Compensation of plant variations in optimal control systems

Control of a linear plant, with bounded control input, may be implemented by constructing a control law generator which produces the optimal control as a function of the state variables. If the plant parameters differ from their nominal values, then maintaining optimal control by changing the control law generator is inconvenient since the control law is usually nonlinear. It is shown that in certain cases optimal control can be maintained without changing the control law generator. This is accomplished by using a linear transformation of state variables as the input to the control law generator. The variations of the plant are compensated for by changing the linear transformation. The conditions under which this is possible are established in this paper. The advantage of this system is that a change in a linear function is easier to implement than a change in a nonlinear function. It is shown how this system can be incorporated into an adaptive system which compensates for plant variations.