Adaptive controller of nonlinear systems with unknown control directions and unknown input powers

Abstract

This article is devoted to global adaptive stabilization for a class of uncertain nonlinear systems. Notably, the systems under investigation admit unknown control directions and unknown input powers, and particularly the latter, which are a new type of system uncertainties, largely challenge the feasibility of continuous feedbacks. This spurs us to pursue a switching adaptive feedback which is actual a discontinuous one with high feedback capability. To solve the control problem, a parameterized controller in a specified form is first introduced, which can globally stabilize the system once the design parameter involved belongs to a certain set. However, the controller cannot directly be implemented since the set depends heavily on the unknown input powers. To make the parameterized controller implementable, a new switching strategy is delicately proposed, which can instantly update the parameters of the controller to compensate the serious system uncertainties. It turns out that the parameterized controller with switching updating mechanism guarantees that all the signals of the closed-loop system are globally bounded and ultimately converge to zero. Simulation examples demonstrate the effectiveness of the proposed design scheme. K E Y W O R D S adaptive controller, global stabilization, nonlinear systems, switching scheme, unknown control directions, unknown input powers ∈ R + : m 1 and m 2 are odd integers, m 1 ≥ m 2 }; unknown nonzero constants g i 's, called the control coefficients of the system, give rise to the unknown control directions for the system (due to their unknown signs).

Adaptive global prescribed performance tracking control of uncertain robotic systems with unknown control directions

“…Remark Compared with the design of SISO nonlinear systems (i.e., References 9,23,27‐30,39, to just name a few), the control of MIMO robotic systems with unknown control directions is rather challenging and difficult, which is shown in the following aspects: The control design and stability analysis of MIMO robotic systems in this article are much more complicated than that of SISO nonlinear systems. This is because MIMO system with unknown and time‐varying control gain matrix exhibits strong coupling relationship among the control inputs, which is the major source of challenge and complexity in control design, and unknown and time‐varying control gain matrix makes the control inputs enter into and impact on the system in an unknown/uncertain way; Due to the MIMO nature of the robotic systems considered, the normally used commutative law for scalar multiplication involved in SISO systems does not apply to matrix multiplication encountered in MIMO systems.…”

“…This has been one of the motivations for inventing “Nussbaum Function”, 25 based on which a Nussbaum Lemma dealing with the problem of unknown control direction was proposed in Reference 26. Since then Nussbaum gain technique has been extensively utilized for coping with the unknown control direction under various settings (References 27‐30, to just name a few).…”

Dynamic event‐triggered control for a class of p‐normal nonlinear time‐delay systems via output feedback

“…It should be noted that many results have been obtained based on state feedback control. [1][2][3][4] However, in many practical systems, state variables are unmeasurable or only partially available. Hence, the output-feedback control has become a hot research spot in the control community.…”

“…In recent years, various control issues of nonlinear systems have attracted great attention. Many significant results on nonlinear systems have been obtained (see References 1‐14 and the references therein). It should be noted that many results have been obtained based on state feedback control 1‐4 .…”

“…Many significant results on nonlinear systems have been obtained (see References 1‐14 and the references therein). It should be noted that many results have been obtained based on state feedback control 1‐4 . However, in many practical systems, state variables are unmeasurable or only partially available.…”