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.


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


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