Global exponential stabilization of language constrained switched linear discrete-time system based on the s-procedure approach

This paper considers global exponential stabilization (GES) of switched linear discrete-time system under language constraint which is generated by non-deterministic finite state automata. A technique in linear matrix inequalities called S-procedure is employed to provide sufficient conditions of GES which are less conservative than the existing Lyapunov-Metzler condition. Moreover, by revising the construction of Lyapunov matrices and the corresponding switching control policy, a more flexible result is obtained such that stabilization path at each moment might be multiple. Finally, a numerical example is given to illustrate the effectiveness of the proposed results

34th Midwest Symposium on Circuits and Systems-Final Program

Organized by the Naval Postgraduate School Monterey California. Cosponsored by the IEEE Circuits and Systems Society. Symposium Organizing Committee: General Chairman-Sherif Michael, Technical Program-Roberto Cristi, Publications-Michael Soderstrand, Special Sessions- Charles W. Therrien, Publicity: Jeffrey Burl, Finance: Ralph Hippenstiel, and Local Arrangements: Barbara Cristi

Dynamical analysis of particular classes of linear time-delay singular control systems defined over finite and infinite time interval

U disertaciji su razmatrani problemi dinamicke analize posebnih klasa singularnih sistema sa cistim vremenskim kašnjenjem prisutnim u stanju sistema, kao i njihovo ponašanje na konacnom i beskonacnom vremenskom intervalu. Pružen je presek savremenih koncepata stabilnosti, prednosti jednih nad drugima i posebno su obraeni tzv neljapunovski koncepti: stabilnost na konacnom vremenskom intervalu i koncept prakticne stabilnosti. Nadograene su osnovne definicije stabilnosti. Isrpno je izložen hronološki sistematican pregled osnovnih koncepata stabilnosti, polazeci od ljapunovske metodologije, kao osnove na kojoj se zasniva dinamicka analiza sistema. Ukazano je na istorijski razvoj i nastanak ideja i rezultata u ovoj oblasti i na taj nacin su izvedene i smernice daljih istraživanja otvorenih problema. U disertaciji su sistemi tretirani sa stanovišta dva savremena pristupa: deskriptivnog i LMI, odnosno sa pozicija linearnih matricnih nejednakosti, koja se svodi na metode konveksne optimizacije. Izvedeni su i saopšteni novi rezultati. Izložen je prilaz koji se bazira na kvaziljapunovskim funkcijama za dobijanje uslova prakticne i stabilnosti na konacnom vremenskom intervalu posebne klase singularnih sistema sa cistim vremenskim kašnjenje, u stanju sistema. Pokazano je da, polazeci od pretpostavke da agregacione funkcije ne moraju da budu odreene po znaku i da njihovi izvodi duž trajektorija sistema ne moraju da budu negativno odrreene funkcije, uz pomoc deskriptivnog prilaza se mogu dobiti novi kriterijumi za ocenu neljapunovske stabilnosti. Kombinovanjem rezultata sa ljapunovskim prilazom, izvedeni su o uslovi atraktivne prakticne stabilnosti. Drugi doprinos je odreivanje dovoljnih uslova stabilnosti na konacnom vremenskom intervalu iste klase sistema pomocu savremenih LMI metoda. Dobijeni i prezentovani rezultati imaju prakticnu primenu u savremenoj teoriji i praksi upravljanja i mogu se primeniti na sve klase proucavanih sistema, pod uslovom da su dostupni verodostojni matematicki modeli. Verifikacija rezultata je izvedena kroz numericke primereIn this thesis the problems of dynamical analysis of particular class of singular control systems with time delays are considered, as well as their behavior on finite and infinite time intervals. Emphasis has been put on the peculiar properties of singular ad descriptor systems, concerning the existence and uniqueness of the solutions, the problems of impulsive behavior, consistent initial conditions and causality of the system itself. On overview of the modern stability frameworks has been presented, starting from the classical Lyapunov ideas and extending through so called non-lyapunov concepts: finite time stability and practical stability in particular. A historical overview of ideas, concepts and results has been presented and the key contributions have been highlighted through key papers from the modern literature. This dissertation follows two main lines of research: the descriptive approach and the LMI (linear matrix inequalities) methodology, the latter being known to reduce control tasks to convex optimization problems, thus making them easily solvable by numerical computation. New results are presented. A new approach, based on lyapunov-like functions, is used in order to establish new sufficient conditions of practical and finite time interval stability of a particular class of singular time delay systems. Another new result is based on the modern LMI approach and gives new sufficient conditions for finite time stability. The obtained results are numerically verified and have great practical value, as they are easy to compute and less restrictive and conservative than their predecessors

Structure-Preserving Model Reduction of Physical Network Systems

This paper considers physical network systems where the energy storage is naturally associated to the nodes of the graph, while the edges of the graph correspond to static couplings. The first sections deal with the linear case, covering examples such as mass-damper and hydraulic systems, which have a structure that is similar to symmetric consensus dynamics. The last section is concerned with a specific class of nonlinear physical network systems; namely detailed-balanced chemical reaction networks governed by mass action kinetics. In both cases, linear and nonlinear, the structure of the dynamics is similar, and is based on a weighted Laplacian matrix, together with an energy function capturing the energy storage at the nodes. We discuss two methods for structure-preserving model reduction. The first one is clustering; aggregating the nodes of the underlying graph to obtain a reduced graph. The second approach is based on neglecting the energy storage at some of the nodes, and subsequently eliminating those nodes (called Kron reduction).</p

Approximation, analysis and control of large-scale systems - Theory and Applications

