Adaptive control with predictable parameter convergence has remained a challenge for several decades. In the special case of set point adaptation, extremum seeking permits predictable parameter convergence by design. This is because persistency of excitation requirements are met by the sinusoidal perturbation that is part of the basic control design. Here we present results of extremum seeking ...

2. Direct Adaptive Control of Scalar Plant. Let us begin with a simple scalar adaptive system, ẋp(t) = apxp(t) + kpu(t) (1) where xp(t) ∈ R is the plant state, u(t) ∈ R is the control input, ap ∈ R is an unknown scalar and only the sign of kp ∈ R is known. For the direct adaptive controller we choose a reference model as ẋm(t) = amxm(t) + kmr(t)− l(x(t)− xm(t)). (2) All of the parameter above a...

This paper extends the conventional Model Reference Adaptive Control systems to fractional ones based on the theory of fractional calculus. A control law and an incommensurate fractional adaptation law are designed for the fractional plant and the fractional reference model. The stability and tracking convergence are analyzed using the frequency distributed fractional integrator model and Lyapu...

Intelligent systems may be viewed as a framework for solving the problems of nonlinear system control. The intelligence of the system in the nonlinear or changing environment is used to recognize in which environment the system currently resides and to service it appropriately. This paper presents a general methodology of adaptive control based on multiple models in fuzzy form to deal with plan...

– When using the Lyapunov synthesis approach to construct a stable fuzzy control system, one important way is to regard the fuzzy systems as approximators to approximate the unknown functions in the system to be controlled. Concerning the unknownness of the unknown functions, generally there are two cases: a completely unknown case, and a partly unknown case. However, most of the schemes presen...

The advantage of the Model Reference Adaptive Scheme is to establish robustness with respect to bounded disturbances and unmodeled dynamics. In the model reference adaptive system (MRAS), the desired index of performance is given by the reference model. The tracking error represents the deviation of the plant output from the desired trajectory. The adaptive control without having robustness pro...

Aderivative-free, delayedweight update law is developed formodel reference adaptive control of continuous-time uncertain systems, without assuming the existence of constant ideal weights. Using a Lyapunov–Krasovskii functional it is proven that the error dynamics are uniformly ultimately bounded, without the need for modification terms in the adaptive law. Estimates for the ultimate bound and t...

Over the few last years the idea of introducing fractional calculus and systems in adaptive control has found a great interest, for the benefit one can win in the performances given by such systems. In adaptive control, the dynamic behavior of the system is defined by a chosen reference model and an adaptation algorithm modifies the correction to minimize the process output error. In this work,...