A collocation-type method for linear quadratic optimal control problems. (English) Zbl 0873.49023
Summary: This communication presents a spectral method for solving time-varying linear quadratic optimal control problems. Legendre-Gauss-Lobatto nodes are used to construct the \(m\)th-degree polynomial approximation of the state and control variables. The derivative \(\dot{\mathbf x}(t)\) of the state vector \({\mathbf x}(t)\) is approximated by the analytic derivative of the corresponding interpolating polynomial. The performance index approximation is based on Gauss-Lobatto integration. The optimal control problem is then transformed into a linear programming problem. The proposed technique is easy to implement, efficient and yields accurate results. Numerical examples are included and a comparison is made with an existing result.
MSC:
| 49N10 | Linear-quadratic optimal control problems |
| 65M70 | Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs |
| 90C05 | Linear programming |
Keywords:
collocation; time-varying linear quadratic optimal control problems; Legendre-Gauss-Lobatto nodes; Gauss-Lobatto integration; linear programming problemReferences:
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