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Costate approximation in optimal control using integral Gaussian quadrature orthogonal collocation methods
| Content Provider | Semantic Scholar |
|---|---|
| Author | Francolin, Camila |
| Copyright Year | 2014 |
| Abstract | Two methods are presented for approximating the costate of optimal control problems in integral form using orthogonal collocation at Legendre-Gauss and Legendre-Gauss-Radau points. It is shown that the derivative of the costate of the continuous-time optimal control problem is equal to the negative of the costate of the integral form of the continuous-time optimal control problem. Using this continuous-time relationship between the differential and integral costate, it is shown that the discrete approximations of the differential costate using Legendre-Gauss and Legendre-Gauss-Radau collocation are related to the corresponding discrete approximations of the integral costate via integration matrices. The approach developed in this paper provides a way to approximate the costate of the original optimal control problem using the Lagrange multipliers of the integral form of the Legendre-Gauss and Legendre-Gauss-Radau collocation methods. The methods are demonstrated on two examples where it is shown that both the differential and integral costate converge exponentially as a function of the number of Legendre-Gauss or Legendre-Gauss-Radau points. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://vdol.mae.ufl.edu/JournalPublications/OCAM-13-0174.pdf |
| Alternate Webpage(s) | http://users.clas.ufl.edu/hager/papers/Control/Integral.pdf |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Approximation algorithm Collocation method Converge Dual First-order predicate Gauss Gaussian quadrature Lagrange multiplier Normal Statistical Distribution Optimal control Orthogonal collocation Polynomial Turing completeness |
| Content Type | Text |
| Resource Type | Article |
