Regulating Constraint-Following Bound for Uncertain Mechanical Systems: An Indirect Control Approach

Abstract

This paper proposes an indirect approach of constraint-following control for mechanical systems with (possibly fast) time-varying uncertainty. It proposes to design controller for the system to render bounded constraint-following error. First, it prescribes a desired hard bound for the constraint-following error. The system is required to lie within the bound at all time. Second, the constraint-following error can eventually be sufficiently small. To accomplish this, the original system is transformed into a constructed system. Then a robust control for the constructed system is designed, with renders uniform boundedness and uniform ultimate boundedness, regardless of the uncertainty. It is further proven that when the constructed system is uniformly bounded and uniformly ultimately bounded, the constraint-following error of the original system stays within the predetermined bounded. In addition, it will become sufficiently small after a finite time. Therefore the desired bounded performance of the constraint-following error can be archived by the robust control. Since the control is not designed based on the original system, the approach is indirect.

Adaptive robust control of unmanned tracked vehicles for trajectory tracking based on constraint modeling and analysis

“…Thus, M( q, δ ,t) q + Ŝ( q, q, δ ,t) q + Ĝ( q, δ ,t) + F( q, q, δ ,t) = Td (27) is the coupled dynamics unmanned tracked vehicle model. Based on the above analysis, a more accurate dynamics model of the unmanned tracked vehicle is established, and its kinematic characteristics are considered in it.…”

“…However, when there are uncertainties in the system, it is essential to propose a new controller to solve more practical problems. Therefore, for the unmanned tank system (27) with uncertainties, the following analysis is performed.…”

“…2. Propose a control problem with trajectory tracking for the coupled unmanned tracked system (27). The original constraints are established and transferred into a problem of approximate constraint-following to slove by establishing the constraint-following error λ f (32).…”

Adaptive constraint‐following control for uncertain nonlinear mechanical systems with measurement error

“…1 In Lagrangian mechanics, the (holonomic or nonholonomic) constraints are applied to describe the system performance. 2,3 There are two kinds of constraint-following problems: the passive form and the servo form. 4 The passive form is to analyze what the Nature will do (the constraint force) to follow the constraints.…”

“…4,[16][17][18] In the case where the bound of uncertainties is known, Song et al, 17 based on the sliding mode approach, proposed a robust motion control scheme for mechanical systems subject to nonholonomic constraints. Sun et al 2 proposed a constraint-following control, which ensured a prescribed bound for the constraint-following error, based on a transformation approach. Yin et al 1 and Yu et al, 19 based on an uncertainty decomposition method, further extended the constraint-following control to consider underactuated mechanical system with mismatched uncertainty.…”