Abstract
The use of first order necessary conditions to solve optimal control problems has two principal drawbacks: a sufficiently close initial approximation is required to ensure local convergence and this initial approximation must be cHosen so that the convergence is to a local optimum. We present a class of algorithms which resolves both of these difficulties and which is ultimately based on the solution of first order necessary conditions. The key ingredients are three smooth penalty functions (the quadratic penalty for equality constraints and the log barrier or quadratic loss for inequality constraints), a parameterized system of nonlinear equations, and efficient predictor-corrector continuation techniques to follow the penalty path to optimality. This parameterized system of equations is essentially a homotopy which is derived from these penalty functions, contains the penalty path as a solution, and represents a perturbation of the first order necessary conditions. However, it differs significantly from Homotopies for nonlinear equations in that an unconstrained optimization technique is required to obtain an initial point.
This work was supported by the Air Force Office of Scientific Research through Grant #AFOSR-88-0059 and by the National Science Foundation through Grant #DMS-87-04679
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© 1989 Birkhäuser Boston
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Hasan, M., Lundberg, B.N., Poore, A.B., Yang, B. (1989). Numerical Optimal Control Via Smooth Penalty Functions. In: Computation and Control. Progress in Systems and Control Theory, vol 1. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-3704-4_7
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DOI: https://doi.org/10.1007/978-1-4612-3704-4_7
Publisher Name: Birkhäuser Boston
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