Papers by Leyla Gören-Sümer
AIMS mathematics, 2023
This paper presents a consensus algorithm for continuous-time double-integrator multi-agent syste... more This paper presents a consensus algorithm for continuous-time double-integrator multi-agent systems with measurement/communication noises under directed fixed and switching topologies. The paper employs the algebraic graph theory and the stochastic tools to develop a consensus protocol in which a time-varying consensus gain is introduced to attenuate the additive white noises corrupting the information exchange between agents. Each agent's control input relies on its own information state and its neighbors' inaccurate information states and does not need the neighbors' information state derivatives. Conditions to guarantee mean square asymptotic convergence under noisy measurement for both fixed and switching topologies are derived. The consensus protocols developed in the noisy measurement case are proved to be still valid in the noise-free case, and they can ensure asymptotic mean square convergence. Finally, to illustrate the approach presented, some numerical simulations are carried out.
IFAC Proceedings Volumes, 1992
There are two aspect to this study. Firstly a new global search method is introduced which was de... more There are two aspect to this study. Firstly a new global search method is introduced which was developed by combining the two well-known global search methods, namely Controlled Random Search (CRS), Global Search Using Brownian Motion. Next, this new method has been applied to design of optimal controller for the speed control of a dc motor. The design has been done for various controller structures (PlO, Cascade PlO and nonlinear feedback) and their performances are co.pared with each other. Moreover, the results are also compared with the ones obtained by the application of classical optimal control theory and it is seen that the methodology has some merits.
Automatica, 2003
This work deals with the Model Matching Problem (MMP) and the Disturbance Rejection Problem (DRP)... more This work deals with the Model Matching Problem (MMP) and the Disturbance Rejection Problem (DRP) with stability by state feedback. Each of these control problems has, separately, received a lot of contributions, but, to our best knowledge, we propose here for the first time a complete structural solution to the stable simultaneous MMP and DRP. Our structural conditions nicely enhance the role played by the zeros, both finite and infinite.
IFAC Proceedings Volumes, 2005
In this study, the model-matching problem (MMP) in two degrees of freedom (2DOF) control structur... more In this study, the model-matching problem (MMP) in two degrees of freedom (2DOF) control structure is considered for discrete-time system in the sense of the H ∞ optimality criterion. The problem is solved in Linear Matrix Inequality (LMI) framework using the results on the standard H ∞ OCP and the recent results given by Gören (2003) on the MMP in 2DOF control structure for continuous-time systems.
IFAC Proceedings Volumes, Sep 1, 1992
Kybernetika, 1996
In this paper, the row by row decoupling problem by static state feedback is studied for regulari... more In this paper, the row by row decoupling problem by static state feedback is studied for regularizable singular square systems. The problem is handled in matrix polynomial equation setting. The necessary and sufficient conditions on decouplability are introduced and an algorithm for calculation of feedback gains is presented. A structural interpretation is also given for decoupled systems.
IFAC Proceedings Volumes, 1993
In this paper, decoupling and closed loop pole placement problem for square generalized systems a... more In this paper, decoupling and closed loop pole placement problem for square generalized systems are studied by regular static state and output feedbacks. The study is based on the previous results on decoupling via state feedback in singular systems. The necessary and sufficient conditions on decouplability by output feedback is introduced and a theorem on assignable closed loop structures for simultaneously decoupled generalized systems is presented.
H<inf>∞</inf> model matching in two degree of freedom control structure
In this study, the model-matching problem (MMP) in two degree of freedom (2DOF) control structure... more In this study, the model-matching problem (MMP) in two degree of freedom (2DOF) control structure is defined and solved in the sense of the H ∞ optimality criterion in the framework Linear Matrix Inequality (LMI) by using the results on the standard H ∞ OCP.
IFAC-PapersOnLine, 2020
We propose a new control design for active vibration suppression of flexible structures with a co... more We propose a new control design for active vibration suppression of flexible structures with a collocated sensor-actuator pair. The proposed controller is based on the inverse form of a well-known input zero vibration (ZV) shaper. The inverse ZV shaper is utilized with a serially interconnected all-pass filter. This way, the appropriate controller frequency response properties for vibration suppression of collocated flexible systems is achieved, when the controller is applied in the positive feedback path. We propose two different cost functions to optimize the parameters of the proposed controller for efficient vibration suppression. The performance of the controller is investigated in both frequency and time domains through the vibration control of a cantilever beam model with a collocated piezoelectric sensor-actuator pair. Furthermore, its performance is compared with a recently improved version of the positive position feedback controller, which is a state-of-the-art work. It is shown via the simulations that the proposed controller suppresses vibrations more efficiently.
