Artificial Delay Based ARC of a Class of Uncertain EL Systems with Only Position Feedback

In this paper, the tracking control problem of an Euler-Lagrange system is addressed with regard to parametric uncertainties, and an adaptive-robust control strategy, christened Time-Delayed Adaptive Robust Control (TARC), is presented. TARC approximates the unknown dynamics through the time-delayed estimation, and the adaptive-robust control provides robustness against the approximation error. The novel adaptation law of TARC, in contrast to the conventional adaptive-robust control methodologies, requires neither complete model of the system nor any knowledge of predefined uncertainty bounds to compute the switching gain, and circumvents the over- and underestimation problems of the switching gain. Moreover, TARC only utilizes position feedback and approximates the velocity and acceleration terms from the past position data. The adopted state-derivatives estimation method in TARC avoids any explicit requirement of external low pass filters for the removal of measurement noise. A new stability notion in continuous-time domain is proposed considering the time delay, adaptive law, and state-derivatives estimation which in turn provides a selection criterion for gains and sampling interval of the controller

A Novel Sliding Mode Control for a Class of Affine Dynamic Systems

This paper proposes a novel sliding mode control (SMC) method for a class of affine dynamic systems. In this type of systems, the high-frequency gain matrix (HFGM), which is the matrix multiplying the control vector in the dynamic equation of the sliding variables vector, is neither deterministic nor positive definite. This case has rarely been covered by general SMC methods, which perform well under the condition that the HFGM is certain or uncertain but positive definite. In this study, the control law is determined by solving a nonlinear vector equation instead of the conventional algebraic expression, which is not applicable when the HFGM is uncertain and non-positive definite. Theorems with some relaxed system parametric uncertainty assumptions are proposed to guarantee the existence and uniqueness of the solution, and proofs of them, based on the principle of the convex cone set, are given in the text. The proposed control strategy can be easily applied in practice, and the chattering caused by the discontinuous control can be suppressed, as it can in general SMCs. The proposed controller was used in two affine dynamic systems, and the simulation results demonstrate its effectiveness