Global tracking for an underactuated ships with bounded feedback controllers

In this paper, we present a global state feedback tracking controller for underactuated surface marine vessels. This controller is based on saturated control inputs and, under an assumption on the reference trajectory, the closed-loop system is globally asymptotically stable (GAS). It has been designed using a 3 Degree of Freedom benchmark vessel model used in marine engineering. The main feature of our controller is the boundedness of the control inputs, which is an essential consideration in real life. In absence of velocity measurements, the controller works and remains stable with observers and can be used as an output feedback controller. Simulation results demonstrate the effectiveness of this method

О повышении качества отслеживания летательным аппаратом программной траектории

Отримано розв’язок задачі про підвищення якості відстежування літальним апаратом програмної траєкторії шляхом подачі в стежачу систему програмної траєкторії з певним випередженням. Істотно, що при даному підході не накладаються ті або інші умови на похідні програмного сигналу. Ефективність пропонованого алгоритму демонструється на прикладі відстежування літальним апаратом програмної траєкторії, яка не має похідних в деяких точках.A problem on improving the quality of tracking the program trajectory by aircraft is considered. This improvement is reached by feeding into a control system of the program trajectory the signal with certain advance. It is essential that this approach needs any conditions on differentiability of the program signal. An efficiency of proposed algorithm is demonstrated on an example of tracking by aircraft the program trajectory that has not derivatives in some points

Predictor-Feedback Stabilization of Multi-Input Nonlinear Systems

We develop a predictor-feedback control design for multi-input nonlinear systems with distinct input delays, of arbitrary length, in each individual input channel. Due to the fact that different input signals reach the plant at different time instants, the key design challenge, which we resolve, is the construction of the predictors of the plant's state over distinct prediction horizons such that the corresponding input delays are compensated. Global asymptotic stability of the closed-loop system is established by utilizing arguments based on Lyapunov functionals or estimates on solutions. We specialize our methodology to linear systems for which the predictor-feedback control laws are available explicitly and for which global exponential stability is achievable. A detailed example is provided dealing with the stabilization of the nonholonomic unicycle, subject to two different input delays affecting the speed and turning rate, for the illustration of our methodology.Comment: Submitted to IEEE Transactions on Automatic Control on May 19 201

LpL_p-stabilization of integrator chains subject to input saturation using Lyapunov-based homogeneous design

Consider the $n$-th integrator $\dot x=J_nx+\sigma(u)e_n$, where $x\in\mathbb{R}^n$, $u\in \mathbb{R}$, $J_n$ is the $n$-th Jordan block and $e_n=(0\ \cdots 0\ 1)^T\in\mathbb{R}^n$. We provide easily implementable state feedback laws $u=k(x)$ which not only render the closed-loop system globally asymptotically stable but also are finite-gain $L_p$-stabilizing with arbitrarily small gain. These $L_p$-stabilizing state feedbacks are built from homogeneous feedbacks appearing in finite-time stabilization of linear systems. We also provide additional $L_\infty$-stabilization results for the case of both internal and external disturbances of the $n$-th integrator, namely for the perturbed system $\dot x=J_nx+e_n\sigma (k(x)+d)+D$ where $d\in\mathbb{R}$ and $D\in\mathbb{R}^n$

Some tracking problems for aerospace models with input constraints

We study tracking controller design problems for key models of planar vertical takeoff and landing (PVTOL) aircraft and unmanned air vehicles (UAVs). The novelty of our PVTOL work is the global boundedness of our controllers in the decoupled coordinates, the positive uniform lower bound on the thrust controller, the applicability of our work to cases where the velocity measurements may not be available, the uniform global asymptotic stability and uniform local exponential stability of our closed loop tracking dynamics, the generality of our class of trackable reference trajectories, and the input-to-state stability of the controller performance under actuator errors of arbitrarily large amplitude. The significance of our UAV results is the generality of the trackable trajectories, the input-to-state stability properties of the tracking dynamics with respect to additive uncertainty on the controllers, and our ability to satisfy command amplitude and command rate constraints as well as state dependent command constraints and a state constraint on the velocity. Our work is based on a Matrosov approach for converting a nonstrict Lyapunov function for the UAV tracking dynamics into a strict one, in conjunction with asymptotic strict Lyapunov function methods and bounded backstepping

Bounded Tracking Controllers and Robustness Analysis for UAVs

International audienceWe study a kinematic model that is suitable for control design for high level formation flight of UAVs. We design controllers that give robust global tracking for a wide class of reference trajectories in the sense of input-to-state stability while satisfying key amplitude and rate constraints on the inputs. We illustrate our work in simulations