New approach to the optimal control of time-varying linear systems via Chebyshev series

The general expression of the shifted Chebyshev series approximation for any two arbitrary functions has been presented by Chou and Horng (1985 a). The expression is recursive and useful in time-varying and non-linear systems. Due to the property, the design of gains for the time-varying optimal control system with a quadratic performance measure is studied by directly solving the Riccati equation in this paper. The method considered is much simpler than other design techniques. An example is illustrated. Only a small number, m = 4, of Chebyshev series is needed to produce a satisfactory outcome.