On the convergence of nonlinear optimal control using pseudospectral methods for feedback linearizable systems
By Wei Kang, Qi Gong, I. Michael Ross, Fariba Fahroo. 2007
66 citations recorded by the source corpus.
We consider the optimal control of feedback linearizable dynamic systems subject to mixed state and control constraints. In contrast to the existing results, the optimal controller addressed in this paper is allowed to be discontinuous. This generalization requires a substantial modification to the existing convergence analysis in terms of both the framework as well as the notion of convergence around points of discontinuity. Although the nonlinear system is assumed to be feedback linearizable, the optimal control does not necessarily linearize the dynamics. Such problems frequently arise in astronautical applications where stringent performance requirements demand optimality over feedback linearizing controls. We prove that a sequence of solutions obtained using the Legendre pseudospectral method converges to the optimal solution of the continuous‐time problem under mild conditions. Published in 2007 by John Wiley & Sons, Ltd.
Subfields: Aerospace Engineering, Astronomy and Astrophysics
View Paper: https://www.semanticscholar.org/paper/8df6ec0dcada126121d8abcd54083e972f5952a9
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Citations in the corpus
- Rate of convergence for the Legendre pseudospectral optimal control of feedback linearizable systems (2010, methodology): “For the problem of convergence, some theorems were published in [14]; and then the results were generalized in [ 15 ] to problems with nonsmooth control.”
- A review of pseudospectral optimal control: From theory to flight (2012, unknown): “From Theorem 2, it can be argued [38, 42, 43, 47, 46] that the feasible set for Problem B N is nonempty and compact; hence, for any given N , an optimal solution t 7→ ( x ∗ N , u ∗ N ) exists because J N is continuous (over a compact domain).”