Dominique Monnet

• Doctor
• PostDoc Position at Polytechnique Montréal

We propose a multi-precision extension of the Quadratic Regularization (R2) algorithm that enables it to take advantage of low-precision computations, and by extension to decrease energy consumption during the solve. The lower the precision in which computations occur, the larger the errors induced in the objective value and gradient, as well as i...

A simple proof is proposed that extends Seeber and Horn’s recent sufficient conditions (Seeber and Horn, 2017) for the finite time convergence of the super twisting algorithm to perturbations in the input gain. The new convergence conditions are compared to state of the art conditions, and turn out to accept sensibly smaller gains.

This paper presents a new algorithm to build feasible solutions to a MILP formulation of the vertical alignment problem in road design. This MILP involves a large number of special ordered set of type 2 variables used to describe piecewise linear functions. The principle of the algorithm is to successively solve LPs adapted from the MILP by replaci...

The twisting algorithm is a second order sliding mode technique for which convergence conditions have been established. However, these conditions are limited to systems that are affine in the control. In this paper, new convergence conditions that are not limited to such systems, are proposed. Furthermore, it is shown that in the affine case, state...

In this work, global optimization techniques based on interval arithmetic are proposed to analyze and synthesize sliding mode (SM) controllers. The proposed methodology allows generating a series of maps, called subpavings, which put in evidence the required relationships among tuning parameters, disturbances and control amplitude to fulfill the su...

This paper proposes a new way to solve the structured H2 synthesis problem under time invariant plant uncertainties. A worst-case minimization approach enables to formulate the synthesis problem as a min-max problem subject to quantified constraints. We propose a global optimization algorithm based on Interval Analysis to solve this problem. This a...

When building a road, it is critical to select a vertical alignment which ensures design and safety constraints. Finding such a vertical alignment is not necessarily a feasible problem, and the models describing it generally involve a large number of variables and constraints. This paper is dedicated to rapidly proving the feasibility or the infeas...

This paper presents a new algorithm to build feasible solutions to a MILPs formulation of the vertical alignment problem in road design. This MILP involves a large number of SOS2 variables used to describe piece-wise linear functions. The principle of the algorithm is to successively solve LPs adapted from the MILP by replacing the SOS2 constraints...

Structured $H_\infty$ regulation provides robust controllers with highly generalized forms, and recent Min-Max Interval Branch Bound Algorithm (MMIBBA) improves the $H_\infty$ synthesis problem by solving global optimized result in a guaranteed way. Due to the advantages such as global optimization over a local result, convex reformulation, and red...

H∞ control is nowadays used in many applications. This control technique enables to synthesize control laws which are robust with respect to external disturbances. Moreover, it allows to take model uncertainty into account in the synthesis process. As a consequence, H∞ control laws are robust with respect to both external disturbances and model unc...

In this paper, we present a method to compute a control law for an Autonomous Underwater Vehicle (AUV) subject to external disturbances. The control law's design objectives are formulated as H∞ objectives used to synthesize a robust controller. Then, a robustness analysis of AUV model uncertainties is performed without conservatism with interval an...

The design of sliding mode (SM) comprises the selection of a sliding manifold on the state space and a switching logic. The sliding manifold design is associated with the desired dynamics and closed loop specifications, whereas the switching logic is designed to drive and keep the state on the prescribe manifold. The classical design can lead to ov...

Given a Linear Time Invariant (LTI) system with parametric uncertainties, we propose a new method to synthesize a structured controller with H∞ constraints. Our approach is based on global optimization. The problem is formulated as a min-max optimization problem. A new version of a global optimization algorithm based on interval arithmetic is imple...

In this paper, a new technique to compute a synthesis structured Robust Control Law is developed. This technique is based on global optimization methods using a Branch-and-Bound algorithm. The original problem is reformulated as a min/max problem with non-convex constraint. Our approach uses interval arithmetic to compute bounds and accelerate the...