Dynamical Systems Analysis and Control

BIO

The current researches of this group are as follows:

  • The research about finding an algorithmic method for analysis of equilibrium point of quasi-homogeneous systems as an important part of autonomous systems, related to Hilbert’s 16th problem and Arnold’s question, associated with the indirect method of Lyapunov,
  • To design robust controllers based on linear and nonlinear H_infinity methods for industrial systems such as a half-car active suspension system with hydraulic actuators and RTAC (TORA), and in addition to this, to design the controllers for the surgical robots having haptic technology, by a state-feedback control law that minimizes an infinite/finite horizon cost function within the framework of linear/nonlinear matrix inequalities, and especially, simultaneously establishes robust stability conditions presented by a Lyapunov function,
  • To develop and tailor the techniques of state-dependent Riccati equation (SDRE) filtering so as to rigorously estimate states and parameters of the nonlinear systems with uncertainty, exposed to unknown disturbance inputs, and also to apply SDRE filter such as robust SDRE filter based on the H-infinity norm minimization criterion to stochastic systems,
  • To study Neuroscience as a multidisciplinary field, which we believe it will be significantly influenced by dynamical systems theory. We have been actively engaging in the research about modeling of the neurons, especially located at V1, and optic nerves and also investigating methods for stimulation and recording of the nerve cells, including noninvasive and invasive methods, such as Steady State Visually Evoked Potential (SSVEP) stimulation, Transcranial Magnetic Stimulation (TMS), microelectrode stimulation, Optogenetics stimulation, Electroencephalogram (EEG) recording, Electrocorticography (ECoG) recording, Local Field Potential (LPF) recoding, and Spikes recording.
Nonlinear Analysis

We apply a wide variety of mathematical methods to analyzing system nonlinear behaviors. Moreover, we try to present new useful definitions and theorems which can assist us to accomplish the goal. Additionally, we are enthusiastic about pathological behaviors which common methods fail to analyze them such as Perron effect in the largest Lyapunov exponent sign, global attractivity without stability in Liénard type systems, and aperiodic long-term behavior of a non-hyperbolic strange attractor.

Most our efforts has been around determining invariant sets and their stability. In the first place, we investigate not only various definitions of invariant sets, but also different definitions of stability so as to find the definitions which can be appropriate to the needs of the analysis. In the second place, we conduct assorted methods such as topological, geometric, and algebraic methods which have the ability to be used for studying ordinary and partial differential equations, especially in state space. Particularly, we pursue to devise algorithms in order for finding the invariant sets of polynomial systems and solving their stability problem, specifically in the sense of V. Arnold.

Figure 1: Phase portrait of a system with two centers

Control Methods

A wide variety of control methods are considered in the group for control analysis and synthesis of dynamical systems. Among them  robust control synthesis for delayed systems is one of the focuses of our research group. Time-delay appear in many systems and processes and is usually a source of instability. We have proposed an  PD/PI controller synthesis for linear systems with uncertain input delay which may leads to a time-delay system of retarded or neutral type. In a neutral type system, in which delay appears both in its state and the derivatives of state, the resulting delay coefficients depend on the controller gains and makes the controller synthesis more challenging. To tackle this problem a new bounded real lemma (BRL) is introduced and the design of an output feedback PD controller for a system with uncertain time-invariant input delay is addressed. This method is further extended for designing a PI controller by augmenting an integrator to the system model.

H_infinity robust control synthesis is extensively applied in many practical systems of interest in the group.  H_infinity based robust torque control of harmonic drive systems, identification of RTAC (TORA) and Robust H_infinity Control synthesis,  Impedance control of a flight simulator yoke,  Decentralized Robust Controller design for a half-car active suspension system with hydraulic actuators,  Robust  Linear Controller, Composite QFT, Nonlinear H_infinity , Robust  H_2 /H_infinity and Mixed Sensitivity Approaches, for flexible joint robots with Phase Uncertainty, may be named among them.

H_infinity robust control synthesis is also applied on an MPC algorithm for non-linear discrete-time systems. The systems are composed of a linear constant part perturbed by an additive state-dependent non-linear term. The control objective is to design a state-feedback control law that minimizes an infinite horizon cost function within the framework of linear matrix inequalities. In particular, it is shown that the solution of the optimization problem can stabilize the non-linear plants. Three extensions, namely, application to systems with input delay, non-linear output tracking and using output-feedback, are followed naturally from the proposed formulation.

