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Analytic predictive controllers for nonlinear systems with ill-defined relative degree

Analytic predictive controllers for nonlinear systems with ill-defined relative degree

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The paper addresses the problem of the control of nonlinear systems with ill-defined relative degree. The analytic solution to an optimal tracking problem in terms of a generalised predictive performance index is presented, where the output tracking error is predicted by Taylor series approximation up to an arbitrarily chosen order. It is shown that the optimal control for nonlinear systems with ill-defined relative degree is discontinuous, and the optimal control law is not unique when the system is within the singular point set. Approximate implementation of the optimal predictive control law is discussed. The nonlinear predictive controller presented is successfully demonstrated by an numerical example.

Inspec keywords: predictive control; nonlinear systems; approximation theory; control system analysis; performance index; optimal control; series (mathematics)

Other keywords: Taylor series; singular point set; approximation; optimal control; nonlinear systems; tracking; performance index; predictive control

Subjects: Interpolation and function approximation (numerical analysis); Nonlinear control systems; Optimal control; Control system analysis and synthesis methods

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