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State-control spectral Chebyshev parameterization for linearly constrained quadratic optimal control problems. (English) Zbl 0871.65054

For linearly constrained quadratic optimal control problems of the form: Maximize or Minimize

J=1 2x T (t f )H(x(t f )+h T x(t f )+1 2 0 t f x T (t)Q(t)x(t)+u T (t)R(t)u(t)++x T (t)S(t)u(t)+q T (t)x(t)+r T (t)u(t))dt

subject to x ˙(t)=A(t)x(t)+B(t)u(t), t[0,t f ], and x(0)=x 0 , E 1 (t)x(t)+E 2 (t)u(t)e(t), the author gives a direct computational method, which is based on a cell averaging method in which the mth degree interpolating polynomial is constructed, using Chebyshev nodes. The given problem is thereby transformed into a quadratic programming one. Illustrative examples are given.

65K10Optimization techniques (numerical methods)
49M37Methods of nonlinear programming type in calculus of variations
49K15Optimal control problems with ODE (optimality conditions)