A Chebyshev approximation for solving optimal control problems (Q1842818)

The paper deals with an optimal control problem governed by an initial value problem \(dx/ dt= f(t, x, u)\) for \(t\in [- 1,1]\) and \(x(-1)= x_0\). The cost functional is of the form \(I(x, u)= \int^1_{-1} g(t, x, u)dt+ h(x (1))\). The Chebyshev spectral approximation of both \(x\) and \(u\) reduces the original problem to a finite-dimensional nonlinearly constrained mathematical programming problem. Numerical results of model examples, in particular of the controlled Duffing oscillator, are presented and compared with other methods.