On the Hybrid Minimum Principle On Lie Groups and the Exponential Gradient HMP Algorithm

This paper provides a geometrical derivation of the Hybrid Minimum Principle (HMP) for autonomous hybrid systems whose state manifolds constitute Lie groups $(G,\star)$ which are left invariant under the controlled dynamics of the system, and whose switching manifolds are defined as smooth embedded time invariant submanifolds of $G$. The analysis is expressed in terms of extremal (i.e. optimal) trajectories on the cotangent bundle of the state manifold $G$. The Hybrid Maximum Principle (HMP) algorithm introduced in \cite{Shaikh} is extended to the so-called Exponential Gradient algorithm. The convergence analysis for the algorithm is based upon the LaSalle Invariance Principle and simulation results illustrate their efficacy

Integrating Low Voltage Distribution Systems to Distribution Automation

The aim of this thesis is to define and study the key elements and the main characteris-tics of the integration of the low voltage (LV) distribution systems to distribution auto-mation (DA). The key elements are defined by studying the development of essential systems in LV distribution networks as well as by studying the development of the net-works by way of evolution phases. The key elements and the main characteristics of the integration to DA are illustrated by a certain model of a LV distribution network under its development. For a start DA is reviewed by generally used functions and by technologies. The review includes the data and the information systems and in addition the communication net-works are studied generally. Thereafter the main elements of LV distribution networks are presented and their evolution visions are introduced. The main elements comprises of the distribution network, distributed generation, smart energy metering, electric vehicles and energy storages. The approach to the integration is the evolution of LV distribution networks, so four main evolution phases are introduced; traditional, boom of distributed generation, mi-crogrid and intelligent microgrid. The evolution phases bases on general research publi-cations and visions of Smart Grids. Management architectures for the networks are pre-sented. Also requirements for communication are evaluated by studying the number of nodes, capacity requirements for transferred data types and fault and event frequencies. In order to define a proposal for integrating LV distribution networks to DA, the man-agement architectures and the studied requirements are compared to produce functions for DA. As a result, the proposal is presented based on the studied architectures and re-quirements. In addition considerable issues are introduced relating to the functions in devices or sub-systems, which are needed for DA applications. This thesis indicates the need for further studies, such as: Which are the desired DA functions to be extended to LV distribution networks? Which device or system should offer the desired functions? How well the potential protocols using some media type serves the functions?fi=Opinnäytetyö kokotekstinä PDF-muodossa.|en=Thesis fulltext in PDF format.|sv=Lärdomsprov tillgängligt som fulltext i PDF-format

Modeling, analysis and control of robot-object nonsmooth underactuated Lagrangian systems: A tutorial overview and perspectives

International audienceSo-called robot-object Lagrangian systems consist of a class of nonsmooth underactuated complementarity Lagrangian systems, with a specific structure: an "object" and a "robot". Only the robot is actuated. The object dynamics can thus be controlled only through the action of the contact Lagrange multipliers, which represent the interaction forces between the robot and the object. Juggling, walking, running, hopping machines, robotic systems that manipulate objects, tapping, pushing systems, kinematic chains with joint clearance, crawling, climbing robots, some cable-driven manipulators, and some circuits with set-valued nonsmooth components, belong this class. This article aims at presenting their main features, then many application examples which belong to the robot-object class, then reviewing the main tools and control strategies which have been proposed in the Automatic Control and in the Robotics literature. Some comments and open issues conclude the article

A semi-Lagrangian algorithm in policy space for hybrid optimal control problems

The mathematical framework of hybrid system is a recent and general tool to treat control systems involving control action of heterogeneous nature. In this paper, we construct and test a semi-Lagrangian numerical scheme for solving the Dynamic Programming equation of an infinite horizon optimal control problem for hybrid systems. In order to speed up convergence, we also propose an acceleration technique based on policy iteration. Finally, we validate the approach via some numerical tests in low dimension

Trajectory tracking and formation control of a platoon of mobile robots

This thesis is concerned with controlling a platoon of wheeled mobile robots (WMR), where the robots are aimed to follow a trajectory while they maintain their formation intact. The control design is carried out by considering unicycle kinematics for each robot, and the leader-follower structure for the formation. It is assumed that every robot except the one located at the end of each platoon can potentially be the leader to the one behind it. It is also assumed that each follower is capable of sensing its relative distance and relative velocity with respect to its preceding robot. The stability of the proposed control law is investigated in the case of perfect sensing and in the presence of input saturation. The impact of measurement noise on the followers is then studied assuming that a known upper bound exists on the measurement error, and a linear matrix inequality (LMI) methodology is proposed to design a control law which minimizes the upper bound on the steady-state error. The problem is then investigated in a more practical setting, where the control input is subject to delay, and that the tracking trajectory can be different in distinct time intervals. It is to be noted that delay often exists in this type of cooperative control system due to data transmission and signal processing, and if neglected in the control design, can lead to poor closed-loop performance or even instability. Furthermore, switching in tracking trajectory can be used as a collision avoidance strategy in the formation control problem. Delay dependent stability conditions are derived in the form of LMIs, and the free-weighting matrix approach is used to obtain less conservative results. Simulations are presented to demonstrate the efficacy of the results obtained in this thesis