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Stochastic Data-Driven Predictive Control with Equivalence to Stochastic MPC

Ruiqi Li, John W. Simpson-Porco, Stephen L. Smith

TL;DR

This work introduces Stochastic Data-Driven Predictive Control (SDDPC), a data-driven receding-horizon control framework for unknown stochastic LTI systems with partial state observation under chance constraints. By constructing an auxiliary data-driven state-space model from offline input-output data and pairing it with a Kalman-like estimator and an affine feedback policy, the method mirrors SMPC while avoiding a parametric plant model. The authors prove that, under idealized conditions, SDDPC and SMPC have identical feasible and optimal sets and trajectories, and they demonstrate recursive feasibility and closed-loop stability for the data-driven scheme. A grid-connected power converter case study shows that SDDPC can achieve lower tracking costs and improved constraint satisfaction compared with SMPC, MPC, DeePC, and SPC, highlighting practical benefits for uncertain, noise-perturbed systems. Future work will focus on computational efficiency, robustness to noisy data, and extensions to non-Gaussian noise and risk-based safety guarantees.

Abstract

We propose a data-driven receding-horizon control method dealing with the chance-constrained output-tracking problem of unknown stochastic linear time-invariant (LTI) systems with partial state observation. The proposed method takes into account the statistics of the process noise, the measurement noise and the uncertain initial condition, following an analogous framework to Stochastic Model Predictive Control (SMPC), but does not rely on the use of a parametric system model. As such, our receding-horizon algorithm produces a sequence of closed-loop control policies for predicted time steps, as opposed to a sequence of open-loop control actions. Under certain conditions, we establish that our proposed data-driven control method produces identical control inputs as that produced by the associated model-based SMPC. Simulation results on a grid-connected power converter are provided to illustrate the performance benefits of our methodology.

Stochastic Data-Driven Predictive Control with Equivalence to Stochastic MPC

TL;DR

This work introduces Stochastic Data-Driven Predictive Control (SDDPC), a data-driven receding-horizon control framework for unknown stochastic LTI systems with partial state observation under chance constraints. By constructing an auxiliary data-driven state-space model from offline input-output data and pairing it with a Kalman-like estimator and an affine feedback policy, the method mirrors SMPC while avoiding a parametric plant model. The authors prove that, under idealized conditions, SDDPC and SMPC have identical feasible and optimal sets and trajectories, and they demonstrate recursive feasibility and closed-loop stability for the data-driven scheme. A grid-connected power converter case study shows that SDDPC can achieve lower tracking costs and improved constraint satisfaction compared with SMPC, MPC, DeePC, and SPC, highlighting practical benefits for uncertain, noise-perturbed systems. Future work will focus on computational efficiency, robustness to noisy data, and extensions to non-Gaussian noise and risk-based safety guarantees.

Abstract

We propose a data-driven receding-horizon control method dealing with the chance-constrained output-tracking problem of unknown stochastic linear time-invariant (LTI) systems with partial state observation. The proposed method takes into account the statistics of the process noise, the measurement noise and the uncertain initial condition, following an analogous framework to Stochastic Model Predictive Control (SMPC), but does not rely on the use of a parametric system model. As such, our receding-horizon algorithm produces a sequence of closed-loop control policies for predicted time steps, as opposed to a sequence of open-loop control actions. Under certain conditions, we establish that our proposed data-driven control method produces identical control inputs as that produced by the associated model-based SMPC. Simulation results on a grid-connected power converter are provided to illustrate the performance benefits of our methodology.
Paper Structure (47 sections, 10 theorems, 120 equations, 2 figures, 2 tables, 3 algorithms)

This paper contains 47 sections, 10 theorems, 120 equations, 2 figures, 2 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. Problem Statement
  3. Stochastic MPC: A Benchmark Model-Based Design
  4. Initial Condition and State Estimation
  5. Interpolation of Initial Condition
  6. Feedback Control Policies
  7. Propagation of Input-Output Distribution
  8. Chance-Constraint Approximation
  9. Terminal Condition
  10. SMPC Optimization Problem and Implementation
  11. Closed-loop Properties
  12. Our Objective: An Equivalent Data-Driven Method
  13. Stochastic Data-Driven Predictive Control
  14. Use of Offline Data
  15. Deterministic Offline Data
  16. ...and 32 more sections

Key Result

Lemma 1

Assume $p \in (0,\frac{1}{2}]$. In Algorithm ALGO:SMPC, if the problem Eq:SMPC_reduced is feasible at control step $k=\kappa$, then it is feasible at next control step $k = \kappa + N_{\rm c}$.

Figures (2)

  • Figure 1: The one-line diagram of a grid-connected power converter DeePC:huang2021.
  • Figure 2: The second output signals with SPC (light blue) and SDDPC (red) in the constraint satisfaction test.

Theorems & Definitions (59)

  • Remark 1: Output Constraints and Output Tracking
  • Remark 2: Input Chance Constraints
  • Remark 3: Gaussian Signals
  • Lemma 1: SMPC Recursive Feasibility
  • Lemma 2: SMPC Closed-loop Stability
  • Lemma 3: Data Representation of Model Quantities
  • proof
  • Lemma 4: Auxiliary Model
  • proof
  • Lemma 5
  • ...and 49 more