A Simultaneous Adaptation Law for a Class of Nonlinearly Parametrized Switched Systems

Abstract

This paper proposes a new adaptive control method for a class of nonlinearly-parametrized switched systems that includes Monod kinetics and Euler-Lagrange systems with nonlinear in parameters form as special cases. As compared to the adaptive switched frameworks proposed in literature, the proposed adaptation framework has the distinguishing feature of updating the gains of the active and inactive subsystems simultaneously: by doing this it avoids high gains for the active subsystems, or vanishing gains for the inactive ones. The design is studied analytically and its performance is validated in simulation with a robotic manipulator example.

Nonsmooth Current-Constrained Control for a DC–DC Synchronous Buck Converter with Disturbances via Finite-Time-Convergent Extended State Observers

“…The feasibility of the proposed method has been verified by experimental results. Since it is still a difficult work to define a prior uncertainty bound in the actual converter system, this will be the focus of our future research [39][40][41].…”

Overcoming the Underestimation and Overestimation Problems in Adaptive Sliding Mode Control

“…The initial condition of the gains are selected aŝ θ i (t 0 ) > 0. Note that the first adaptive law in (11) forces the gains to increase if at least one gain tends to go negative (i.e., (…”

“…The integral of a piecewise continuous function over a finite duration is finite [36]. Sinceθ i is piecewise continuous (from (11)) and gains only increase for finite time uptot ,θ i 's remain finite and thus bounded for Case (3). For ||s|| < , system remains bounded inside the ball B {b : b = ||Γξ|| < } as s = Γξ.…”

“…Remark 5. The proposed stability result does not impose any restriction on the choice of the scalars α i and α i in (11) as long as they are positive. However, proper tuning might be beneficial to performance balance, as these parameters decide the adaptation rates for the switching gainsθ i leading to a trade off between tracking accuracy (high gain) and reduced control effort (low gain).…”

“…A considerable amount of research has been carried out recently on various adaptive-robust control designs (comprising neural network-based designs [1]- [3], switched-based designs [4]- [11], functional observer-based designs [12], [13], time delay-based designs [14]- [16] etc.). Adaptive-robust control aims at reducing structural knowledge of the system like conventional adaptive control, while being intrinsically robust to bounded uncertainties.…”