ISSN:
1573-2878
Keywords:
Optimal control
;
mixed control-state constraints
;
Hamilton-Jacobi inequality
;
second-order sufficient conditions
;
parametric optimization
;
Riccati equations
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract References 1–4 develop second-order sufficient conditions for local minima of optimal control problems with state and control constraints. These second-order conditions tighten the gap between necessary and sufficient conditions by evaluating a positive-definiteness criterion on the tangent space of the active constraints. The purpose of this paper is twofold. First, we extend the methods in Refs. 3, 4 and include general boundary conditions. Then, we relate the approach to the two-norm approach developed in Ref. 5. A direct sufficiency criterion is based on a quadratic function that satisfies a Hamilton-Jacobi inequality. A specific form of such a function is obtained by applying the second-order sufficient conditions to a parametric optimization problem. The resulting second-order positive-definiteness conditions can be verified by solving Riccati equations.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF02192163
