An Explicit Dual Control Approach for Constrained Reference Tracking of Uncertain Linear Systems

• Published in: IEEE transactions on automatic control Vol. 68; no. 5; pp. 2652 - 2666
• Main Authors: Parsi, Anilkumar, Iannelli, Andrea, Smith, Roy S.
• Format: Journal Article
• Language: English
• Published: New York IEEE 01-05-2023; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Active control; Active learning; Adaptive control; Algorithms; Constraints; Control theory; dual control; Dynamical systems; Electron tubes; Linear systems; Machine learning; Measurement uncertainty; model predictive control; Optimization; Parameter identification; Parameter uncertainty; Predictive control; reference tracking; Robust control; Robustness; safe adaptive control; Tracking problem; Uncertain systems; Uncertainty
• DOI: 10.1109/TAC.2022.3176800
• EISSN: 1558-2523
• ISSN: 0018-9286

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 tradeoff using a robust performance metric.