Optimal control

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