Finance

Stability (learning theory)

Value (mathematics)

Mathematics

Evolutionary biology

Biology

Statistics

Mathematical optimization

Bellman equation

Machine learning

Mathematical analysis

Function (biology)

Artificial intelligence

Economics

Control (management)

Sequence (biology)

Computer science

Discounting

Monotonic function

Control theory (sociology)

Genetics

Optimal control

Linear-quadratic regulator

IEEE Transactions on Neural Networks and Learning Systems

For discounted optimal regulation design, the stability of the controlled system is affected by the discount factor. If an inappropriate discount factor is employed, the optimal control policy might be unstabilizing. Therefore, in this article, the effect of the discount factor on the stabilization of control strategies is discussed. We develop the system stability criterion and the selection rules of the discount factor with respect to the linear quadratic regulator problem under the general discounted value iteration algorithm. Based on the monotonicity of the value function sequence, the method to judge the stability of the controlled system is established during the iteration process. In addition, once some stability conditions are satisfied at a certain iteration step, all control policies after this iteration step are stabilizing. Furthermore, combined with the undiscounted optimal control problem, the practical rule of how to select an appropriate discount factor is constructed. Finally, several simulation examples with physical backgrounds are conducted to demonstrate the present theoretical results.

System Stability of Learning-Based Linear Optimal Control With General Discounted Value Iteration