Titlebook: Optimal Control; Leonid T. Ashchepkov,Dmitriy V. Dolgy,Ravi P. Agar Textbook 2021Latest edition The Editor(s) (if applicable) and The Auth

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https://doi.org/10.1007/978-3-030-91029-7linear systems; optimal control; nonlinear systems; Cauchy formula; Kalman theorem; Krasovskii theorem; Po

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Controllability of Linear SystemsWe study the controllability of linear systems – the existence of processes with specified conditions on the ends of a trajectory. The criteria of point-to-point and complete controllability are established. We investigate the features of uncontrolled systems.

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Synthesis of the Optimal System PerformanceThe concept of the synthesized control and synthesis for optimal performance system is introduced. The reverse motion method is described. Examples of applying this method for the synthesis of stationary second-order systems are given.

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The Observability ProblemThe problem of observability – the possibility to define and calculate the position of a controlled object at a given time by observable data is explored. We establish the criteria of observability for homogeneous, non-homogeneous, and stationary observability systems. The relationship between observability and controllability is showed.

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