My passion is control systems. The reason, or one of the many reasons, I love control systems so much as a research area and applied science is that it brings together multiple fields in a synergetic way, such as differential equations, linear algebra, real and complex analysis, numerical methods, optimization, and others. I feel incredibly lucky to have been able to learn, apply, and build on many different mathematical tools, all in the context of the analysis and synthesis of control systems. This is also the reason why I am excited to be part of GERAD; I look forward to collaborating with GERAD members, where we each bring our expertise to bear on exciting research problems both in control systems and related fields.

One of my research interests is input-output (I-O) stability theory. Roughly speaking, I-O stability is all about “nice inputs” leading to “nice outputs”. In the context of control systems, the idea is to design a controller so that the closed-loop system is I-O stable. I-O stability theory applies equally well to linear as well as nonlinear systems. Recent research has focused on reducing the conservatism of I-O results. By characterizing the I-O properties of the system to be controlled in a less conservative way, and by optimally designing the I-O properties of the controller, robust yet high performance closed-loop control can be realized with a simultaneous guarantee of I-O stability.

Another research interest of mine is optimal yet robust control design. The word “optimal” means the controller should minimizes a closed-loop performance metric. The word “robust” means the controller must guarantee stabilization of the “nominal” system under control, but also a class of systems described by the nominal system subject to a perturbation, where the perturbation represents model uncertainty. The approach I take to solve optimal yet robust control design problems is to convert the problems into convex optimization problems. One of the issues of such a conversion is that a solution to the newly formulated convex optimization problem is usually more conservative than a solution of the original problem. How to reduce such conservatism is one of the focuses of my research.

The applications of my research are not limited in the sense that the theory is very general and can be applied in almost any field. However, I have historically applied the theory I’ve developed to aerospace and robotics problems. More recently I’ve developed an interest in autonomous vehicles, where all the hallmarks of a good control problem are present: the need for high performance control in the presence of model uncertainty, noise, and disturbances.

Member of GERAD since February 2017