Numerical Approaches to Optimal Control: Tackling Nonlinear Systems and Constraints

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Optimal control theory formulates control problems as optimization challenges, offering systematic solutions that surpass traditional methods like PID control. While it provides clear analytical expressions for simpler scenarios, such as unconstrained linear systems with quadratic cost functions, it struggles with the complexity of nonlinear systems constrained by physical limitations. In these instances, deriving exact solutions is challenging, necessitating the use of approximate methods to tackle the optimization problems effectively.