2022 Optimization Days

HEC Montréal, Québec, Canada, 16 — 18 May 2022

Schedule Authors My Schedule

WB10 - Systems and Control

May 18, 2022 01:30 PM – 03:10 PM

Location: Banque Scotia (blue)

Chaired by Jérôme Le Ny

4 Presentations

  • 01:30 PM - 01:55 PM

    Model Predictive Control of a Tandem-rotor Helicopter

    • James Richard Forbes, presenter, McGill University

    Model predictive control (MPC) of a tandem-rotor helicopter is considered. A quadratic program with control input and attitude constraints is posed and solved. To realize a quadratic program, the nonlinear equations of motion are linearized about a reference trajectory using error defined on a matrix Lie group, specifically the group of double direct isometries. Additionally, the nonlinear attitude constraints are linearized. The reference trajectory is generated using finite-horizon linear quadratic control. To realize a tractable control problem a non-uniformly spaced prediction horizon is used. Monte-Carlo simulations highlight the robust nature of the proposed MPC control to model uncertainty, environmental disturbances, and initial conditions.

  • 01:55 PM - 02:20 PM

    System Norm Regularization Methods for Koopman Operator Approximation

    • Steven Dahdah, presenter, McGill University
    • James Richard Forbes, McGill University

    This presentation summarizes recently submitted work on approximating the Koopman operator from data using a system norm regularizer. The regression problem required to approximate the Koopman operator is numerically challenging when many lifting functions are considered. Even low-dimensional systems can yield unstable or ill-conditioned results in a high-dimensional lifted space. In this work, the regression problem is reformulated as a convex optimization problem with linear matrix inequality constraints. Hard asymptotic stability constraints and system norm regularizers are considered as methods to improve the numerical conditioning of the approximate Koopman operator. In particular, the H-infinity norm is used as a regularizer to penalize the input-output gain of the linear system defined by the Koopman operator. Weighting functions are then applied to penalize the system gain at specific frequencies. Experimental results using data from an aircraft fatigue structural test rig and a soft robot arm highlight the advantages of the proposed regression methods.

  • 02:20 PM - 02:45 PM

    Efficient Quantum Optimal Control

    • Sri Hari Krishna Narayanan, presenter, Argonne National Laboratory
    • Jan Hueckelheim, Argonne National Laboratory

    Quantum optimal control problems are typically solved by gradient-based algorithms such as GRAPE, which suffer from exponential growth in storage with increasing number of qubits and linear growth in memory requirements with increasing number of time steps. These memory requirements are a barrier for simulating large models or long time spans. We have created a nonstandard automatic differentiation technique that can compute gradients needed by GRAPE by exploiting the fact that the inverse of a unitary matrix is its conjugate transpose. Our approach significantly reduces the memory requirements for GRAPE, at the cost of a reasonable amount of recomputation. We present benchmark results based on an implementation in JAX.

  • 02:45 PM - 03:10 PM

    Differentially Private Linear Quadratic Gaussian Control

    • Kwassi Holali Degue, Ecole Polytechnique de Montreal
    • Jérôme Le Ny, presenter, GERAD - Polytechnique Montréal

    Real-time monitoring and control systems enabling a more intelligent infrastructure increasingly rely on privacy-sensitive data obtained from individuals to operate, e.g., location traces collected from the users of an intelligent transportation system. To encourage the participation of these individuals, it becomes important to develop estimation and control algorithms that protect their privacy. This talk presents a methodology for the design and optimization of a two-stage architecture for Kalman filtering and LQG control that enforces differential privacy, a state-of-the-art formal notion of privacy. The first stage aggregates the private signals, while the second stage reconstructs perturbed global statistics of interest. Performance is optimized by reducing the design problem to a semi-definite program.