The energy shaping method, Controlled Lagrangian, is a well-known approach to stabilize the under... more The energy shaping method, Controlled Lagrangian, is a well-known approach to stabilize the under-actuated Euler Lagrange (EL) systems. In this approach, to construct a control rule, some nonlinear, nonhomogeneous partial differential equations (PDEs), which are called matching conditions, must be solved. In this paper, a method is proposed to obtain an approximate solution of these matching conditions for a class of under-actuated EL systems. To develop the method, the potential energy matching condition is transformed to a set of linear PDEs using an approximation of inertia matrices. So the assignable potential energy function and the controlled inertia matrix, both are constructed as a common solution of these PDEs. Afterwards, the gyroscopic and dissipative forces are found as the solution of the kinetic energy matching condition. Finally, the control rule is constructed by adding energy shaping rule and additional dissipation injection to provide asymptotic stability. The stability analysis of the closed loop system which used the control rule derived with the proposed method is also given. To demonstrate the success of the proposed method, the stability problem of the inverted pendulum on a cart is considered.
2016 National Conference on Electrical, Electronics and Biomedical Engineering (ELECO), Dec 1, 2016
The energy shaping method, Controlled Lagrangian, is a well-known approach to stabilize the under... more The energy shaping method, Controlled Lagrangian, is a well-known approach to stabilize the under-actuated Euler Lagrange (EL) systems. In this approach, to construct a control rule, some nonlinear, nonhomogeneous partial differential equations (PDEs), which are called matching conditions, must be solved. In this paper, a method is proposed to obtain an approximate solution of these matching conditions for a class of under-actuated EL systems. To develop the method, the potential energy matching condition is transformed to a set of linear PDEs using an approximation of inertia matrices. So the assignable potential energy function and the controlled inertia matrix, both are constructed as a common solution of these PDEs. Afterwards, the gyroscopic and dissipative forces are found as the solution of the kinetic energy matching condition. Finally, the control rule is constructed by adding energy shaping rule and additional dissipation injection to provide asymptotic stability. The stability analysis of the closed loop system which used the control rule derived with the proposed method is also given. To demonstrate the success of the proposed method, the stability problem of the inverted pendulum on a cart is considered.
IFAC Proceedings Volumes, Jun 1, 1996
In this paper, the row by row decoupling problem by static state feedback is studied for regulari... more In this paper, the row by row decoupling problem by static state feedback is studied for regularizable singular square systems. The problem is handled in matrix polynomial equation setting. The necessary and sufficient conditions on decouplability are introduced and an algorithm for calculation of feedback gains is presented. A structural interpretation is also given for decoupled systems.
Stabilization of Controller-Driven Nonuniformly Sampled Systems via Digital Redesign
IFAC-PapersOnLine, 2016
Abstract This paper deals with the stabilization problem of nonuniformly sampled systems, assumin... more Abstract This paper deals with the stabilization problem of nonuniformly sampled systems, assuming that the controller/scheduler can select the sampling period. In this setting, we proposed a sampling-period-varying state feedback controller that stabilizes the closed-loop system for arbitrary selection of bounded sampling periods. The proposed controller is based on the digital redesign technique, which also makes the closed-loop sampled system state response close to a pre-selected closed-loop continuous system.
İTÜDERGİSİ/d, May 5, 2010
Bu çalışmada bir ön kontrolörün eşdeğeri olan dinamik durum geribeslemesi ile ayrık H ∞ model eşl... more Bu çalışmada bir ön kontrolörün eşdeğeri olan dinamik durum geribeslemesi ile ayrık H ∞ model eşleme probleminin doğrusal matris eşitsizlikleri yaklaşımı ile çözümü amaçlanmıştır. Ayrık H ∞ model eşleme problemi, ayrık H ∞ optimal kontrol probleminin özel bir halidir. Bu nedenle ayrık H ∞ optimal kontrol probleminin doğrusal matris eşitsizlikleri ile elde edilen çözümü ayrık H ∞ model eşleme probleminin çözülmesi için kullanılabilir. Makalede ayrık H ∞ model eşleme probleminin dinamik durum geribeslemesi ile çözümünün tek doğrusal matris eşitsizliğine indirgenebildiği gösterilmiş ve kontrolör tasarımı için gereken sentez teoremi ve algoritma verilmiştir. Anahtar Kelimeler: H ∞ kontrol, H ∞ model eşleme problemi, doğrusal matris eşitsizlikleri.
