Overview
This research addresses the robust tracking control of linear systems characterized by unknown parameters and disturbances, which are specified as bounded within ellipsoidal sets. The study introduces an adaptive robust control methodology designed to actively learn these ellipsoidal sets. This learning mechanism aims to mitigate system uncertainties by integrating recursive set-membership state estimation into the control process.
Research Context
The problem investigated concerns linear uncertain systems. In these systems, both the unknown system parameters and external disturbances are assumed to reside within definable ellipsoidal bounds. The objective is to achieve robust tracking control despite these inherent uncertainties.
Approach
The proposed control strategy, termed adaptive robust control, incorporates active learning of the ellipsoidal sets that define system uncertainties. Key elements of the approach include:
- Active Learning Mechanism: The method employs recursive set-membership state estimation to learn the unknown ellipsoidal sets. This learning process is intended to reduce the impact of uncertainties on system control.
- Robust Control Construction: Following the recognition of uncertainties through the learned sets, a robust control law is formulated. This control law incorporates a one-step prediction mechanism specifically for system output tracking.
- Optimization Objective Reformulation: To derive an optimized control law, the problem's optimization objective is reformulated into a second-order cone programming problem. This reformulation is chosen for its computational tractability.
- Information Enrichment for Learning: To enhance the active learning process, the study suggests enriching the information utilized for learning. This involves maximizing the volume of the ellipsoid set, which is hypothesized to improve learning accuracy and accelerate the reduction of uncertainty.
Findings
The research reports on numerical simulations conducted to verify the proposed approach. These simulations involved:
- Comparing the new adaptive robust control with a fixed-ellipsoidal-set robust control.
- Investigating the positive effect of the designed active learning component within the uncertain system control process.
While specific quantitative results are not detailed in the abstract, the verification through numerical simulations aimed to demonstrate the efficacy and positive impact of the active learning strategy.
Why This Matters
The development of adaptive robust control strategies for linear uncertain systems, particularly those that can actively learn and mitigate unknown parameters and disturbances, is relevant for maintaining desired system performance under varying or unpredictable conditions.