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Bin Li Chang Jun Yu Kok Lay Teo Guang Ren Duan 《Journal of Optimization Theory and Applications》2011,151(2):260-291
In this paper, we consider a class of optimal control problems subject to equality terminal state constraints and continuous
state and control inequality constraints. By using the control parametrization technique and a time scaling transformation,
the constrained optimal control problem is approximated by a sequence of optimal parameter selection problems with equality
terminal state constraints and continuous state inequality constraints. Each of these constrained optimal parameter selection
problems can be regarded as an optimization problem subject to equality constraints and continuous inequality constraints.
On this basis, an exact penalty function method is used to devise a computational method to solve these optimization problems
with equality constraints and continuous inequality constraints. The main idea is to augment the exact penalty function constructed
from the equality constraints and continuous inequality constraints to the objective function, forming a new one. This gives
rise to a sequence of unconstrained optimization problems. It is shown that, for sufficiently large penalty parameter value,
any local minimizer of the unconstrained optimization problem is a local minimizer of the optimization problem with equality
constraints and continuous inequality constraints. The convergent properties of the optimal parameter selection problems with
equality constraints and continuous inequality constraints to the original optimal control problem are also discussed. For
illustration, three examples are solved showing the effectiveness and applicability of the approach proposed. 相似文献
445.
Canghua Jiang Qun Lin Changjun Yu Kok Lay Teo Guang-Ren Duan 《Journal of Optimization Theory and Applications》2012,154(1):30-53
In this paper, we consider a class of optimal control problems with free terminal time and continuous inequality constraints. First, the problem is approximated by representing the control function as a piecewise-constant function. Then the continuous inequality constraints are transformed into terminal equality constraints for an auxiliary differential system. After these two steps, we transform the constrained optimization problem into a penalized problem with only box constraints on the decision variables using a novel exact penalty function. This penalized problem is then solved by a gradient-based optimization technique. Theoretical analysis proves that this penalty function has continuous derivatives, and for a sufficiently large and finite penalty parameter, its local minimizer is feasible in the sense that the continuous inequality constraints are satisfied. Furthermore, this local minimizer is also the local minimizer of the constrained problem. Numerical simulations on the range maximization for a hypersonic vehicle reentering the atmosphere subject to a heating constraint demonstrate the effectiveness of our method. 相似文献
446.
There are many reports1 of the pyrolysis of fluorinated organic compounds, including the defluorination of cyclic fluorocarbons over iron to give aromatic compounds. Extending this technique we have investigated the flow pyrolysis of some readily accessible unsaturated fluorocarbons, such as I, II, and III, and found these to be synthetically useful routes to fluorinated dienes, cyclobutenes, and furans. Pyrolyses were carried out using a nitrogen flow over platinum, iron or caesium fluoride heated at 430–700°. The various products can all be rationalized in terms of intermediate allylic radicals, and the solid substrate influences which allylic radicals are formed.We are also investigating the chemistry of those now accessible compounds, such as IV, V, and VI, and some of the preliminary results are described. For example the fluoride ion induced dimerisation of IV gave two major products VII and VIII via a particular interesting mechanism. 相似文献