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Lectures Year : 2022

Introduction to Optimal Control

Thierry Miquel


The application of optimal control theory to the practical design of multivariable control systems started in the 1960s1: in 1957 R. Bellman applied dynamic programming to the optimal control of discrete-time systems. His procedure resulted in nonlinear feedback schemes. By 1958, L.S. Pontryagin has developed the maximum principle relying on the calculus of variations developed by L. Euler (1707-1783). He solved the minimum-time problem, deriving in 1962 an on/o relay control law as an optimal control. In 1960 three major papers were published by R. Kalman and coworkers, working in the U.S. One of these publicized the vital work of Lyapunov (1857-1918) in the time-domain control of nonlinear systems. The next discussed the optimal control of systems, providing the design equations for the Linear Quadratic Regulator (LQR). The third paper has provided the design equations for the discrete Kalman lter. The continuous Kalman lter was developed by Kalman and Bucy in 1961.


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hal-02987731 , version 1 (04-11-2020)
hal-02987731 , version 2 (17-10-2022)


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  • HAL Id : hal-02987731 , version 2


Thierry Miquel. Introduction to Optimal Control. Master. Introduction to optimal control, ENAC, France. 2022, pp.188. ⟨hal-02987731v2⟩


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