Solution of finite-time optimal control problems with mixed end constraints in the s-domain

The solution of linear quadratic optimal control problems having mixed end conditions is considered. The plant is assumed to be linear, time invariant, and multivariable, and the cost function is quadratic, and defined over a Finite time interval. At the terminal time some of the system responses are required to achieve desired values and the remaining responses are free. The solution in the
s
-domain is more direct than previous methods and simple problems can be solved by hand calculations. Open- and clused-loop solutions can be determined and the method enables new insight to be gained into the relationship between the fixed and free end-point control problems.