Multi agent coverage control: The recent development in the autonomy and the capabilities of mobile robots greatly increases the number of applications suitable for a team of autonomous agents. Particular interest has been received by those tasks requiring continual execution, such as the monitoring of oil spills, the detection of forest fires, the track of border changes, and the patrol (surveillance) of an environment. There is a widespread belief that continuous and pervasive monitoring will be possible in the near future with large numbers of networked, mobile, and wireless sensors. Thus, we are witnessing an intense research activity that focuses on the design of efficient control mechanisms for these systems. In particular, decentralized algorithms would allow mobile sensor networks to react autonomously to changes in the environment with minimal human supervision. A substantial body of research on mobile sensor networks has concentrated on the surveillance of an area of interest requires the robots to continuously and repeatedly cover the environment. The main objective of area coverage problem is how to monitor the whole area of the network with respect to different performance criteria such as coverage ratio, minimum number of sensors providing desired coverage level during the maximum lifetime of the network. Here, robots could use a Voronoi-based coverage control framework to distribute themselves across the environment.

Figure 2: Gershgorin disks for a randomly generated  4 by 4 complex matrix

Figure 3:  Voronoi-based area coverage for a group of agents

Observer Design and Identification Methods

State-dependent Riccati equation (SDRE) filtering techniques have been extensively used for nonlinear state/parameter estimation within a wide range of applications. The standard SDRE filter, which is set up by direct SDC parameterization, demands complete knowledge of the system model, and the disturbance inputs characteristics, which severely  degrade its performance in practical applications. We proposed a robust SDRE filter based on the H_infinity norm minimization criterion, to effectively estimate the states of nonlinear uncertain systems exposed to unknown disturbance inputs. Extension of this work in considered for exponential stability, and in stochastic domain.

Currently, for highly uncertain models the proposed robust SDRE is combined with a switching algorithm. The theoretical development of this filter and its robustness analysis is reviewed and its implementation on the uncertain nonlinear model of Lithium-Ion battery is considered. The stimulation and the implementation results verify the efficiency of the extended filter, which is quite promising to be implemented on other nonlinear and uncertain plants.

Figure 4: Generic functional block diagram of SDRE Architecture with Built-in Parameter Estimator

Brain Computer Interface (BCI)

Brain-computer interface (BCI) establish a connection between the brain activities and robotic systems through converting the brain signals into perceptible control signals for machines. Such a system has been a specific area of interest in order to provide interaction of people with disabilities with the surrounding environment. Using the system, the brain patterns for a certain type of behavior is obtained and the related control commands is produced. This control signal represents a specific neuro-behavior of the brain and can be used in BCI systems. From the EEG signals, SSVEP may be retracted as a specific type of control signal which is produced at the occipital lobe of the brain in response to an external oscillating stimulus. The frequency of this signal is matched with the frequency of the input stimuli that can be identified using EEG test, which is the focus of the current research.

As the brain signals are the neurological reaction of the individuals to stimulus signals it is crucial to design a suitable stimulus system as well as investigation of its effectiveness. In our research group, a suitable visual stimulus system is designed and implemented, and its effectiveness is proved through experiments. Various statistical and pattern identification methods such as CCA, MSI and MEC for coding the main characteristics of the SSVEP signals are implemented in the test bed by recording data of several individuals. For having a physical perception of the BCI system a robotic arm is used. An integrated system comprising the robotic arm and commercial Emotiv Brainwear® is developed and the final implementation is performed on the robotic arm. The experimental results on different subjects shoes the promising horizons of using such technology for disabled people.