IFAC Proceedings Volumes, Aug 1, 1990
To simulate the motion of a manipulator. one must make use of a model of real robot dynamics, whe... more To simulate the motion of a manipulator. one must make use of a model of real robot dynamics, where the robot dynamics is usually given by the Newton-Euler equations. A reliable model of a robot is essential not only for simulation purposes but also to let the designer to develop better control algorithms. In literature. the models usually used are given by state-equations; the basic disadvantage of using these models is that they create cumulative errors in simulation. In this study. a new method is proposed which determines the error between the discrete. linear. time-variant model and the real robot dynamics over torques. This error dynamic whi ch possess a predictive character produced very efficient results in obtaining error-free model of a robot.
arXiv (Cornell University), Dec 6, 2022
This article considers consensus problem of multiagent systems with double integrator dynamics un... more This article considers consensus problem of multiagent systems with double integrator dynamics under nonuniform sampling. It is considered the maximum sampling time can be selected arbitrarily. Moreover, the communication graph can change to any possible topology as long as its associated graph Laplacian has eigenvalues in a given region, which can be selected arbitrarily. Existence of a controller that ensures consensus in this setting is shown when the changing topology graphs are balanced and has a spanning tree. Also, explicit bounds for controller parameters are given. A novel sufficient condition is given to solve the consensus problem based on making the closed loop system matrix a contraction using a particular coordinate system for general linear dynamics. It is shown that the given condition immediately generalizes to changing topology in the case of balanced topology graphs. This condition is applied to double integrator dynamics to obtain explicit bounds on the controller.
IFAC Proceedings Volumes, 2008
The discrete-time disturbance attenuation problem for a class of Hamiltonian systems is considere... more The discrete-time disturbance attenuation problem for a class of Hamiltonian systems is considered. In order to give a sufficient condition for the solution of the considered problem, firstly an appropriate discrete gradient is proposed, which enables the derivation of the discrete time version of the given Hamiltonian systems. The disturbance attenuation problem characterised by means of L 2 gain is redefined in the discrete-time setting. The proposed direct discrete-time design method is used to solve the disturbance attenuation problem for the double pendulum system in simulations.
IFAC Proceedings Volumes, 2002
In this paper, the multiobjective 31, control problem of model matching and disturbance rejection... more In this paper, the multiobjective 31, control problem of model matching and disturbance rejection by dynamic state feedback and disturbance measurement feedforward is studied via Linear Matrix Inequality (LMI) approach. To solve the problem, first, the multiobjective 31, control problem is defined and shown that this problem can be reduced in two independent 31, Model Matching Problems (MMP) and then the LMI-based solution of the 31, MMP is derived by using the solution of the 31, Optimal Control Problem (OCP) in the formulation of the LMI. The LMIbased solvability conditions for the multiobjective X, control problem and a design procedure for the controller are given.
Stabilization of a class of underactuated Euler Lagrange system using an approximate model
Transactions of the Institute of Measurement and Control, Dec 7, 2021
The energy shaping method, Controlled Lagrangian, is a well-known approach to stabilize the under... more The energy shaping method, Controlled Lagrangian, is a well-known approach to stabilize the underactuated Euler Lagrange (EL) systems. In this approach, to construct a control rule, some nonlinear and nonhomogeneous partial differential equations (PDEs), which are called matching conditions, must be solved. In this paper, a method is proposed to obtain an approximate solution of these matching conditions for a class of underactuated EL systems. To develop this method, the potential energy matching condition is transformed to a set of linear PDEs using an approximation of inertia matrices. Hence, the assignable potential energy function and the controlled inertia matrix both are constructed as a common solution of these PDEs. Subsequently, the gyroscopic and dissipative forces are determined as the solution for kinetic energy matching condition. Conclusively, the control rule is constructed by adding energy shaping rule and additional dissipation injection to provide asymptotic stability. The stability analysis of the closed-loop system which used the control rule derived with the proposed method is also provided. To demonstrate the success of the proposed method, the stability problem of the inverted pendulum on a cart is considered.
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Papers by Leyla Gören-Sümer