A Theory of Controller Design for Distributionally Uncertain Systems

A study conducted by Yuji Ito in collaboration with Kyoto University was published in the IEEE Transactions on Automatic Control.

Dynamical systems with randomness, such as networked systems with random communication delays and traffic flows consisting of many vehicles, should be appropriately controlled or guided by efficient controllers that take into account the stochasticity. We have developed theories for the design of various controllers considering the characteristics of randomness. However, the characteristics of randomness in systems, such as the mean and variance of noise, are difficult to estimate. Systems with such randomness are called distributionally uncertain systems.

To overcome this problem, this study establishes “second moment polytopic (SMP) systems*” theory for designing controllers of distributionally uncertain systems. If the randomness characteristics are estimated with bounded errors, stabilizing controllers of the systems can be obtained by solving an optimization problem. The proposed SMP systems theory is efficient for solving the abovementioned problem caused by randomness in complex systems.

^*Second moment polytopic (SMP) systems are linear systems with stochastic parameters whose second moment is uncertain and contained in a polytope. The SMP system representation can be combined with existing robust control design methods to provide stabilizing controllers for distributionally uncertain systems.

Title: Second Moment Polytopic Systems: Generalization of Uncertain Stochastic Linear Dynamics
Authors: Ito, Y., Fujimoto, K.
Journal Name: IEEE Transactions on Automatic Control
Published: September 17, 2024
https://doi.org/10.1109/TAC.2024.3462532