Analytical computation of differential equations involved in dynamical nonlinear optimal problems. (English) Zbl 0891.70001
Summary: We present two programs, written in Reduce, for non-constrained free endpoint nonlinear dynamical optimal problems, in fixed time, in closed loop and in open loop, which compute analytically the optimal feedback laws in terms of differential equations. The open loop case leads to ordinary differential equations, and the closed loop leads to partial differential equations. In the case of closed loop problems, the program uses nonstandard Reduce programming for the declarations of dependencies of \(u\) and its partial derivatives. Algorithms are presented for the open loop and closed loop cases, and the same example is computed in both these cases.
MSC:
| 70-08 | Computational methods for problems pertaining to mechanics of particles and systems |
| 70Q05 | Control of mechanical systems |
| 70-04 | Software, source code, etc. for problems pertaining to mechanics of particles and systems |
| 93-04 | Software, source code, etc. for problems pertaining to systems and control theory |
Keywords:
non-constrained free endpoint problem; Reduce; closed loop; open loop; optimal feedback lawsSoftware:
REDUCEReferences:
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