[Paper Review] Dual Stochastic MPC for Systems with Parametric and Structural Uncertainty

Elena Arcari, Lukas Hewing+2 more|arXiv (Cornell University)|Dec 20, 2019

Advanced Control Systems Optimization15 references4 citations

TL;DR

This paper proposes a dual stochastic model predictive control (DMPC) framework for nonlinear systems with both parametric and structural uncertainty, using a scenario-based approach that splits the prediction horizon into dual (learning-focused) and exploitation (control-focused) phases. By actively exploring to identify unknown model structures and parameters, the method enables faster fault detection and improved control performance compared to passive adaptive MPC, as demonstrated in an aircraft altitude control case study with 75% actuator fault.

ABSTRACT

Designing controllers for systems affected by model uncertainty can prove to be a challenge, especially when seeking the optimal compromise between the conflicting goals of identification and control. This trade-off is explicitly taken into account in the dual control problem, for which the exact solution is provided by stochastic dynamic programming. Due to its computational intractability, we propose a sampling-based approximation for systems affected by both parametric and structural model uncertainty. The approach proposed in this paper separates the prediction horizon in a dual and an exploitation part. The dual part is formulated as a scenario tree that actively discriminates among a set of potential models while learning unknown parameters. In the exploitation part, achieved information is fixed for each scenario, and open-loop control sequences are computed for the remainder of the horizon. As a result, we solve one optimization problem over a collection of control sequences for the entire horizon, explicitly considering the knowledge gained in each scenario, leading to a dual model predictive control formulation.

Motivation & Objective

• To address the challenge of controlling systems with both parametric and structural uncertainty, where model inaccuracies can degrade performance.
• To explicitly balance the trade-off between control performance and system identification (dual control) in nonlinear systems.
• To develop a computationally tractable, sampling-based approximation of the dual control problem that maintains theoretical soundness.
• To extend existing stochastic MPC methods to handle multiple operating modes with uncertain parameters and structural changes.
• To demonstrate improved fault detection and control performance through simulation on an aircraft system with actuator degradation.

Proposed method

• The method splits the prediction horizon into a dual phase (for active learning) and an exploitation phase (for control optimization), using a scenario tree to represent possible model and parameter realizations.
• A rollout-based approximate dynamic programming approach is employed to compute optimal control sequences that account for knowledge gained in each scenario.
• Each scenario corresponds to a combination of operating mode (e.g., nominal or fault) and sampled parameter values, with probabilities updated using Bayesian inference.
• The dual control effect is embedded implicitly through the optimization structure, ensuring that control inputs contribute to both performance and information gain.
• The approach uses a sampling-based approximation of the stochastic dynamic programming solution, avoiding the computational intractability of the exact dual control formulation.
• The controller is implemented as a receding horizon optimization that re-optimizes at each time step using updated belief states over modes and parameters.

Experimental results

Research questions

• RQ1 How can a dual control strategy be effectively integrated into model predictive control for systems with both parametric and structural uncertainty?
• RQ2 Can a sampling-based, scenario-tree approach provide a computationally feasible yet theoretically sound approximation of the dual control problem in nonlinear systems?
• RQ3 How does active exploration for model identification affect control performance and convergence speed in systems with unknown structural faults?
• RQ4 What is the performance gain of dual MPC over passive adaptive MPC in terms of fault detection and control response?
• RQ5 To what extent does the dual control formulation improve parameter estimation accuracy under uncertainty?

Key findings

• The dual MPC controller achieved faster fault identification, detecting the 75% actuator gain loss within one time step after the reference change, whereas the passive CEMPC controller delayed detection.
• The DMPC controller initiated aggressive input excitation 20 time steps before the reference change, enabling early and accurate model identification.
• The probability of the nominal mode dropped to 0.05 at k=40, indicating rapid belief update and effective fault detection.
• Parameter estimates for the fault mode converged toward the true value of γ² = 0.25, with the mean estimate stabilizing after sufficient excitation.
• The CEMPC controller exhibited input saturation and delayed response due to insufficient excitation, highlighting the limitations of passive adaptation.
• The DMPC controller reduced control error and improved tracking performance by proactively learning the system's true mode and parameters before critical control actions.