Application of shifted Chebyshev series to the optimal control of linear distributed-parameter systems

By use of a particular property of the shifted Chebyshev series, the optimal control of a distributed-parameter system is simplified into the optimal control of a linear time-invariant lumped-parameter system. Next, a directly computational formulation for evaluating the optimal control and trajectory of a linear distributed-parameter system is developed. The formulation is straightforward, and convenient for digital computation. An illustrative example is given to demonstrate the applicability of the proposed method