Optimal Control in Both Steady State and Transient Process with Unknown Disturbances

TL;DR

This paper develops controllers for linear systems that optimize both steady-state and transient performance under unknown disturbances, introducing a near-optimal controller that balances transient and steady-state goals.

Contribution

It introduces a disturbance-independent near-optimal control scheme that achieves steady-state optimality and approaches transient overtaking optimality without knowing disturbances.

Findings

The proposed controller guarantees steady-state optimality.

It approaches overtaking optimality in the transient process.

Performance gap decreases with higher control gains.

Abstract

The scheme of online optimization as a feedback controller is widely used to steer the states of a physical system to the optimal solution of a predefined optimization problem. Such methods focus on regulating the physical states to the optimal solution in the steady state, without considering the performance during the transient process. In this paper, we simultaneously consider the performance in both the steady state and the transient process of a linear time-invariant system with unknown disturbances. The performance of the transient process is illustrated by the concept of overtaking optimality. An overtaking optimal controller with known disturbances is derived to achieve the transient overtaking optimality while guaranteeing steady-state performance. Then, we propose a disturbance independent near-optimal controller, which can achieve optimal steady-state performance and approach the overtaking optimal performance in the transient process. The system performance gap between the overtaking optimal controller and the proposed controller proves to be inversely proportional to the control gains. A case study on a power system with four buses is used to validate the effectiveness of the two controllers.