Data-Driven Control

Find controllers for all plants that are consistent with the observed data.

Data-Driven Control (DDC) is a methodology that formulates controllers directly from observations without requiring a system identification step. Our work in (Miller & Sznaier, 2022) extended the Quadratic Matrix Inequality (QMI) framework towards data-driven gain-scheduled control of Linear Parameter-Varying (LPV) systems.

Stabilizing control of an LPV system given data observations. The left side highlights stabilization of the ground-truth in red, and the blue trajectories are other systems in the data consistency set. The right side samples additional parameter sequences and demonstrates stabilization.

The introduction of input and measurement noise is called the Error-in-Variables (EIV) setting, and adds a bilinearity that results in NP-hard system identification and control problems. We developed a polynomial-optimization based framework to perform stabilizing and robust control of all consistent plants in the EIV setting when all noise processes are L-infinity norm bounded (Miller et al., 2022). The moment-Sum-of-Squares (SOS) hierarchy is used to find a superstabilizing or quadratically stabilizing controller, where each nonnegativity constraint is posed over the set of unknown plants and unknown noise processes. We a used theorem of alternatives is used to eliminate the unknown noise variables and improve computational scalability. This SOS-based framework may be extended towards the control of autoregressive models with input-output data (Miller et al., 2023).

Data-Driven techniques may also be applied to peak estimation. The data-consistency set in (missing reference) is modeled as a parameter-affine differential inclusion for a polytope-bounded uncertainty process.

The left plot charts 100 noisy derivative observations of a 3-state cubic polynomial dynamical system. The right plots a series of trajectories (cyan) compatible with data-consistent systems, as well as an upper bound (red) on the maximal vertical coordinate that any of these systems will obtain.

Relevant Publications:

Journal Articles

  1. LCSS
    Data-Driven Gain Scheduling Control of Linear Parameter-Varying Systems using Quadratic Matrix Inequalities
    Miller, Jared, and Sznaier, Mario
    IEEE Control Systems Letters 2022

Conference Articles

  1. IFAC
    Superstabilizing Control of Discrete-Time ARX Models under Error in Variables
    Miller, JaredDai, Tianyu, and Sznaier, Mario
    In 22nd IFAC World Congress (upcoming) 2023
    Facial Input Decompositions for Robust Peak Estimation under Polyhedral Uncertainty
    Miller, Jared, and Sznaier, Mario
    In 10th IFAC Symposium on Robust Control Design (ROCOND) 2022
  3. CDC
    Data-Driven Superstabilizing Control of Error-in-Variables Discrete-Time Linear Systems
    Miller, JaredDai, Tianyu, and Sznaier, Mario
    In 61st IEEE Conference on Decision and Control (CDC) 2022


  1. Data-Driven Control of Positive Linear Systems using Linear Programming
    Miller, JaredDai, TianyuSznaier, Mario, and Shafai, Bahram
    Preprint 2023
  2. Robust Data-Driven Safe Control using Density Functions
    Zheng, Jian, Dai, TianyuMiller, Jared, and Sznaier, Mario
    Preprint 2023
  3. Quantifying the Safety of Trajectories using Peak-Minimizing Control
    Miller, Jared, and Sznaier, Mario
    Preprint 2023
  4. Analysis and Control of Input-Affine Dynamical Systems using Infinite-Dimensional Robust Counterparts
    Miller, Jared, and Sznaier, Mario
    Preprint 2023
  5. Data-Driven Stabilizing and Robust Control of Discrete-Time Linear Systems with Error in Variables
    Miller, JaredDai, Tianyu, and Sznaier, Mario
    Preprint 2022