Pontryagin's maximum principle is used for computing the optimum control function u(t) for a given plant and a given performance criterion. If u(t) is bounded, the control is of the bang-bang type in many cases. If u(t) is expressed as the function of the state variables, that means, u(t) = sgn f(xi), the equation f(xi) = 0 determines the switching surface in the state space. In general these surfaces...
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