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Stochastic Optimal Linear Control for Generalized Cost Functions With Time-Invariant Stochastic Parameters.

Yuji Ito, Kenji Fujimoto, Yukihiro Tadokoro

IEEE Transactions on Cybernetics

|April 8, 2023

Summary

This study introduces a new method for designing feedback controllers for stochastic optimal control problems with generalized cost functions. The approach optimizes controller gains for improved system performance and robust stability under uncertainty.

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Area of Science:

Control Theory
Optimization
Stochastic Systems

Background:

Stochastic optimal control problems often involve complex, generalized cost functions.
Time-invariant stochastic parameters in linear systems present challenges for conventional control methods like the principle of optimality.

Purpose of the Study:

To design feedback controllers for stochastic optimal control problems with generalized cost functions.
To overcome limitations of conventional methods when dealing with nonlinear and polynomial cost functions.

Main Methods:

Deriving an explicit relationship between the generalized cost function and the linear feedback gain.
Optimizing the feedback gain using a gradient-based method with guaranteed convergence.
Developing a suboptimal feedback controller for generalized cost functions.

Main Results:

An explicit relation between cost function and feedback gain was derived.
A gradient method for optimizing feedback gain was proposed and its convergence proven.
The designed controller ensures robust stability for systems with stochastic parameters.
The generalized cost function can represent various cost types, including quadratic, risk-sensitive, and polynomial costs.

Conclusions:

The proposed method effectively designs feedback controllers for stochastic optimal control with generalized cost functions.
The controller guarantees robust stability, addressing system uncertainty.
Numerical simulations confirm the method's effectiveness and the versatility of the generalized cost function.