Optimization and Systems Theory Seminar
Wednesday May 25 at 11.00. Lindstedtsvägen 25, room 3721

Romeo Ortega  Laboratoire des Signaux et Systemes, Supelec

Control by Interconnection of Port-Hamiltonian Systems

Abstract: As vividly illustrated by the quintessential Watt's governor a natural procedure to modify the behavior of a dynamical system is to interconnect it with another dynamical system. Examples of this approach abound in modern high-performance practical applications and are proven to be very robust and reliable. These include, among many others, mechanical suspension and flapper systems, flotation devices, damping windings and impedance matching filters in electrical systems, (it may be even argued that drug infusion and vaccine injection techniques are best studied invoking interconnection principles instead of simplistic cause-effect preconceptions.) Adopting the interconnection perspective allows us to formulate the control problem in terms of the physical properties of the systems like energy-shaping and damping injection, it furthermore underscores the role of interconnection to achieve these objectives. This should be contrasted with the classical actuator-plant-sensor paradigm that leads to a signal-processing view of control in which the systems physical properties are difficult to incorporate. In our previous works we have proposed a mathematical framework to design controllers using the afore-mentioned systems interconnection perspective that we called Control by Interconnection (CbI). Towards this end we restricted ourselves to systems described by Port-Hamiltonian (PH) models, which suitably describe the dynamics of many physical processes, and where the importance of the energy function, the interconnec- tion pattern and the dissipation of the system is highlighted. In CbI the controller is another PH system connected to the plant (through a power-preserving interconnection) to add up their energy functions. In spite of the conceptual appeal of formulating the control problem as the interaction of dynamical systems, the current version of CbI imposes a severe restriction on the plant dissipation structure that stymies its practical application. The purpose of this talk is to propose some extensions to the CbI method to make it more widely applicable -- in particular, to overcome the dissipation obstacle [1]. Furthermore, we establish the connections between CbI and Standard PassivityBased Control (PBC). Standard PBC, where energy shaping is achieved via static state feedback, is one of the most successful controller design techniques. However, the control law is usually derived from an uninspiring and non-intuitive "passive output generation" viewpoint. We prove in this talk that Standard PBC is obtained restricting CbI to a suitable subset of the state space -- providing a nice geometric interpretation to Standard PBC.

Calendar of seminars Last update: May 17, 2011.