Daniel Liberzon's research interests

Hybrid control:
We are interested in developing control algorithms in which continuous dynamics are coupled with discrete logic. The resulting closed-loop systems are known as hybrid because they are described by an interaction of differential equations and discrete automata. The motivating applications are those in which the controller is implemented on a digital computer or communicates with the process remotely over a network. A particular focus of our research is on developing hybrid control laws for nonlinear systems subject to communication constraints. Relevant Publications

Supervisory control of uncertain systems:

This research area can be regarded as a subtopic of hybrid control, which focuses on systems with large modeling uncertainties. The basic paradigm is to design a high-level decision maker, called a supervisor, which orchestrates logic-based switching among a family of candidate controllers. Such switching control techniques provide an alternative to more traditional continuously tuned adaptive control laws, and are more suitable for computer implementation. Our primary objective is to develop a systematic supervisory control methodology for nonlinear uncertain systems. Relevant Publications

Analysis of switched systems:

The aim of this research is to provide a theoretical foundation for the analysis of systems that result from applying switching control methods described above. We are developing stability criteria for switched systems which utilize common, multiple, and weak Lyapunov functions. These are complemented by tools for hybrid systems developed by computer scientists to verify stability. We are also exploring mathematical methods from the theory of Lie algebras. Going beyong stability, we are investigating basic properties of switched systems with inputs and outputs. Relevant Publications Nonlinear control theory:
We are working on several aspects of nonlinear control theory. A specific topic of interest is the use of control Lyapunov functions for achieving various forms of disturbance attenuation, such as input-to-state stability. These problems are motivated in part by questions that arise in the design of logic-based switching control algorithms for nonlinear systems. Our recent work also re-examines the concepts of a minimum-phase nonlinear system and of nonlinear observability. Relevant Publications Stochastic differential equations:
This research is concerned with investigating steady-state properties of systems described by stochastic differential equations. The most recent direction is stability of stochastic switched systems. In our earlier work, we singled out systems for which one can obtain explicit formulas for steady-state probability densities and characterize the speed of convergence to steady-state via the analysis of the Fokker-Planck operator. We are also exploring how the steady-state properties of controlled stochastic systems are affected by the choice of control. Relevant Publications

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