By Nikolai Michailovich Filatov, Heinz Unbehauen
This monograph demonstrates how the functionality of assorted recognized adaptive controllers might be greater considerably utilizing the twin influence. The changes to include twin keep watch over are discovered individually and independently of the most adaptive controller with no complicating the algorithms. a brand new bicriterial technique for twin regulate is constructed and utilized to varied kinds of renowned linear and nonlinear adaptive controllers. sensible functions of the designed controllers to a number of real-time difficulties are offered. This monograph is the 1st publication offering an entire exposition at the twin keep watch over challenge from the inception within the early Sixties to the current state-of-the-art aiming at scholars and researchers in adaptive keep watch over in addition to layout engineers in undefined.
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4. 7. Simulation results for the adaptive controller based on the CE assumption Upper and lower limits of ±500 are used for the control signal. The controller based on the CE assumption can be obtained from eq. 61), with P(k) set to 0. 8. 9. The simulation results for the GDC according to eq. 5 are shown in Fig. 10. 10, the adaptive dual controller provides better control 4. BICRITERIAL SYNTHESIS METHOD FOR DUAL CONTROLLERS 48 performanc and a smaller overshoot. The control of the same plant with a larger time delay is considered in the next section.
N − k − 1} . 12) In the case of the approximate assumption described by eq. 12), the system is designed with feedback, but at every time instant k the OLF control policy is calculated. It is known that the OLF control policy provides a superior control performance compared with the OL control using the ρ-approximation from eq. 11) (Bertsekas, 1976). u The well-known and generally used CE approach can also be interpreted in terms of the ρ -approximation. For the considered control problem the ρ-approximation (Filatov and Unbehauen, 1995b) of the probability densities for the performance index according to eq.
1. The parameters correspond to the parameters of the model, according to eqs. 5). 2. 001I . 3 obtained by the linear estimator, according to eqs. 9). 4. 1. 2. 2. 3. 2. 3, the bicriterial approach is based on the minimization of two cost functions, which correspond to the two control goals of dual control. 4. First, the control losses J kc are mini- mized, and the result is the cautious control action uc (k ) . Then the second cost function J ka is minimized in the domain Ω k around the cautious control.