Page 37 - Neural Network Modeling and Identification of Dynamical Systems

1.2 DYNAMICAL SYSTEMS AND THE PROBLEM OF ADAPTABILITY 25

FIGURE 1.2 Theschemefor adjustingthe parameters of
FIGURE 1.1 Scheme of a system with an adjustable con- the control law implemented by the controller in accordance
trol law implemented by the controller: r(t) is the reference with the GS scheme: r(t) is the reference signal; u(t) is the
signal; u(t) is the control; y(t) is the output of the controlled control; y(t) is the output of the controlled object; ξ(t) is the
object (plant); ξ(t) is the adjusting effect for the controller; adjusting effect for the controller; ψ(λ), λ ∈ is additional
ψ(λ), λ ∈ is additional information that should be taken information used to produce the adjusting action. From [56],
into account when developing an adjusting action (for ex- used with permission from Moscow Aviation Institute.
ample, the speed and altitude of an aircraft in the problem
of controlling its angular motion).
fects ξ as a function of ψ(λ) must be computed
in advance (off-line). Then, this function remains
the state of the system is used not only to gen- unchanged during the control process. In the
erate a control action (as is the case of non- full version of the adaptation scheme, the ad-
adaptive systems), but also to change (adjust) justment algorithm operates on-line during the
the control algorithm. In general, the structure operation of the system, taking into account not
of the adaptive system can be represented as only external data but other information con-
showninFig. 1.1. We can see that the adjust- cerning the state of the controlled object.
ing action ξ(t) for the controller is generated Despite the limited adaptation capabilities of
using an adaptation mechanism. This mecha- the GS approach, it is used often in practice.
nism uses as its inputs such signals as control For example, this approach was applied for con-
u(t), the output of the object y(t),and some trol of test flights for the experimental hyper-
additional (“external”) information ψ(λ), λ ∈ . sonic vehicle X-43A [55]. Gains in the longitudi-
We need to take these data into account in the nal control law of this vehicle are scheduled with
development of an adjusting action. For exam- the angle of attack and Mach number as “exter-
ple, in the problem of controlling the angular nal data” mentioned above.
motion of an aircraft, the composition of these Adaptive control schemes are usually di-
data can include the airspeed and altitude of vided into two main types: direct adaptive con-
flight. trol and indirect adaptive control.
Various types of this scheme are possible, dif- Direct adaptive control schemes are often
fering from each other by the composition of based on the use of some reference model (RM)
the input data used to generate the adjusting that specifies the required (desired) behavior
action ξ(t). One such option is that the adjust- of the system under consideration. 25 The struc-
ment is performed only based on the “external”
data ψ(λ), λ ∈ ; it is referred to as the Gain
25 The purpose of the control is to make the dynamical sys-
Scheduling (GS) approach. The principal differ-
tem behavior as close as possible to the behavior defined by
ence of this approach (Fig. 1.2) from the full ver-
the reference model. The correction of the control goal men-
sion of the adaptation scheme (Fig. 1.1)isthat tioned in Section 1.1.1.1 canbecarried outinthiscaseby
in the GS approach the values of adjusting ef- replacing one reference model with another.