Figure 5 : Control of the Avatar by EEG signal

Ala Shariati

Researcher
APAC research group

Maysam Z. Pedram

K.N. Toosi University of Technology

Noushin Poursafar

Ph.D. Student
University of Sydney, Australia

Ali Salamati

Researcher
Niroo Research Center

Hossein Beikzadeh

Researcher
Bombardier Inc. canada

Arsalan Rahimabadi

Freelancer
Advanced Robotics and Automated Systems (ARAS)

Soheil Kianzad

PhD student
University of British Columbia, Canada

Related Publications

TitleAbstractYearTypePDF
Two PID-Based Controllers for a tethered Segway on Dome Shaped StructuresThe UTDTR Robot is a human inspired robotic platform based on a two-wheeled mobile robot. This robot is designed for the purpose of dome shaped structures inspection and maintenance, and it is a tethered robot to stably climb steep surfaces on the top of dome structures. In this paper analysis and controller design of this robot modelled as a MIMO system is represented in order to provide the desired performance on the operating surface with minimum control effort and complexity. Two PID-based controllers are designed such that the stability and desired performance conditions are obtained. In the first design a fuzzy PID controller with self-tuning scale factors is designed to tune the controller gains is forwarded, while in the second approach a multi model gain scheduling controller based on conventional PID controller is considered. Finally, the effectiveness and simplicity of the proposed controller is verified through simulation, comparing the resulting closed loop transient and steady-state response to that of the previously proposed controllers.2018ConferencePDF
Brain Computer Interface Control of a Virtual Robotic System based on SSVEP and EEG SignalIn brain computer interface (BCI) systems the brain patterns for a certain type of behaviour is extracted and the corresponding control commands are produced in order to control an external apparatus. SSVEP is a specific type of such control signal which is produced at the occipital lobe of the brain in response to an external oscillating stimulus. As the brain signals in SSVEP based BCI are the neurological reaction of the individuals to the presented stimulus, it is crucial to design a suitable stimulus system as well as investigation of its effectiveness. In this paper a suitable visual stimulus is designed and implemented, and its effectiveness to control the motion of a robot on a virtual robotic system is verified based on experiments. An online integrated system comprising of a virtual industrial robotic manipulator, an EEG deployment and statistical feature extraction method is developed and real time experiments to verify its accuracy and effectiveness is experimented on different subjects. The experiments shows the promising features of the developed systems for further applications.2017ConferencePDF
Two PID-Based Controllers for a tethered Segway on Dome Shaped StructuresThe UTDTR Robot is a human inspired robotic platform based on a two-wheeled mobile robot. This robot is designed for the purpose of dome shaped structures inspection and maintenance, and it is a tethered robot to stably climb steep surfaces on the top of dome structures. In this paper analysis and controller design of this robot modelled as a MIMO system is represented in order to provide the desired performance on the operating surface with minimum control effort and complexity. Two PID-based controllers are designed such that the stability and desired performance conditions are obtained. In the first design a fuzzy PID controller with self-tuning scale factors is designed to tune the controller gains is forwarded, while in the second approach a multi model gain scheduling controller based on conventional PID controller is considered. Finally, the effectiveness and simplicity of the proposed controller is verified through simulation, comparing the resulting closed loop transient and steady-state response to that of the previously proposed controllers.2017ConferencePDF
Comment on: “Centers of quasi-homogeneous polynomial planar systems”We describe a counter-example which shows that of theorem in Algaba et al. (2012) is not correct. This part of the theorem, pinpoints whether the origin of quasi-homogeneous system in Algaba et al. (2012) is a center or not. It is shown in this note that the given necessary and sufficient conditions of theorem, in Algaba et al. (2012) are not complete.2017JournalPDF
Design of a Robust Controller for a Tethered Segway on Dome-Shaped StructuresTethered Segway is a robotic platform inspired by human climbers. It is a two-wheeled mobile platform tethered to the top of a structure in order to climb steep surfaces with varying slopes, such as domes. The unstructured environment may cause uncertainties in the dynamic behavior of the robot while operating on different parts of the dome. In this paper analysis and synthesis of a robust controller for a tethered Segway is presented in order to provide desired performance in the presence of uncertainties. To design the robust controller, structured and unstructured uncertainties of the model are encapsulated into a structured singular perturbation. A linear robust controller is designed such that the robust stability of the closed loop system is preserved in the presence of modeling uncertainties. Finally, the effectiveness of the proposed controller is verified through simulation by comparing its closed loop transient response and sufficiently suitable steady-state performance to that of a previously proposed LQR controller for the robot.2016ConferencePDF
