An explicit dual control approach for constrained reference tracking of uncertain linear systems

TL;DR

This paper introduces a model predictive control-based explicit dual control method for constrained reference tracking of uncertain linear systems, actively learning uncertainties while ensuring robustness and constraint satisfaction.

Contribution

It presents a novel algorithm for designing robust terminal sets and controllers, integrating set membership identification and worst-case cost prediction for active uncertainty learning.

Findings

Ensures robust constraint satisfaction and recursive feasibility.

Balances exploration and exploitation in uncertain systems.

Provides a systematic approach for online uncertainty update.

Abstract

A finite horizon optimal tracking problem is considered for linear dynamical systems subject to parametric uncertainties in the state-space matrices and exogenous disturbances. A suboptimal solution is proposed using a model predictive control (MPC) based explicit dual control approach which enables active uncertainty learning. A novel algorithm for the design of robustly invariant online terminal sets and terminal controllers is presented. Set membership identification is used to update the parameter uncertainty online. A predicted worst-case cost is used in the MPC optimization problem to model the dual effect of the control input. The cost-to-go is estimated using contractivity of the proposed terminal set and the remaining time horizon, so that the optimizer can estimate future benefits of exploration. The proposed dual control algorithm ensures robust constraint satisfaction and recursive feasibility, and navigates the exploration-exploitation trade-off using a robust performance metric.