Andrzej Manitius - Profile on Academia.edu (original) (raw)

Papers by Andrzej Manitius

Optimal control of hereditary systems

A systems identification approach to estimating the connectivity in a neuronal population model

Mapping the brain and its complex networked structure has been one of the most researched topics ... more Mapping the brain and its complex networked structure has been one of the most researched topics in the last decade and continues to be the path towards understanding brain diseases. In this paper we present a new approach to estimating the connectivity between neurons in a network model. We use systems identification techniques for nonlinear dynamic models to compute the synaptic connections from other pre-synaptic neurons in the population. We are able to show accurate estimation even in the presence of model error and inaccurate assumption of post-synaptic potential dynamics. This allows to compute the connectivity matrix of the network using a very small time window of membrane potential data of the individual neurons. The specificity and sensitivity measures for randomly generated networks are reported.

The increasing need of knowledge in the treatment of brain diseases has driven a huge interest in... more The increasing need of knowledge in the treatment of brain diseases has driven a huge interest in understanding the phenomenon of neural spiking. Researchers have successfully been able to create mathematical models which, with specific parameters, are able to reproduce the experimental neuronal responses. The spiking activity is characterized using spike trains and it is essential to develop methods for parameter estimation that rely solely on the spike times or interspike intervals (ISI). In this paper we describe a new technique for optimization of a single neuron model using an experimental spike train from a biological neuron. We are able to fit model parameters using the gradient descent method. The optimized model is then used to predict the activity of the biological neuron and the performance is quantified using a spike distance measure.

Estimation of connections in a hybrid neuronal network

Journal | MESA, Feb 28, 2016

The paper describes a new method of reconstructing the connections in a neuronal network based on... more The paper describes a new method of reconstructing the connections in a neuronal network based on a simulation using the Izhikevich hybrid model of a neuron expressed by nonlinear differential equations with jump discontinuities. The estimation of synaptical connections is accomplished by using an Unscented Kalman Filter to first synchronize the spiking in the network model with the observed impulses in membrane potentials and then using the recursive least-squares method to estimate the strength of each connection. The algorithm was tested on data generated by the Hodgkin-Huxley models and Hindmarsh-Rose models. The algorithm produced results for networks of sizes up to 70 neurons, and was able to accurately capture and track the changes in the connectivity.

Dynamical observer for a flexible beam via finite element approximations

ABSTRACT The purpose of this view-graph presentation is a computational investigation of the clos... more ABSTRACT The purpose of this view-graph presentation is a computational investigation of the closed-loop output feedback control of a Euler-Bernoulli beam based on finite element approximation. The observer is part of the classical observer plus state feedback control, but it is finite-dimensional. In the theoretical work on the subject it is assumed (and sometimes proved) that increasing the number of finite elements will improve accuracy of the control. In applications, this may be difficult to achieve because of numerical problems. The main difficulty in computing the observer and simulating its work is the presence of high frequency eigenvalues in the finite-element model and poor numerical conditioning of some of the system matrices (e.g. poor observability properties) when the dimension of the approximating system increases. This work dealt with some of these difficulties.

A new technique to optimize single neuron models using experimental spike train data

ABSTRACT We propose a new method for fitting model parameters to the neural spike train obtained ... more ABSTRACT We propose a new method for fitting model parameters to the neural spike train obtained from an experimental neuron. Due to the uncertainty associated with measuring the accurate voltage in a noisy environment, it is essential to develop methods that rely solely on the interspike intervals (ISI). Existing techniques do not provide a smooth and continuous cost function and optimal estimation of model parameters is difficult. In this paper we formulate a new cost function using the spike times of the neuron and determine the analytical gradient with respect to the model parameters. The optimal parameters are calculated using gradient based optimization techniques. We first use data generated by models to establish the accuracy of our technique. We also optimize the model to fit an experimental spike train of a biological neuron. We are able to find the optimal parameter set using a hybrid algorithm which is a combination of the gradient descent method and global optimization techniques.

Differentiability and Convergence Rates of Approximating Semigroups for Retarded Functional Differential Equations

SIAM Journal on Numerical Analysis, 1988

In this paper the averaging approximations (i.e., semidiscrete finite-difference scheme) for line... more In this paper the averaging approximations (i.e., semidiscrete finite-difference scheme) for linear retarded functional differential equations are considered in the context of the semigroups on the Hilbert space RntimesL2R^n \times L^2 RntimesL2. It is shown that the approximating semigroups are all differentiable uniformly with respect to the index N determining the mesh size. This fact makes it possible to prove the existence of a uniform exponential decay (or growth) rate for the approximating semigroups, which can be made arbitrarily close to the decay (respectively, growth) rate of the original semigroup. More importantly, the uniform differentiability makes it possible to establish convergence rates that improve with time, and to prove the convergence of the approximating semigroups in the uniform operator topology. The dependence of the convergence rate on the initial conditions and system parameters is also established.

An application of a finite spectrum assignment technique to the design of control laws for a wind tunnel

1982 21st IEEE Conference on Decision and Control, 1982

ABSTRACT An application of a finite spectrum assignment method for time-delay systems to a feedba... more ABSTRACT An application of a finite spectrum assignment method for time-delay systems to a feedback control of Mach number in a wind tunnel is presented. The linearized model of Mach number control is a system of three state equations with a delay in one of the state variables. The proposed feedback is a linear combination of state variables and weighted integrals of some of the state variables over a period equal to time delay. The spectrum of the closed loop system is finite and consists of three eigenvalues that can be placed arbitrarily. Four possible variants of the feedback control law are presented. The calculation of feedback coefficients is very simple. Systems dynamics and feedback laws were simulated numerically.

