Contraction and Robustness of Continuous Time Primal-Dual Dynamics

The Primal-Dual (PD) algorithm is widely used in convex optimization to determine saddle points. While the stability of the PD algorithm can be easily guaranteed, strict contraction is nontrivial to establish in most cases. This work focuses on continuous, possibly non-autonomous PD dynamics arising in a network context, in distributed optimization, or in systems with multiple time-scales. We show that the PD algorithm is indeed strictly contracting in specific metrics and analyze its robustness establishing stability and performance guarantees for different approximate PD systems. We derive estimates for the performance of multiple time-scale multi-layer optimization systems, and illustrate our results on a primal-dual representation of the Automatic Generation Control of power systems.Comment: 6 pages, 1 figures, published on LCSS and CDC 201

A Non-Fragile H∞ Output Feedback Controller for Uncertain Fuzzy Dynamical Systems with Multiple Time-Scales

This paper determines the designing of a non-fragile H∞ output feedback controller for a class of nonlinear uncertain dynamical systems with multiple timescales described by a Takagi-Sugeno (TS) fuzzy model. Based on a linear matrix inequality (LMI) approach, we develop a non-fragile H∞ output feedback controller which guarantees the L2-gain of the mapping from the exogenous input noise to the regulated output to be less than some prescribed value for this class of uncertain fuzzy dynamical systems with multiple time-scales. A numerical example is provided to illustrate the design developed in this paper

Estimation and control of non-linear and hybrid systems with applications to air-to-air guidance

Issued as Progress report, and Final report, Project no. E-21-67

Nonlinear control for Two-Link flexible manipulator

Recently the use of robot manipulators has been increasing in many applications such as medical applications, automobile, construction, manufacturing, military, space, etc. However, current rigid manipulators have high inertia and use actuators with large energy consumption. Moreover, rigid manipulators are slow and have low payload-to arm-mass ratios because link deformation is not allowed. The main advantages of flexible manipulators over rigid manipulators are light in weight, higher speed of operation, larger workspace, smaller actuator, lower energy consumption and lower cost. However, there is no adequate closed-form solutions exist for flexible manipulators. This is mainly because flexible dynamics are modeled with partial differential equations, which give rise to infinite dimensional dynamical systems that are, in general, not possible to represent exactly or efficiently on a computer which makes modeling a challenging task. In addition, if flexibility nature wasn\u27t considered, there will be calculation errors in the calculated torque requirement for the motors and in the calculated position of the end-effecter. As for the control task, it is considered as a complex task since flexible manipulators are non-minimum phase system, under-actuated system and Multi-Input/Multi-Output (MIMO) nonlinear system. This thesis focuses on the development of dynamic formulation model and three control techniques aiming to achieve accurate position control and improving dynamic stability for Two-Link Flexible Manipulators (TLFMs). LQR controller is designed based on the linearized model of the TLFM; however, it is applied on both linearized and nonlinear models. In addition to LQR, Backstepping and Sliding mode controllers are designed as nonlinear control approaches and applied on both the nonlinear model of the TLFM and the physical system. The three developed control techniques are tested through simulation based on the developed dynamic formulation model using MATLAB/SIMULINK. Stability and performance analysis were conducted and tuned to obtain the best results. Then, the performance and stability results obtained through simulation are compared. Finally, the developed control techniques were implemented and analyzed on the 2-DOF Serial Flexible Link Robot experimental system from Quanser and the results are illustrated and compared with that obtained through simulation

Application of robust order reduction in modeling and control of real systems and objects in mechanical engineering

