Optimal control trajectories with minimax objective functions by linear programming

A standard linear programming code may be used to compute optimal trajectories for a linear discrete-time system with respect to a minimax criterion on either state or control trajectories. Arbitrary linear constraints, equality or inequality, constant or time-varying, may be placed on linear combinations of the state or control variables along their trajectories or at a fixed terminal time. An important feature of the method is that the dimension of the linear programming problem is independent of the dimension of the state space but depends entirely on the numbers of control variables, constraints, and time intervals. Optimal trajectories for a 21st- order system have been calculated in a few minutes of computer time.