In this paper, we consider a class of nonlinear optimal control problems subject to control constraints. We assume that an initial condition for the dynamical system is specified. Then, we can easily compute an open-loop optimal control using the software MISER3. Now, suppose the optimal trajectory is perturbed due to a change in initial conditions or uncertainty in the model equations. If the perturbations are not too large, it is known that the neighbouring extremal approach can be used to obtain a feedback law which adjusts the open-loop optimal control accordingly provided there are no bounds on the control variables. In this paper, our aim is to develop a computational method for the more general case of fixed-time problems with control constraints.

Key Words. Nonlinear systems control, neighbouring extremals, feedback controller, control constraints.

1 -- Fisher, M.E., Grantham, W.J., and Teo, K.L., ``Neighboring Extremals for Nonlinear Systems with Control Constraints," Dynamics and Control, Vol. 5, No. 3, July 1995, pp. 225-240.
2 -- Work partially supported by a research grant from the Australian Research Council.
3 -- Department of Mathematics, The University of Western Australia, Nedlands, Western Australia 6009, Australia.
4 -- Department of Mechanical and Materials Engineering, Washington State University, Pullman, Washington 99164-2920, USA.

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