Distributed model predictive control of positive Markov jump systems.

Area of Science:

• Control Systems Engineering
• Stochastic Systems Analysis
• Optimization Theory

Background:

• Positive Markov jump systems are crucial in modeling systems with state-dependent parameters and positivity constraints.
• Existing control strategies often struggle with uncertainties and complex constraints in such systems.
• Robust and efficient control methods are needed for reliable system operation.

Purpose of the Study:

• To develop a novel distributed model predictive control (DMPC) framework for positive Markov jump systems.
• To address interval and polytopic uncertainties and 1-norm inequality constraints.
• To ensure system positivity and stochastic stability with reduced computational load.

Main Methods:

• A linear DMPC framework incorporating a linear performance index and robust stability conditions.
• Utilizing a stochastic linear co-positive Lyapunov function and a cone invariant set.
• Decomposition of the global system into subsystems with local controllers and matrix decomposition for stability analysis.

Main Results:

• The proposed DMPC framework guarantees positivity and stochastic stability for the uncertain systems.
• Stability conditions are transformed into a linear programming problem, simplifying computation.
• A computationally efficient DMPC algorithm is presented for the min-max optimization problem.

Conclusions:

• The developed DMPC approach effectively controls positive Markov jump systems under uncertainties and constraints.
• The method ensures both positivity and stochastic stability.
• The approach offers a reduced computational burden compared to existing methods.