Observability can be analyzed by considering the (repeated) Lie derivatives of the output mapping with respect to the system vector fields. The key ingredient to analyze controllability of a nonlinear system turns out to be the geometric concept of (higher-order) Lie brackets of the associated system vector fields. The first topic in the course is concerned with the extension of the fundamental concepts of controllability and observability from linear to nonlinear control systems. The course deals with the mathematical modeling, analysis and control of such complex dynamical systems, illustrated by a variety of examples from mechanical systems, electrical systems, mechatronics, power systems, as well as (bio-)chemical systems. In many areas of engineering and exact sciences one is confronted with systems which exhibit intrinsic nonlinearities. critically evaluate control aims and pertinent control strategies to achieve these aims. apply dissipativity theory, and in particular the passivity and small-gain theorem, for robust control of nonlinear systems, and for set-point regulation.Ĩ. investigate stability of equilibria of nonlinear systems by the use of Lyapunov's first or second method, and is able to compare and combine these two methods.ħ. perform asymptotic output tracking of nonlinear control systems by employing the notion of relative degree.Ħ. apply Frobenius theorem for the solvability of nonlinear pde's to the problem of feedback linearization, and for determining uncontrollable dynamics.ĥ.
analyze controllability and observability of nonlinear systems by performing Lie bracket tests.Ĥ.
formulate relevant examples from the engineering and exact sciences into nonlinear systems descriptions.ģ.
mathematically model nonlinear system dynamics and consequences for qualitative dynamical behavior, and to evaluate its engineering relevance.Ģ. Modeling and Control of Complex Nonlinear Engineering Systemsġ. Modeling and Control of Complex Nonlinear Engineering System
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