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Approximation design of optimal controllers for nonlinear systems with sinusoidal disturbances. (English) Zbl 1104.93030

Summary: This paper considers an infinite-time optimal damping control problem for a class of nonlinear systems with sinusoidal disturbances. A successive approximation approach (SAA) is applied to design feedforward and feedback optimal controllers. By using the SAA, the original optimal control problem is transformed into a sequence of nonhomogeneous linear two-point boundary value (TPBV) problems. The existence and uniqueness of the optimal control law are proved. The optimal control law is derived from a Riccati equation, matrix equations and an adjoint vector sequence, which consists of accurate linear feedforward and feedback terms and a nonlinear compensation term. And the nonlinear compensation term is the limit of the adjoint vector sequence. By using a finite term of the adjoint vector sequence, we can get an approximate optimal control law. A numerical example shows that the algorithm is effective and robust with respect to sinusoidal disturbances.

MSC:

93B51 Design techniques (robust design, computer-aided design, etc.)
49M29 Numerical methods involving duality
93B40 Computational methods in systems theory (MSC2010)
93B35 Sensitivity (robustness)
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