The MAC Team does research in the field of systems and control theory. We develop a mathematical and theoretical basis for dynamical systems control including modeling, analysis, optimization and design. Generic theoretical and numerical tools are designed for complex systems possibly affected by information limitations and uncertainty. Complexity may arise from essential features present in the system to be controlled or its environment: switches, jumps, isolated nonlinearities, delays or exogenous disturbances. New methods are developed for handling heterogeneous performance requirements and generating performance certificates. We share a common objective: developing constructive theoretical conditions characterizing solutions to various control problems while providing effective efficient computational algorithms. A particular attention is given to validated computation for control in the presence of information limitation and uncertainty.

We carry out impactful research ranging from fundamental theory to applied control engineering. Advanced tools are applied to practical control problems, including robust analysis and synthesis for satellite attitude control and anti-windup systems, design and analysis of flight control laws, control and observation of TCP/IP based networks, robust control of power electronic devices, observation of bio(techno)logical and environmental processes. Although the scope of the team’s interests has recently extended to a broader range of control systems applications (control of the depth of anesthesia, including the control of the analgesic drug, robotics, flexible structures), much of the applied research is centered around the development and application of advanced control techniques to aerospace systems (space rendezvous and proximity operations problems, attitude control, flight control laws).

HISTORY:

The MAC team emerged from the reorganization of research activites in systems control at LAAS-CNRS in the mid 1990s. The team led by Jacques Bernussou from 1995 to 2002 was originally named CSC (for Continuous Systems Control) and its activities were initially centered essentially around Lyapunov-based control techniques for systems modeled by linear ordinary differential equations. Lyapunov functions were constructed either analytically or numerically to certify stability and performance (H2, Hinf) of control systems, in the presence of uncertainties and/or nonlinearities like actuator saturations. In this context, the team was one of the first worldwide to recognize the relevance of linear matrix inequalities (LMI) and semidefinite programming (SDP) as a unifying framework for addressing robust control problems.

The MAC team was then successively led by Sophie Tarbouriech (2002-2005), Isabelle Queinnec (2006-2010), Denis Arzelier (2011-2014), Didier Henrion (2015-2017), Dimitri Peaucelle (2018-2020). Research activites at MAC gradually evolved toward non-linear controlled systems with time-delays and/or saturations and/or modeled by partial differential equations, and towards optimal control and polynomial optimization. For example, the moment relaxations and polynomial sum-of-squares LMI hierarchies have been developed in the MAC team by Jean-Bernard Lasserre and its collaborators since the late 1990s. More recent research activites include the control of hybrid systems and infinite dimensional systems. In 2021, the POP team was created, separating the polynomial optimization topics from the control oriented research that remained in the MAC team.