This work presents some contributions to the fields of approximation, analysis and control of large-scale systems. Consequently the Thesis consists of three parts. The first part covers approximation topics and includes several contributions to the area of model reduction. Firstly, model reduction by moment matching for linear and nonlinear time-delay systems, including neutral differential time-delay systems with discrete-delays and distributed delays, is considered. Secondly, a theoretical framework and a collection of techniques to obtain reduced order models by moment matching from input/output data for linear (time-delay) systems and nonlinear (time-delay) systems is presented. The theory developed is then validated with the introduction and use of a low complexity algorithm for the fast estimation of the moments of the NETS-NYPS benchmark interconnected power system. Then, the model reduction problem is solved when the class of input signals generated by a linear exogenous system which does not have an implicit (differential) form is considered. The work regarding the topic of approximation is concluded with a chapter covering the problem of model reduction for linear singular systems. The second part of the Thesis, which concerns the area of analysis, consists of two very different contributions. The first proposes a new "discontinuous phasor transform" which allows to analyze in closed-form the steady-state behavior of discontinuous power electronic devices. The second presents in a unified framework a class of theorems inspired by the Krasovskii-LaSalle invariance principle for the study of "liminf" convergence properties of solutions of dynamical systems. Finally, in the last part of the Thesis the problem of finite-horizon optimal control with input constraints is studied and a methodology to compute approximate solutions of the resulting partial differential equation is proposed.Open Acces

Friction compensation in the swing-up control of viscously damped underactuated robotics

A dissertation submitted to the Faculty of Engineering and the Built Environment, University of the Witwatersrand, Johannesburg, in fulfilment of the requirements for the degree of Master of Science in Engineering in the Control Research Group School of Electrical and Information Engineering, Johannesburg, 2017In this research, we observed a torque-related limitation in the swing-up control of underactuated mechanical systems which had been integrated with viscous damping in the unactuated joint. The objective of this research project was thus to develop a practical work-around solution to this limitation. The nth order underactuated robotic system is represented in this research as a collection of compounded pendulums with n-1 actuators placed at each joint with the exception of the first joint. This system is referred to as the PAn-1 robot (Passive first joint, followed by n-1 Active joints), with the Acrobot (PA1 robot) and the PAA robot (or PA2 robot) being among the most well-known examples. A number of friction models exist in literature, which include, and are not exclusive to, the Coulomb and the Stribeck effect models, but the viscous damping model was selected for this research since it is more extensively covered in existing literature. The effectiveness of swing-up control using Lyapunov’s direct method when applied on the undamped PAn-1 robot has been vigorously demonstrated in existing literature, but there is no literature that discusses the swing-up control of viscously damped systems. We show, however, that the application of satisfactory swing-up control using Lyapunov’s direct method is constrained to underactuated systems that are either undamped or actively damped (viscous damping integrated into the actuated joints only). The violation of this constraint results in the derivation of a torque expression that cannot be solved for (invertibility problem, for systems described by n > 2) or a torque expression which contains a conditional singularity (singularity problem, for systems with n = 2). This constraint is formally summarised as the matched damping condition, and highlights a clear limitation in the Lyapunov-related swing-up control of underactuated mechanical systems. This condition has significant implications on the practical realisation of the swing-up control of underactuated mechanical systems, which justifies the investigation into the possibility of a work-around. We thus show that the limitation highlighted by the matched damping condition can be overcome through the implementation of the partial feedback linearisation (PFL) technique. Two key contributions are generated from this research as a result, which iii include the gain selection criterion (for Traditional Collocated PFL), and the convergence algorithm (for noncollocated PFL). The gain selection criterion is an analytical solution that is composed of a set of inequalities that map out a geometric region of appropriate gains in the swing-up gain space. Selecting a gain combination within this region will ensure that the fully-pendent equilibrium point (FPEP) is unstable, which is a necessary condition for swing-up control when the system is initialised near the FPEP. The convergence algorithm is an experimental solution that, once executed, will provide information about the distal pendulum’s angular initial condition that is required to swing-up a robot with a particular angular initial condition for the proximal pendulum, along with the minimum gain that is required to execute the swing-up control in this particular configuration. Significant future contributions on this topic may result from the inclusion of more complex friction models. Additionally, the degree of actuation of the system may be reduced through the implementation of energy storing components, such as torsional springs, at the joint. In summary, we present two contributions in the form of the gain selection criterion and the convergence algorithm which accommodate the circumnavigation of the limitation formalised as the matched damping condition. This condition pertains to the Lyapunov-related swing-up control of underactuated mechanical systems that have been integrated with viscous damping in the unactuated joint.CK201

Low-Complexity Switch Scheduling Algorithms: Delay Optimality in Heavy Traffic

Motivated by applications in data center networks, in this paper, we study the problem of scheduling in an input queued switch. While throughput maximizing algorithms in a switch are well-understood, delay analysis was developed only recently. It was recently shown that the well-known MaxWeight algorithm achieves optimal scaling of mean queue lengths in steady state in the heavy-traffic regime, and is within a factor less than $2$ of a universal lower bound. However, MaxWeight is not used in practice because of its high time complexity. In this paper, we study several low complexity algorithms and show that their heavy-traffic performance is identical to that of MaxWeight. We first present a negative result that picking a random schedule does not have optimal heavy-traffic scaling of queue lengths even under uniform traffic. We then show that if one picks the best among two matchings or modifies a random matching even a little, using the so-called flip operation, it leads to MaXWeight like heavy-traffic performance under uniform traffic. We then focus on the case of non-uniform traffic and show that a large class of low time complexity algorithms have the same heavy-traffic performance as MaxWeight, as long as it is ensured that a MaxWeight matching is picked often enough. We also briefly discuss the performance of these algorithms in the large scale heavy-traffic regime when the size of the switch increases simultaneously with the load. Finally, we use simulations to compare the performance of various algorithms.Comment: 14 pages paper with 3 page appendix. 4 figures and 1 table. Journa