Indirect model reference adaptive control with dynamic adjustment of parameters

Abstract

SUMMARYThe paper discusses in detail a new method for indirect model reference adaptive control (MRAC) of linear time-invariant continuous-time plants with unknown parameters. The method involves not only dynamic adjustment of plant parameter estimates but also those of the controller parameters. Hence the overall system can be described by a set of non-linear differential equations as in the case of direct control. Many of the difficulties encountered in the conventional indirect approach, where an algebraic equation is solved to determine the control parameters, are consequently bypassed in this method.The proof of stability of the equilibrium state of the overall system is found to be different from that used in direct control. Using Lyapunov's theory, it is first shown that the parameter errors between the parameter estimates of the identifier and the true parameters of the plant, as well as those between the actual parameters of the controller and their desired values, are bounded. Following this, using growth rates of signals in the adaptive loop as well as order arguments, it is shown that the error equations are globally uniformly stable and that the tracking (control) error tends to zero asymptotically. This in turn establishes the fact that both direct and indirect model reference adaptive schemes require the same amount of prior information to achieve stable adaptive control.KEY WORDS model reference adaptive control; indirect adaptive control; dynamic adaptive control; robust adaptive control

Adaptive Output Tracking Control of Piecewise Affine Systems With Prescribed Performance

“…To solve this singularity problem, we use the dynamic gain adjustment technique in this work. This concept is originally introduced by [37] and extended to MRAC of PWA systems in [12]. We extend this method to the context of adaptive control of PWA systems with prescribed performance.…”

Adaptive Output Tracking Control of Piecewise Affine Systems With Prescribed Performance

“…To solve this singularity problem, we use the dynamic gain adjustment technique in this work. This concept is originally introduced by [37] and extended to MRAC of PWA systems in [12]. We extend this method to the context of adaptive control of PWA systems with prescribed performance.…”

Adaptive robust H∞ state feedback control for linear uncertain systems with time‐varying delay

“…then, under controller (20) with K 00 = Y 00 X −T , F 00 = W 00 X −T , system (1) with controller (20) is…”

“…Here, the disturbance (t) = [ 1 (t) 2 (t)] T that is used is (4) and robust H ∞ controller with fixed gains (20), respectively. It is easy to see that our adaptive robust H ∞ controller has more disturbance attenuation ability than that of the robust H ∞ controller with fixed gains as theory has proved.…”

Similar model reference adaptive control with bounded control effort

“…For instance in [3], an MRAC with a low-order controller is derived in such a way that the asymptotic error is made arbitrarily small. Another approach related to the adaptive controller adjustment is presented in [4] in which the controller parameters are not only updated by the identified parameters (i.e. indirect control) but are also updated in a direct way.…”

Adaptive Output Tracking Control of Piecewise Affine Systems With Prescribed Performance

“…To solve this singularity problem, we use the dynamic gain adjustment technique in this work. This concept is originally introduced by [37] and extended to MRAC of PWA systems in [12]. We extend this method to the context of adaptive control of PWA systems with prescribed performance.…”

Adaptive robust H∞ state feedback control for linear uncertain systems with time‐varying delay

“…then, under controller (20) with K 00 = Y 00 X −T , F 00 = W 00 X −T , system (1) with controller (20) is…”

“…Here, the disturbance (t) = [ 1 (t) 2 (t)] T that is used is (4) and robust H ∞ controller with fixed gains (20), respectively. It is easy to see that our adaptive robust H ∞ controller has more disturbance attenuation ability than that of the robust H ∞ controller with fixed gains as theory has proved.…”

Similar model reference adaptive control with bounded control effort

“…For instance in [3], an MRAC with a low-order controller is derived in such a way that the asymptotic error is made arbitrarily small. Another approach related to the adaptive controller adjustment is presented in [4] in which the controller parameters are not only updated by the identified parameters (i.e. indirect control) but are also updated in a direct way.…”

Adaptive Output Tracking Control of Piecewise Affine Systems With Prescribed Performance

“…To solve this singularity problem, we use the dynamic gain adjustment technique in this work. This concept is originally introduced by [37] and extended to MRAC of PWA systems in [12]. We extend this method to the context of adaptive control of PWA systems with prescribed performance.…”

Adaptive robust H∞ state feedback control for linear uncertain systems with time‐varying delay

“…then, under controller (20) with K 00 = Y 00 X −T , F 00 = W 00 X −T , system (1) with controller (20) is…”

“…Here, the disturbance (t) = [ 1 (t) 2 (t)] T that is used is (4) and robust H ∞ controller with fixed gains (20), respectively. It is easy to see that our adaptive robust H ∞ controller has more disturbance attenuation ability than that of the robust H ∞ controller with fixed gains as theory has proved.…”

Similar model reference adaptive control with bounded control effort

“…For instance in [3], an MRAC with a low-order controller is derived in such a way that the asymptotic error is made arbitrarily small. Another approach related to the adaptive controller adjustment is presented in [4] in which the controller parameters are not only updated by the identified parameters (i.e. indirect control) but are also updated in a direct way.…”