Optimization-Based Control Design Techniques and Tools

International audienceStructured output feedback controller synthesis is an exciting new concept in modern control design, which bridges between theory and practice in so far as it allows for the first time to apply sophisticated mathematical design paradigms like H∞-or H2-control within control architectures preferred by practitioners. The new approach to structured H∞-control, developed during the past decade, is rooted in a change of paradigm in the synthesis algorithms. Structured design may no longer be based on solving algebraic Riccati equations or matrix inequalities. Instead, optimization-based design techniques are required. In this essay we indicate why structured controller synthesis is central in modern control engineering. We explain why non-smooth optimization techniques are needed to compute structured control laws, and we point to software tools which enable practitioners to use these new tools in high technology applications. I. MOTIVATIONS In the modern high technology field control engineers usually face a large variety of concurring design specifications such as noise or gain attenuation in prescribed frequency bands, damping, decoupling, constraints on settling-or rise-time, and much else. In addition, as plant models are generally only approximations of the true system dynamics, control laws have to be robust with respect to uncertainty in physical parameters or with regard to un-modeled high frequency phenomena. Not surprisingly, such a plethora of constraints presents a major challenge for controller tuning, due not only to the ever growing number of such constraints, but also because of their very different provenience. The dramatic increase in plant complexity is exacerbated by the desire that regulators should be as simple as possible, easy to understand and to tune by practitioners, convenient to hardware implement, and generally available at low cost. Such practical constraints explain the limited use of black-box controllers, and they are the driving force for the implementation of structured control architectures, as well as for the tendency to replace hand tuning methods by rigorous algorithmic optimization tools. II. STRUCTURED CONTROLLERS Before addressing specific optimization techniques, we introduce some basic terminology for control design problems with structured controllers. Given a plant P in state-space Pierre Apkarian is with ONERA