By Nikolai Michailovich Filatov, Heinz Unbehauen

This monograph demonstrates how the functionality of varied recognized adaptive controllers should be superior considerably utilizing the twin impact. The ameliorations to include twin keep an eye on are learned individually and independently of the most adaptive controller with out complicating the algorithms. a brand new bicriterial strategy for twin keep watch over is built and utilized to varied different types of renowned linear and nonlinear adaptive controllers. sensible purposes of the designed controllers to numerous real-time difficulties are offered. This monograph is the 1st publication supplying an entire exposition at the twin regulate challenge from the inception within the early Sixties to the current cutting-edge aiming at scholars and researchers in adaptive keep watch over in addition to layout engineers in undefined.

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4. Implicit Dual Control The implicit dual control methods are based on various approximations that still maintain the dual properties of the system and are generally complex. Some of them, for example, the original dual control problem, are even unsolvable in spite of the approximations. , N-k-1, only incomplete information ℑk +i from future measurements will be used. 5. , u(0)} , y (⋅) is the partial observation vector that does not contain all the elements of y(⋅) and has dimension ny ≤ ny .

The vari- ous suboptimal stochastic adaptive control approaches are based on different approximations ρk (ρ-approximations) in eq. 10), as shown below: u For the open-loop (OL) control policy, the system is assumed to be without feedback, and the optimal control is found from a priori information about the system parameters and states. This simplifying assumption is equivalent to the following approximation of the probability densities for eq. , u(N-1)} for this case. u To find the control input for the known open-loop feedback (OLF) control policy, the system is assumed to be without feedback in the future steps (from time k+1 to N), but with feedback at time k.

3. 4. Classification of adaptive controllers of type III (The bicriterial approach allows the design of dual versions of all type III controllers. 2. Dual Effect and Neutral Systems An example of a system where the dual effect cannot appear is considered below. 2), c is an unknown parameter with the initial estimate cˆ(0) and variance of the estimate P(0), and the disturbance ξ (k ) has the properties as in eq. 8). This simplified model is an integrator with an unknown additive parameter. 2. Dual Effect and Neutral Systems for control optimization, eq.

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