Defence Hailong Chen: "Data-driven control of complex systems"
Promotors: 1st promotor: Prof Claudio De Persis, 2nd promotor: Prof Nima Monshizadeh, 3rd promotor: Prof Pietro Tesi
Abstract: Complex engineering systems are inherently nonlinear, and accurate models of them are rarely available. This thesis develops direct data-driven methods that design controllers and certify stability for such systems from noisy input/state data, combining data-based descriptions of all dynamics consistent with the data with Lyapunov theory and sum-of-squares (SOS) optimization. First, for input-affine polynomial systems, we derive conditions---biconvex, solved alternately, or natively convex through a tailored parametrization---to design, for all dynamics consistent with noisy data, controllers enforcing input-to-state stability (ISS) with respect to measurement errors as well as actuator and process disturbances, together with an ISS Lyapunov function and comparison functions. Second, we propose an overall data-based design of event-triggered controllers for nonlinear systems: following the emulation approach, a state-feedback law is synthesized from data by approximate nonlinearity cancellation or contractivity, and two triggering policies, based on the state error and the library error, guarantee a positive minimum inter-event time. Third, for autonomous systems with trigonometric nonlinearities and unknown parameters---motivated by transient stability analysis of power systems---we recast the dynamics into polynomial systems with algebraic constraints and formulate data-based SOS programs, solved via an expanding-interior algorithm, to estimate and systematically enlarge the basin of attraction, as verified on a pendulum and a single-machine infinite-bus system.