Chance Constrained Stochastic Optimal Control for Linear Systems with Time Varying Random Plant Parameters

TL;DR

This paper introduces a control method for linear systems with time-varying stochastic parameters, using chance constraints reformulated via Vysochanskij-Petunin inequality, demonstrated on power systems with better computational efficiency.

Contribution

It presents a novel open loop control scheme for systems with time-varying random parameters, employing a tractable reformulation of chance constraints under known moments.

Findings

Faster solve times compared to situation approach.

Effective handling of joint chance constraints.

Successful application to power system example.

Abstract

We propose an open loop control scheme for linear systems with time-varying random elements in the plant's state matrix. This paper focuses on joint chance constraints for potentially time-varying target sets. Under assumption of finite and known expectation and variance, we use the one-sided Vysochanskij-Petunin inequality to reformulate joint chance constraints into a tractable form. We demonstrate our methodology on a two-bus power system with stochastic load and wind power generation. We compare our method with situation approach. We show that the proposed method had superior solve times and favorable optimally considerations.