ECS-9707891 Isidori In the last few years, new powerful ideas and concepts have contributed to the development of a number of systematic methods for global analysis and design of nonlinear feedback systems. A common goal of these research efforts has been the synthesis of feedback controllers yielding asymptotic stability (with prescribed region of attraction) and/or asymptotic tracking (rejection) of selected exogenous commands (disturbances), in the presence of structured uncertainties, such as parameter variations, and/or unstructured uncertainties, such has unmodeled dynamics. The actual setup in which these robust design methods have to be implemented is that in which only a set of variables (and not the full state) is available for feedback. In this case the entire design problem becomes of course more demanding, in view of the need of including; some kind of "state observer" in the feedback architecture. This problem is particularly felt in the case of tracking, when the most realistic situation is indeed the one in which only the "tracking error" (and not the entire reference trajectory) would be available for control purposes. As it happens for any design scheme dealing with the selection of specific output maps, the possibility of implementing the above-mentioned methods for feedback design is deeply influenced by the asymptotic properties of the so-called "zero dynamics" of the system (the dynamics which arise internally in a system when input and initial state are such as to constrain the output to be identically zero). More precisely, a consistent number of these methods for feedback design require the zero dynamics to be asymptotically stable: systems having this property are - in analogy with a terminology en vogue for linear systems called "minimum phase systems". In particular, if a system is minimum phase it is possible to achieve an arbitrarily small level of attenuation between disturbances and output, with obvious positive consequences on the ability of solving pr oblems of robust stabilization in the case of unmodeled dynamics. However, many physical systems exhibit a non-minimum phase behavior. Motivated by the importance of being able to robustly control also non-minimum phase nonlinear systems and by the scarcity of available results in this area, this research will focus on two directions. The first one deals with problems of robust stabilization of non-minimum phase nonlinear systems, in the presence of unmodeled dynamics. Robustness with respect to this kind of uncertainty is usually dealt with by looking at the controlled system as to the feedback interconnection of two subsystems, only one of which is accurately modeled, and then seeking a control law which lowers, as much as possible, some suitably defined "gain" of the interconnection modeled/unmodeled component. In this setup, the research will address the problem of finding, for various classes of non-minimum phase systems, estimates of the lowest achievable "gains" (so as to reduce the conservativeness of the design). The other direction is to study problems of robust tracking in the presence of parametric uncertainties. Unlike the case of linear systems, where the presence of unstable zero dynamics is generally not an obstruction to asymptotic tracking of prescribed families of trajectories, in the case of non-minimum phase nonlinear system no method is available yet to achieve asymptotic tracking, in the presence of large parameter uncertainties and for arbitrarily large initial conditions. This part of the proposed research is directed toward the development of systematic methods yielding semiglobal robust tracking for nonlinear systems having unstable zero dynamics.
