Journées de l'optimisation 2022
HEC Montréal, Québec, Canada, 16 — 18 mai 2022
WB10  Systems and Control
18 mai 2022 13h30 – 15h10
Salle: Banque Scotia (bleu)
Présidée par Jérôme Le Ny
4 présentations

13h30  13h55
Model Predictive Control of a Tandemrotor Helicopter
Model predictive control (MPC) of a tandemrotor 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 finitehorizon linear quadratic control. To realize a tractable control problem a nonuniformly spaced prediction horizon is used. MonteCarlo simulations highlight the robust nature of the proposed MPC control to model uncertainty, environmental disturbances, and initial conditions.

13h55  14h20
System Norm Regularization Methods for Koopman Operator Approximation
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 lowdimensional systems can yield unstable or illconditioned results in a highdimensional 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 Hinfinity norm is used as a regularizer to penalize the inputoutput 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.

14h20  14h45
Efficient Quantum Optimal Control
Quantum optimal control problems are typically solved by gradientbased 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.

14h45  15h10
Differentially Private Linear Quadratic Gaussian Control
Realtime monitoring and control systems enabling a more intelligent infrastructure increasingly rely on privacysensitive 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 twostage architecture for Kalman filtering and LQG control that enforces differential privacy, a stateoftheart 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 semidefinite program.