Predictive Optimal Control with Data-Based Disturbance Scenario Tree Approximation

TL;DR

This paper introduces a data-based clustering approach to approximate disturbance scenario trees for predictive optimal control, reducing computational complexity while improving control performance compared to Markov chain methods.

Contribution

A novel clustering-based approximation method for scenario trees that retains historical information and reduces computational load in stochastic optimal control.

Findings

The proposed method outperforms Markov chain approaches in control performance.

It maintains relevant historical information while keeping the state space manageable.

Numerical examples validate the efficiency and effectiveness of the approach.

Abstract

Efficiently computing the optimal control policy concerning a complicated future with stochastic disturbance has always been a challenge. The predicted stochastic future disturbance can be represented by a scenario tree, but solving the optimal control problem with a scenario tree is usually computationally demanding. In this paper, we propose a data-based clustering approximation method for the scenario tree representation. Differently from the popular Markov chain approximation, the proposed method can retain information from previous steps while keeping the state space size small. Then the predictive optimal control problem can be approximately solved with reduced computational load using dynamic programming. The proposed method is evaluated in numerical examples and compared with the method which considers the disturbance as a non-stationary Markov chain. The results show that the proposed method can achieve better control performance than the Markov chain method.