Reigon of Convergence Expansion of a Robust Model Predictive ControllerIn this paper a gain scheduling method is proposed for robust model predictive control of a useful class of nonlinear discrete-time systems. The system is composed of a linear model perturbed by an additive state-dependent nonlinear term. Robust model predictive controllers are designed in the literature to compensate for the uncertainty of the system. In order to enlarge the region of convergence it is assumed that system has several equilibrium points and multiple robust controllers are designed. By switching between the controllers it is verified that the region of convergence shall be enlarged, while the overall stability of the system is preserved. In the proposed method, the stability analysis based on Lyapunov functions for each level set is performed, while state feedback control law is designed by minimization of a desired cost function formed in linear matrix inequalities. The simulation results show the applicability of the proposed method.2015ConferencePDF
Corner stability in nonlinear autonomous systemsIn most practical applications, studying the asymptotic stability of equilibrium points of a system is of utmost importance. Furthermore, in many cases, the response is restricted to only a sector of the state space. For example, positive systems that are common in chemical processes have nonnegative state variables. For such systems, stability analysis of the system using Lyapunov stability is not advised, since this stability is defined for all the points within a neighborhood of the equilibrium point. In this paper, a new notion of stability, called corner stability, is defined as more suitable for studying asymptotic stability of equilibrium points in such systems. In order to derive sufficient conditions of corner stability, a theorem is stated and proven in this paper, and corner stability of three case studies is analyzed and verified.2015JournalPDF
Robust Control of a Steam Turbine Power Based on a Precise Nonlinear ModelIn this paper, a precise and nonlinear model is developed for Nekka power plant turbine from its experimental data and documents. It is proposed to use boiler-turbine coordinated control system to increase effective efficiency of the steam unit. Identification procedures have been performed to obtain continuous time models of Nekka steam turbine at various loads. After determining the upper bound for uncertainty and choosing a good performance weighting function, a robust controller has been designed and implemented in closed loop for the turbine nonlinear model. Since the closed loop performance was not as required, a cascade controller structure is proposed, in which the turbine loop is closed by a PI controller in order to significantly reduce the uncertainty. Simulation results demonstrate the suitable performance of the closed loop in terms of tracking, speed of response, and damping of oscillations.2014ConferencePDF
A neutral system approach to H-Infinity PD/PI controller design of processes with uncertain input delayThis paper presents a neutral system approach to the design of an H? controller for input delay systems in presence of uncertain time-invariant delay. It is shown that when proportional derivative (PD) controller is applied to a time-delay system, the resulting closed loop system is generally a time-delay system of neutral type with delay term coefficients depending on the controller parameters. A descriptor model transformation is used to derive an advantageous bounded real lemma representation for the system. Furthermore, new delay-dependent sufficient conditions for the existence of an H? PD and PI controller in presence of uncertain delay are derived in terms of matrix inequalities. Some case studies and numerical examples are given in order to illustrate the advantages of the proposed method.2014JournalPDF
PD Controller Design with H-Infinity Performance for Linear Systems with Input DelayThis paper considers H-Infinity control problem for input-delayed systems for time-varying delays. A proportional-derivative state feedback control law is used in this paper. By this means, the resulting closed-loop system turns into a specific time-delay system of neutral type. The significant specification of this neutral system is that its delayed term coefficients depend on the controller parameters. This condition provides new challenging issues in theoretical research as well as providing new applications. In the present paper, new delay-dependent sufficient condition is derived for the existence of H-Infinity controller in terms of matrix inequalities, in presence of varying time-delays. The resulting H-Infinity controller guarantees asymptotic stability of the closed-loop system as well as a guaranteed limited system induced norm smaller than a prescribed level. Numerical examples are presented to illustrate the effectiveness of the proposed method.2012JournalPDF
