Now the problem becomes an optimal regulator problem of system (18) under the performance index (19).
Then we can use the method for single-rate systems to study the optimal regulator problem of the lifted system.
This guide introduces geometric control design methodologies for asymptotic tracking and disturbance rejection of infinite-dimensional systems governed by partial differential equations, focusing on the state feedback regulator problem
, in which the controller is provided with full information on the state of the control system and exosystem.
Section 3 presents the SDRE finite-horizon regulator problem. In Section 4, the finite-horizon tracking problem is discussed.
The summary of the nonlinear regulator problem is shown in Figure 3, and the overview of the process of finite-horizon SDDRE regulation technique for stochastic systems is summarized in Figure 4.
The entire algorithm of combined estimation and control leading to the nonlinear regulator problem is shown in the following steps.
Consider a fixed target; in this case the desired seeker angle will be z(t) = 0[degrees]; that is, the problem is now a regulator problem.
Figure 8 shows that the finite-horizon differential SDRE nonlinear regulating algorithm gives excellent results and the developed technique is able to solve the differential SDRE finite-horizon nonlinear regulator problem with a zero average error and 0.003[degrees] standard deviation.
We add to the regulator problem the participation constraint for the bank.
Therefore, we can use the optimal values found in (23) and (22) to rewrite the regulator problem as
Transforming the tracking problem into optimal regulator problem
using equations (1) and (2) we get new augmented system in the state space as follows:
With increased challenges to natural gas utilities from deregulation, downsizing and the pressures of marketplace economics, utilities are seeking more cost-effective solutions to recurring regulator problems
such as shutoff, boot erosion and excessive noise.