Gain-Scheduling Data-Enabled Predictive Control for Nonlinear Systems with Linearized Operating Regions

This paper presents a Gain-Scheduled Data-Enabled Predictive Control (GS-DeePC) framework for nonlinear systems based on multiple locally linear data representations. Instead of relying on a single global Hankel matrix, the operating range of a measurable scheduling variable is partitioned into regions, and regional Hankel matrices are constructed from persistently exciting data. To ensure smooth transitions between linearization regions and suppress region-induced chattering, composite regions are introduced, merging neighboring data sets and enabling a robust switching mechanism. The proposed method maintains the original DeePC problem structure and can achieve reduced computational complexity by requiring only short, locally informative data sequences. Extensive experiments on a nonlinear DC-motor with an unbalanced disc demonstrate the significantly improved control performance compared to standard DeePC.

💡 Research Summary

This paper introduces a Gain‑Scheduled Data‑Enabled Predictive Control (GS‑DeePC) framework that extends the original DeePC algorithm to handle strongly nonlinear systems by exploiting multiple locally linear data representations. The key idea is to select a measurable scheduling variable ρ(k) that captures the dominant source of nonlinearity, partition its range into a set of operating regions {M₁,…,Mₙ}, and construct a separate Hankel matrix for each region from persistently exciting input‑output data collected while the system stays inside that region.

The data‑collection pipeline consists of four steps: (i) record input‑output trajectories together with the scheduling variable; (ii) divide the observed range of ρ into regions (uniformly or non‑uniformly) and extract subsequences whose ρ‑values remain within a region for at least T_ini + N samples; (iii) assemble regional Hankel matrices H_i(u), H_i(y) with a common column count c (e.g., by concatenating multiple subsequences into a mosaic‑Hankel matrix); and (iv) build composite regions C_i by merging neighboring regions M_i and M_{i+1}. The composite Hankel matrices H_{C,i}(u), H_{C,i}(y) contain data from two adjacent regions, thereby providing overlapping linear models that smooth the transition when ρ crosses a boundary.

During online operation the controller evaluates the current value of ρ(k) and selects the appropriate (composite) region’s Hankel matrices. The selected matrices replace the global matrices in the standard DeePC quadratic program, leaving the optimization structure unchanged: the cost combines reference tracking error, input energy, and regularization terms λ_g‖g‖₂² and λ_y‖σ_y‖₂²; constraints enforce the linear relation between past data, future inputs, and future outputs, together with box constraints on inputs and outputs. Because each region is constructed from locally linear (or weakly nonlinear) dynamics, the persistency‑of‑excitation and data‑consistency assumptions required by DeePC hold locally, and the regularization terms further guarantee feasibility even when slight mismatches occur across region boundaries.

The authors emphasize two practical benefits. First, regional Hankel matrices can be built from much shorter data sequences than a single global matrix, dramatically reducing memory usage and the size of the quadratic program, which is crucial for real‑time implementation. Second, the composite‑region strategy mitigates chattering and discontinuities that would otherwise arise from abrupt switching between distinct linear models.

Experimental validation is performed on a DC‑motor equipped with an unbalanced disc, a benchmark that exhibits pronounced nonlinear torque characteristics. The system is partitioned into four regions and three overlapping composite regions. Compared with standard (global) DeePC and with the LPV‑DPC approach, GS‑DeePC achieves a 35 % reduction in tracking RMSE, a 28 % decrease in input variation, and a 40 % reduction in quadratic‑program solve time. A sensitivity analysis varying the number of regions shows the expected trade‑off: too few regions lead to poor linear approximations, while too many regions cause insufficient data per region, violating the persistency‑of‑excitation condition. The results confirm that an appropriately chosen number of regions yields the best performance.

In summary, GS‑DeePC merges the data‑driven predictive control paradigm with classical gain‑scheduling. By constructing local Hankel matrices, introducing overlapping composite regions, and employing a simple switching rule, the method retains the original DeePC’s theoretical guarantees within each region while delivering high‑performance control for strongly nonlinear plants and reducing computational burden. The paper concludes with suggestions for future work, including formal global stability analysis under switching, automated region selection (e.g., via clustering), and extensions to multi‑dimensional scheduling variables and higher‑order LPV representations.