Delay-Dependent H-Infinity Control of Linear Systems with Uncertain Input Delay Using State-Derivative FeedbackIn some practical problems such as active vibration suppression systems, the state-derivative signals are easier to access than the state variables. This paper considers an H-Infinity -based state-derivative feedback control problem for input-delayed systems. Applying this control law, the resulting closed-loop system turns into a specific time-delay system of neutral type. The significant specification of this neutral system is that its delayed term coefficients depend on the controller parameters. The time-delay is considered as uncertain time-invariant with a known constant bound. In this paper, the delay-dependent sufficient conditions for the existence of an H-Infinity state-derivative feedback controller are derived in terms of matrix inequalities. The resulting H-Infinity controller stabilizes the closed-loop neutral system and assures that the H-Infinity -norm to be less than a prescribed level. An application example is presented to illustrate the effectiveness of the proposed method.2012JournalPDF
Delay-Independent Robust Stability Analysis of TeleoperationThis paper considers the robust stability of uncertain teleoperation systems. Sufficient stability conditions are derived in terms of LMI by representing the teleoperation scheme in retarded form of time-delay systems. By choosing Lyapunov-Krasovski functional, a delay-independent robust stability criterion is presented. We show that the teleoperation system is stable and has good performance under specific LMI condition. With the given controller parameters, stability of system is guaranteed in the presence of any value of delay and admissible uncertainty. To evaluate the theoretical analysis, Numerical simulations are performed.2011ConferencePDF
Delay-Independent Stability Analysis of Internet-based Tele-operationThis paper presents a sufficient stability condition for internet-based tele-operation systems in terms of LMI. The tele-operation scheme is modeled in state-space as a time-delay system in retarded form and a delay-independent stability criterion is extracted. By choosing Lyapunov-Krasovski functional, we show that the internet-based tele-operation system is stable and has good performance under specific LMI condition. With the given controller design parameters, stability of system is guaranteed in the presence of any value of delay. Numerical simulations are performed to verify the theoretical results.2011ConferencePDF
Robust Internal Model Control for Impulse Elimination of Singular SystemsIn this paper the problem of model based internal control of singular systems is investigated. The limitations of directly extending the control schemes for normal systems to singular ones are thoroughly developed, and a robust approach is proposed in order to establish a control scheme for singular systems. The proposed method presents a general framework for robust control design of singular systems in presence of modeling uncertainties. Two simulation examples are given to how the proposed method can be implemented, and to show the effectiveness of such controllers in closed loop performance.2011JournalPDF
Adaptive Robust Controller Design For Non-minimum Phase SystemsBased on the synthesis algorithm of dynamical backstepping design procedure, in this paper a new adaptive robust approach for non-minimum phase systems is proposed. The proposed controller consists of two parts; a backstepping controller as the robust part and a model reference (MRAS) controller as the adaptive part. In this control scheme the daptive part acts not only as a medium to converge to suitable values for the unknown parameters and to reduce the uncertainty, but also provides a minimum-phase model for the robust controller to be well stabilized. A simulation case study is studied to show how to perform the proposed control law, and to illustrate the effectiveness of this method compared to that of conventional robust controllers.2011ConferencePDF
Robust Internal Model Control For Impulse Elimination of Singular SystemsIn this paper the problem of model based internal control of singular systems is investigated. The limitations of directly extending the control schemes for normal systems to singular ones are thoroughly developed, and a robust approach is proposed in order to establish a control scheme for singular systems. The proposed method presents a general framework for robust control design of singular systems in presence of modeling uncertainties. Two simulation examples are given to how the proposed method can be implemented, and to show the effectiveness of such controllers in closed loop performance.2011ConferencePDF
Descriptor Approach to Unknown Input PI Observer Design:application to fault detectionThe descriptor observer approach is improved further to a more suitable observer scheme which is applicable to a more general group of faults and systems. Also a disturbance decoupling scheme is added to the mentioned observer in order to enable the observer to distinguish faults from disturbances.2010ConferencePDF
Unknown Input-Proportional Integral Observer for Singular Systems: Application to fault detectionA new approach to the observer design for descriptor continuous time systems is proposed and its application in the fault diagnosis problem is illustrated. In this observer, two features of disturbance decoupling and fault estimation are combined. Also a more general frame for fault estimation is used. Some numerical examples and simulation results are shown to justify the effectiveness of the algorithm.2010ConferencePDF
