Controlling functionally undefined nonlinear objects with random relative order and unstable equilibrium state

A control laws synthesis algorithm was proposed for uncertain n-th order nonlinear functional plants with a mathematical model in the normal form and an arbitrary relative order. Moreover, the output matrix might have the right eigenvalues. The algorithm is based on the setting of the desired control system trajectory and solving the inverse dynamics problem for compensating feedback transformed plant. Said differential constraint is introduced over the error between reference and calculated via the corresponding differentiating filter values of the n-th plant state variable derivative. Differentiating connection compensates the plant functional uncertainty by equalizing the signals of its own feedback. The specific observer is used to obtain the remaining plant's state variables estimates that are necessary to formulate the desired trajectory of the system.