Robustness of a class of three-dimensional curve tracking control laws under time delays and polygonal state constraints

Abstract

We analyze the robustness of a class of controllers that enable three-dimensional curve tracking of free moving particles. By building a strict Lyapunov function and robustly forwardly invariant sets, we show input-to-state stability under predictable tolerance and safety bounds that guarantee robustness under control uncertainty, input delays, and a class of polygonal state constraints. Such understanding may provide certified performance when the control laws are applied to real life systems. We demonstrate our findings in simulations.

Predictor-Feedback Stabilization of Multi-Input Nonlinear Systems

“…Such systems serve as models for the dynamics of traffic [22], [47], teleoperators [24] and robotic manipulators [2], [20], motors [34], [50], multi-agent systems [1], [18], [40], autonomous ground vehicles [39], unmanned aerial vehicles [23] and planar vertical take-off and landing aircrafts [21], [48], and the human musculoskeletal system in applications such as neuromuscular electrical stimulation [32], [38], [51], to name only a few. Motivated by the negative effects of input delays on the stability and performance of such control systems, in this article we present control designs that achieve delay compensation.…”

An adaptive control design for 3D curve tracking based on robust forward invariance

“…This note gives 3D, input delayed analogs of our adaptive robust curve tracking and parameter identification work [8], which was limited to adaptive 2D dynamics without delays. Our main tools are our recent strict Lyapunov function and robust forward invariant approaches for nonadaptive 3D curve tracking systems from [9], combined with a new construction of Lyapunov-Krasovskii functionals.…”

“…For the much simpler case of 2D adaptive dynamics, or for 3D nonadaptive dynamics, our Lyapunov and robust forward invariance set (RFIS) approaches from [6], [9] involved decomposing the state space into a nested sequence S 1 ⊆ S 2 ⊆ S 3 ⊆ . .…”

“…Although this note owes a lot to [9], extending [6], [8], [9] to 3D adaptive curve tracking and control gain identification under delays is challenging. We review the background from [9] in the next section.…”

Predictor-feedback stabilization of multi-input nonlinear systems

“…Such systems serve as models for the dynamics of traffic [22], [47], teleoperators [24] and robotic manipulators [2], [20], motors [34], [50], multi-agent systems [1], [18], [40], autonomous ground vehicles [39], unmanned aerial vehicles [23] and planar vertical take-off and landing aircrafts [21], [48], and the human musculoskeletal system in applications such as neuromuscular electrical stimulation [32], [38], [51], to name only a few. Motivated by the negative effects of input delays on the stability and performance of such control systems, in this article we present control designs that achieve delay compensation.…”