A Pseudospectral Method for the Optimal Control of Constrained Feedback Linearizable Systems
Ross, I. Michael
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We consider the optimal control of feedback linearizable dynamical systems subject to mixed state and control constraints. In general, a linearizing feedback control does not minimize the cost function. Such problems arise frequently in astronautical applications where stringent performance requirements demand optimality over feedback linearizing controls. In this paper, we consider a pseudospectral (PS) method to compute optimal controls. We prove that a sequence of solutions to the PS-discretized constrained problem converges to the optimal solution of the continuous-time optimal control problem under mild and numerically verifiable conditions. The spectral coefficients of the state trajectories provide a practical method to verify the convergence of the computed solution. The proposed ideas are illustrated by several numerical examples.
The article of record as published may be located at http://ieeexplore.ieee.orgIEEE Transactions on Automatic Control, v. 51, no. 7 (2006 : July)
RightsThis publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.
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Ross, I.M. (Elsevier, 2019);The Karush–Kuhn–Tucker conditions for a given nonlinear programming problem are generated as the transversality conditions of an optimal control problem. The directional derivatives of the objective- and constraint-functions ...
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