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The interactions with physical dynamic systems, governed by control laws, aim to achieve a desired behavior in closed-loop systems while considering the physical constraints of the plant during controller design. This work presents a system- and control-theoretical analysis of coupled lumped- and distributed-parameter systems, where time evolution is described by nonlinear ordinary and/or partial differential equations. By employing differential geometrical and functional analytical methods, a formal approach is developed to explore these dynamic systems. Although the questions and problem-solving methods are similar to those for finite-dimensional systems, handling infinite-dimensional systems necessitates a more sophisticated mathematical framework. The initial focus is on a formal description of dynamic systems using differential geometrical methods, particularly emphasizing the distributed parameter case. Systems are associated with geometric objects that reflect their dynamics, enabling a covariant description. The core of the work investigates qualitative properties of systems and their solutions, notably observability, reachability, and accessibility along fixed trajectories, which are crucial for controller design. An approach utilizing transformation groups is proposed to formalize these considerations into criteria for proving or disproving concepts. Additionally, a comparative discussion highlights the similarities
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Analysis and control of infinite dimensional systems, Karl Rieger
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- 2009
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