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We consider optimal control of a bilinear parabolic equation. The determination of such control requires to minimize a given energy performance measure. The performance measure of the system is taken as a combination of its modified total energy and the penalty term describing the approach used in the control process. Using an appropriate transformation modal expansion, the optimal control of a distributed parameter system (DPS) is simplified into the optimal control of a bilinear time-varying lumped parameter system (LPS). A computational efficient formulation to evaluate the optimal trajectory and control of the system is determined. It is based on the parametrization of the state and control variables by using finite wavelets. Numerical examples are provided to demonstrate the applicability and the efficiency of the proposed method and the results are quite satisfactory.
We consider optimal control of a bilinear parabolic equation. The determination of such control requires to minimize a given energy performance measure. The performance measure of the system is taken as a combination of its modified total energy and the penalty term describing the approach used in the control process. Using an appropriate transformation modal expansion, the optimal control of a distributed parameter system (DPS) is simplified into the optimal control of a bilinear time-varying lumped parameter system (LPS). A computational efficient formulation to evaluate the optimal trajectory and control of the system is determined. It is based on the parametrization of the state and control variables by using finite wavelets. Numerical examples are provided by demonstrate the applicability and the efficiency of the proposed method and the results are quite satisfactory.