Дисертација „Примена робусне редукције реда система у моделовању и управљању реалним објектима у машинству“ је посвећена техникама и методама за редукцију реда линеарних модела, представљених у простору стања, као и условима и ограничењима за њихову примену. Приказан је концепт сингуларних пертурбација и његова примена у редукцији сложености модела система. Размотрене су различите карактеризације линеарних модела великог реда, чије репрезентације моделима у простору стања имају различите временске скале или и мали параметар (имају матрице великих димензија са пуно нула-елемената или са елементима, чији се редови величине веома разликују). Представљени су: сингуларно пертурбовани слабо повезани системи, слабо повезани системи, сингуларно пертурбовани системи, квази сингуларно пертурбовани системи и квази слабо повезани системи. Свака од ових класа представљена је одговарајућим моделом у простору стања неког реалног система. Детаљније је изложен прорачун регулатора за линеаран сингуларно пертурбован систем. Описана је метода балансирања, као и технике за редукцију реда линеарних модела, познате из литературе, које захтевају примену трансформације балансирања: балансирано одсецање, балансирана резидуализација, генералисана балансирана резидуализација, кориговано балансирано одсецање, метода заснована на брзом подсистему уз одбацивање спорог, модификована генералисана балансирана резидуализација, као и реверзна техника резидуализације. Свака од ових техника даје по један модел редукованог реда, полазећи од балансираног модела пуног реда. Технике изложене у овој тези, примењене су на редуковање реда четири модела реалних система. Први је модел бинарне дестилационе колоне са прегревачем и девет подова. Други је модел у простору стања борбене летелице L-1011. Трећи је математички модел каталитички контролисане реакције, из процесне технике. Четврти је математички модел дела електроенергетског система Србије, сачињен од две машине. Изложена је и редукција реда модела нестабилних линеарних система, на основу изабране литературе...The dissertation Application of Robust Order Reduction for Modeling and Control of Real Systems in Mechanical Engineering is dealing with techniques and methods of order reduction for linear models in the state space representation, as well as with conditions and limitations of their applicability. Well known concept of singular perturbations is described with its application in reduction of complexity of the system’s model. Different characterizations of large scale linear models are overviewed, having state space representations who exhibit different time scales or small parameter, too. These models have matrices of large dimensions with many zero-elements or elements with different size order, some very large and others very small. The singularly perturbed and weakly coupled systems, the weakly coupled systems, the singularly perturbed systems, the quasy singularly perturbed systems and the quasy weakly coupled systems are listed and represented here. Each class of these is represented with corresponding state space model of one real system. The design of the regulator for the linear singularly perturbed system is described in detail. The balancing method is analyzed, as well as techniques for the order reduction of linear model’s, known from the literature. These require application of the balancing transformation: the balancing truncation, the balancing residualization, the generalized balancing residualization, the corrected balancing truncation, the method based on the fast subsystem with rejection of the slow subsystem, the modified generalized balancing residualization, as well as the reversed residualization technique. Each of these techniques mentioned gives one model of reduced order, starting from the balanced full order model. Techniques represented in this thesis are applied on order reduction of four real system’s models. The first is the state space model of binary distillation column, with condenser, reboiler and nine plates. The second is the state space model of L-1011 fighter aircraft. The third is a mathematical model of the controlled catalytic reaction, from process engineering. The fourth part is a mathematical model of the part of electric power system of Serbia, consisting of two machines. Described here is the order reduction for models of unstable linear systems as well, based on the chosen references..

Stokesian dynamic simulations and analyses of interfacial and bulk colloidal fluids

Understanding dynamics of colloidal dispersions is important for several applications ranging from coatings such as paints to growing colloidal crystals for photonic bandgap materials. The research outlined in this dissertation describes the use of Monte Carlo and Stokesian Dynamic simulations to model colloidal dispersions, and the development of theoretical expressions to quantify and predict dynamics of colloidal dispersions. The emphasis is on accurately modeling conservative, Brownian, and hydrodynamic forces to model dynamics of colloidal dispersions. In addition, we develop theoretical expressions for quantifying self-diffusion in colloids interacting via different particle-particle and particle-wall potentials. Specifically, we have used simulations to quantitatively explain the observation of anomalous attraction between like-charged colloids, develop a new criterion for percolation in attractive colloidal fluids, and validate the use of analytical expressions for quantifying diffusion in interfacial colloidal fluids. The results of this work contribute to understanding dynamics in interfacial and bulk colloidal fluids