Most of the signal processing that we will study in this course involves local operations on a signal, namely transforming the signal by applying linear combinations of values in the neighborhood of each sample point. You are familiar with such operations from Calculus, namely, taking derivatives and you are also familiar with this from optics namely blurring a signal. We will be looking at sampled signals only. Let's start with a few basic examples. Local difference Suppose we have a 1D image and we take the local difference of intensities, DI(x) = 1 2 (I(x + 1) − I(x − 1)) which give a discrete approximation to a partial derivative. (We compute this for each x in the image.) What is the effect of such a transformation? One key idea is that such a derivative would be useful for marking positions where the intensity changes. Such a change is called an edge. It is important to detect edges in images because they often mark locations at which object properties change. These can include changes in illumination along a surface due to a shadow boundary, or a material (pigment) change, or a change in depth as when one object ends and another begins. The computational problem of finding intensity edges in images is called edge detection. We could look for positions at which DI(x) has a large negative or positive value. Large positive values indicate an edge that goes from low to high intensity, and large negative values indicate an edge that goes from high to low intensity. Example Suppose the image consists of a single (slightly sloped) edge:

http://ieeexplore.ieee.org/iel5/5/31307/01456462.pdf

Linear systems

Adaptive tracking control of uncertain MIMO nonlinear systems with input constraints

Formation control analysis and design problems for unmanned aerial vehicle (UAV) swarm systems to achieve time-varying formations are investigated. To achieve predefined time-varying formations, formation protocols are presented for UAV swarm systems first, where the velocities of UAVs can be different when achieving formations. Then, consensus-based approaches are applied to deal with the time-varying formation control problems for UAV swarm systems. Necessary and sufficient conditions for UAV swarm systems to achieve time-varying formations are proposed. An explicit expression of the time-varying formation center function is derived. In addition, a procedure to design the protocol for UAV swarm systems to achieve time-varying formations is given. Finally, a quadrotor formation platform, which consists of five quadrotors is introduced. Theoretical results obtained in this brief are validated on the quardrotor formation platform, and outdoor experimental results are presented.

Time-Varying Formation Control for Unmanned Aerial Vehicles: Theories and Applications

In this paper, robust adaptive neural network (NN) control is investigated for a general class of uncertain multiple-input-multiple-output (MIMO) nonlinear systems with unknown control coefficient matrices and input nonlinearities. For nonsymmetric input nonlinearities of saturation and deadzone, variable structure control (VSC) in combination with backstepping and Lyapunov synthesis is proposed for adaptive NN control design with guaranteed stability. In the proposed adaptive NN control, the usual assumption on nonsingularity of NN approximation for unknown control coefficient matrices and boundary assumption between NN approximation error and control input have been eliminated. Command filters are presented to implement physical constraints on the virtual control laws, then the tedious analytic computations of time derivatives of virtual control laws are canceled. It is proved that the proposed robust backstepping control is able to guarantee semiglobal uniform ultimate boundedness of all signals in the closed-loop system. Finally, simulation results are presented to illustrate the effectiveness of the proposed adaptive NN control.

Robust Adaptive Neural Network Control for a Class of Uncertain MIMO Nonlinear Systems With Input Nonlinearities

Time-varying formation tracking analysis and design problems for second-order Multi-Agent systems with switching interaction topologies are studied, where the states of the followers form a predefined time-varying formation while tracking the state of the leader. A formation tracking protocol is constructed based on the relative information of the neighboring agents. Necessary and sufficient conditions for Multi-Agent systems with switching interaction topologies to achieve time-varying formation tracking are proposed together with the formation tracking feasibility constraint based on the graph theory. An approach to design the formation tracking protocol is proposed by solving an algebraic Riccati equation, and the stability of the proposed approach is proved using the common Lyapunov stability theory. The obtained results are applied to solve the target enclosing problem of a multiquadrotor unmanned aerial vehicle (UAV) system consisting of one leader (target) quadrotor UAV and three follower quadrotor UAVs. A numerical simulation and an outdoor experiment are presented to demonstrate the effectiveness of the theoretical results.

Time-Varying Formation Tracking for Second-Order Multi-Agent Systems Subjected to Switching Topologies With Application to Quadrotor Formation Flying

Time-varying formation control for unmanned aerial vehicles with switching interaction topologies

Robust attitude control problem for a three-degree-of-freedom (3-DOF) laboratory helicopter is investigated. The helicopter dynamics involves nonlinearity, uncertainties, and strong interaxis coupling. A robust controller is proposed with three parts: a nominal feedforward controller, a nominal linear quadratic regulation (LQR) controller, and a robust compensator. The LQR controller is applied to deal with a nominal linear error system derived by the feedforward control strategy and linearized approximation, while the robust compensator is designed to restrain the effects of uncertainties, nonlinear properties, and external disturbances. It is shown that the attitude tracking error of the closed-loop system can be guaranteed to converge to any given small neighborhood of the origin in a finite time. Experimental results on the 3-DOF laboratory helicopter demonstrate the effectiveness of the proposed control strategy.

Robust LQR Attitude Control of a 3-DOF Laboratory Helicopter for Aggressive Maneuvers

Formation-containment control problems for multiple multirotor unmanned aerial vehicle (UAV) systems with directed topologies are studied, where the states of leaders form desired formation and the states of followers converge to the convex hull spanned by those of the leaders. First, formation-containment protocols are constructed based on the neighboring information of UAVs. Then, sufficient conditions for multi-UAV systems to achieve formation-containment are presented. An explicit expression to describe the relationship among the states of followers, the time-varying formation for the leaders and the formation reference is derived. It is shown that the states of followers not only converge to the convex hull formed by those of leaders but also keep certain formation specified by the convex combination of the formation for the leaders. Moreover, an approach to determine the gain matrices of the formation-containment protocol is proposed by solving an algebraic Riccati equation. Finally, a formation-containment platform with five quadrotor UAVs is introduced, and both the simulation and experimental results are presented to demonstrate the effectiveness of the obtained results. Note to Practitioners —This paper addresses the problem of formation-containment control for multi-UAV systems over directed topologies. In practical applications, there may exist multiple leaders and multiple followers in a multi-UAV system. Formation-containment means that the states of leaders form the desired time-varying formation and at the same time the states of the followers converge to the convex hull spanned by those of the leaders. Formation-containment control provides a unified framework for formation control and containment control, and has potential applications in the cooperative source seeking, load transportation, and surveillance. Although formation control and containment control problems have been studied a lot, the formation-containment control problem for multi-UAV system is still open and challenging. This paper proposed a distributed formation-containment protocol for the multi-UAV system using local neighboring information. Sufficient conditions for multi-UAV systems to achieve formation-containment are presented. It is proven that the states of followers not only converge to the convex hull formed by those of leaders but also keep certain formation specified by the convex combination of the formation for the leaders. An approach to design the formation-containment protocol is given. A remarkable point for this paper is that the obtained results are demonstrated by practical experiments with five quadrotor UAVs.

Yisheng Zhong

Papers

Time-Varying Formation Control for Unmanned Aerial Vehicles: Theories and Applications

Time-Varying Formation Tracking for Second-Order Multi-Agent Systems Subjected to Switching Topologies With Application to Quadrotor Formation Flying

Time-varying formation control for unmanned aerial vehicles with switching interaction topologies

Robust LQR Attitude Control of a 3-DOF Laboratory Helicopter for Aggressive Maneuvers

Theory and Experiment on Formation-Containment Control of Multiple Multirotor Unmanned Aerial Vehicle Systems