Optimal Control

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Since the late 1950s, attitudes toward optimal control have varied significantly within the scientific and engineering communities, oscillating between excessive enthusiasm for its problem-solving capabilities and a rejection of it as mere abstract mathematics. The reality lies somewhere in between these extremes. Ongoing research, particularly in robust control, has established optimization as a valuable source of powerful and flexible tools for control system designers. This emerging research is grounded in the well-established linear quadratic Gaussian control theory, which is crucial for understanding optimization effectively. Additionally, there is a consensus that variational techniques yield results well-suited for addressing nonlinear solutions in complex control problems. Despite the initial significant achievements in the field dating back around forty years, a contemporary presentation of classical optimal control theory from a tutorial perspective remains relevant. This text draws extensively from the Italian language textbook "Controllo ottimo," published by Pitagora and utilized in various courses at the Politecnico of Milan.