Uncertainty propagation and perturbation pose significant challenges for control design.
• Existing methods struggle with individual and coupling constraints under probabilistic uncertainty.

Purpose of the Study:

• To develop a robust control scheme for complex, multi-subsystem systems with multiplicative uncertainty.
• To address both individual and coupling constraints using probabilistic formulations.
• To enhance control design by integrating stochastic stability and computational efficiency.

Main Methods:

• A centralized stochastic model predictive control (SMPC) scheme integrating system dynamics and chance constraints.
• Utilizing multi-step probabilistic invariant sets and linear matrix inequalities (LMIs) to handle chance constraints.
• Developing a distributed SMPC with a sequential update scheme to reduce computational and communication burdens.

Main Results:

• A novel semidefinite programming problem formulation for online implementation, replacing intractable chance-constrained optimization.
• Guaranteed stochastic stability and recursive feasibility for the closed-loop system.
• Demonstrated efficacy and validity of the proposed distributed control algorithm through a numerical example.

Conclusions:

• The proposed distributed SMPC effectively manages complex systems with multiplicative uncertainty and coupling constraints.
• The method ensures stochastic stability and recursive feasibility while significantly reducing computational complexity.
• This approach offers a practical solution for real-world applications involving large-scale, uncertain systems.