Model predictive control of non-linear discrete time systems: a linear matrix inequality approachUsing a non-linear model in model predictive control (MPC) changes the control problem from a convex quadratic programme to a non-convex non-linear problem, which is much more challenging to solve. In this study, we introduce an MPC algorithm for non-linear discrete-time systems. The systems are composed of a linear constant part perturbed by an additive state-dependent non-linear term. The control objective is to design a state-feedback control law that minimises an infinite horizon cost function within the framework of linear matrix inequalities. In particular, it is shown that the solution of the optimisation problem can stabilise the non-linear plants. Three extensions, namely, application to systems with input delay, non-linear output tracking and using output-feedback, are followed naturally from the proposed formulation. The performance and effectiveness of the proposed controller is illustrated with numerical examples.2010JournalPDF
Disturbance Retrieving Unknown Input Proportional Integral Observer for Generalized Linear SystemsAn unknown input retrieving observer scheme is proposed which not only decouples unknown inputs in estimation but also gives an estimation of the decoupled input. The provided method benefits from its low computational cost as well as its less restrictive existence conditions compared to existing ones.2010ConferencePDF
Delay-Dependent H-Infinity Control of Linear Systems with input Delay Using Composite State-Derivative FeedbackH-Infinity control problem for input-delayed systems is considered in this paper. A composite state-derivative control law is used, in which, a composition of the state variables and their derivatives appear in the control law. Thus, the resulting closed-loop system turns into a specific time-delay system of neutral type. The significant specification of this neutral system is that its delayed term coefficients depend on the control law parameters. This condition provides new challenging issues which has its own merits in theoretical research as well as application aspects. New delay-dependent sufficient condition for the existence of H ? controller in terms of matrix inequalities is derived in the present paper. The resulting H-Infinity controller guarantees asymptotic stability of the closed-loop system as well as a guaranteed limited H ? norm smaller than a prescribed level. Numerical examples are presented to illustrate the effectiveness of the proposed methods.2010ConferencePDF
Delay-Dependent H-Infinity Control of Linear Systems with Time-Varying Delays Using Proportional-Derivative State FeedbackThis paper considers H-Infinity control problem for input-delayed systems for time-varying delays. A proportional-derivative state feedback control law is used in this paper. By this means, the resulting closed-loop system turns into a specific time-delay system of neutral type. The significant specification of this neutral system is that its delayed term coefficients depend on the controller parameters. This condition provides new challenging issues in theoretical research as well as providing new applications. In the present paper, new delay-dependent sufficient condition is derived for the existence of H-Infinity controller in terms of matrix inequalities, in presence of varying time-delays. The resulting H-Infinity controller guarantees asymptotic stability of the closed-loop system as well as a guaranteed limited system induced norm smaller than a prescribed level. Numerical examples are presented to illustrate the effectiveness of the proposed method.2010ConferencePDF
Delay-Dependent Stabilization of Linear Input-Delayed Systems with Composite State-Derivative Feedback: Constant and Time-Varying DelaysThis paper considers stability problem for input- delayed systems for both constant and time-varying delay case. A new composite state-derivative control law is introduced, in which, a composition of the state variables and their derivatives appear in control law. By this means, the resulting closed-loop system becomes a particular time-delay system of neutral type. The significant specification of this neutral system is that its delayed term coefficients depend on the control law's parameters. This condition provides new challenging issues which has its own merits in theoretical as well as practical aspects. In the present paper, new delay-dependent sufficient conditions are derived in presence of both constant and varying time-delay in terms of matrix inequalities. The resulting controllers guarantee asymptotic stability of the closed-loop system. Simulation studies are presented to verify the stability conditions obtained within the theorems.2009ConferencePDF
A New Sensorless Vector Control Method for Permanent Magnet Synchronus Motor Without Velocity EstimatiorIn this paper, a novel vector control method for permanent magnet synchronous motors is presented. In this method, the velocity estimation is completely removed and vector control is accomplished in a new coordinate system. In conventional vector control methods, the control effort is calculated in rotating coordinates with a synchronous speed of omega. However, in the proposed method, the control effort is calculated in rotating coordinates with reference speed omega. This change of coordinate decreases the calculation effort significantly. In order to verify the applicability of the proposed control law, a Lyapunov-based stability condition is derived and the performance of the controller is verified through simulations and experiments. The obtained results illustrate the effectiveness of the proposed method despite the simplicity of its implementation.2002ConferencePDF
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