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Suboptimal control for nonlinear systems: a successive approximation approach. (English) Zbl 1129.49303

Summary: This paper presents a successive approximation approach (SAA) designing optimal controllers for a class of nonlinear systems with a quadratic performance index. By using the SAA, the nonlinear optimal control problem is transformed into a sequence of nonhomogeneous linear two-point boundary value (TPBV) problems. The optimal control law obtained consists of an accurate linear feedback term and a nonlinear compensation term which is the limit of an adjoint vector sequence. By using the finite-step iteration of the nonlinear compensation sequence, we can obtain a suboptimal control law. Simulation examples are employed to test the validity of the SAA.

MSC:

49K15 Optimality conditions for problems involving ordinary differential equations
49M05 Numerical methods based on necessary conditions
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