Computational approach to synthesis of feedback controllers for multivariable systems with delays

1974 IEEE Conference on Decision and Control including the 13th Symposium on Adaptive Processes, 1974

ABSTRACT We shall discuss techniques for the design of feedback controllers for multivariable sys... more ABSTRACT We shall discuss techniques for the design of feedback controllers for multivariable systems with delays. First, techniques for the design of feed-back controllers using the linear-quadratic theory will be presented. Applicability of a new method based on "spectral decomposition" for delay systems will be considered.

Commandabilite des systèmes retardes du point de vue des semi-groupes d’opérateurs

Annales des Sciences Mathematiques du Quebec

Convergence of Projection Series for Functional Differential Equations with Applications to Control Theory

Optimal Control Theory and its Applications, 1974

This paper presents several new results, obtained recently by the authors, for the problem of con... more This paper presents several new results, obtained recently by the authors, for the problem of convergence of projection series for linear retarded functional differential equations (FDE) and for the application of this series to optimal control problems involving FDE’s with boundary conditions in function space.

Joint node H/sub ∞/ control synthesis for connected flexible beams

Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171)

ABSTRACT Describes a method of stabilizing an interconnected system of Timoshenko beams by using ... more ABSTRACT Describes a method of stabilizing an interconnected system of Timoshenko beams by using a finite dimensional model of a Timoshenko beam along with an H∞ control design. The control consists of two types of control: a robust control at the joint nodes (common nodes) of the beams, and local control for each beam after the H ∞ control has been applied at the joint nodes. Based on simulations, we observe that a fast decay rate for vibrations and smooth transients can be achieved. The example shown in the paper is the known “carpenter square” of two beams joined at a common node

Finite dimensional approximations for functional differential equations with input and output delays

29th IEEE Conference on Decision and Control, 1990

ABSTRACT The authors present some results on the numerical approximations for linear retarded fun... more ABSTRACT The authors present some results on the numerical approximations for linear retarded functional differential equations with delays in control and observation. Specifically, they consider the averaging approximation scheme for such systems treated as evolution equations with unbounded input and output operators in the state space set-up developed by A.J. Pritchard and D. Salamon (Technical Report no.2624, Mathematics Research Center, University of Wisconsin, Madison, WI, 1984)

Control Theory

Encyclopedia of Operations Research and Management Science

Dynamical observer for a flexible beam via finite element approximations

The purpose of this view-graph presentation is a computational investigation of the closed-loop o... more The purpose of this view-graph presentation is a computational investigation of the closed-loop output feedback control of a Euler-Bernoulli beam based on finite element approximation. The observer is part of the classical observer plus state feedback control, but it is finite-dimensional. In the theoretical work on the subject it is assumed (and sometimes proved) that increasing the number of finite elements will improve accuracy of the control. In applications, this may be difficult to achieve because of numerical problems. The main difficulty in computing the observer and simulating its work is the presence of high frequency eigenvalues in the finite-element model and poor numerical conditioning of some of the system matrices (e.g. poor observability properties) when the dimension of the approximating system increases. This work dealt with some of these difficulties.

Conference proceedings : ... Annual International Conference of the IEEE Engineering in Medicine and Biology Society. IEEE Engineering in Medicine and Biology Society. Annual Conference, 2012

The increasing need of knowledge in the treatment of brain diseases has driven a huge interest in... more The increasing need of knowledge in the treatment of brain diseases has driven a huge interest in understanding the phenomenon of neural spiking. Researchers have successfully been able to create mathematical models which, with specific parameters, are able to reproduce the experimental neuronal responses. The spiking activity is characterized using spike trains and it is essential to develop methods for parameter estimation that rely solely on the spike times or interspike intervals (ISI). In this paper we describe a new technique for optimization of a single neuron model using an experimental spike train from a biological neuron. We are able to fit model parameters using the gradient descent method. The optimized model is then used to predict the activity of the biological neuron and the performance is quantified using a spike distance measure.

A systems identification approach to estimating the connectivity in a neuronal population model

2014 36th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, 2014

Mapping the brain and its complex networked structure has been one of the most researched topics ... more Mapping the brain and its complex networked structure has been one of the most researched topics in the last decade and continues to be the path towards understanding brain diseases. In this paper we present a new approach to estimating the connectivity between neurons in a network model. We use systems identification techniques for nonlinear dynamic models to compute the synaptic connections from other pre-synaptic neurons in the population. We are able to show accurate estimation even in the presence of model error and inaccurate assumption of post-synaptic potential dynamics. This allows to compute the connectivity matrix of the network using a very small time window of membrane potential data of the individual neurons. The specificity and sensitivity measures for randomly generated networks are reported.

A new technique to optimize single neuron models using experimental spike train data

2013 American Control Conference, 2013

ABSTRACT We propose a new method for fitting model parameters to the neural spike train obtained ... more ABSTRACT We propose a new method for fitting model parameters to the neural spike train obtained from an experimental neuron. Due to the uncertainty associated with measuring the accurate voltage in a noisy environment, it is essential to develop methods that rely solely on the interspike intervals (ISI). Existing techniques do not provide a smooth and continuous cost function and optimal estimation of model parameters is difficult. In this paper we formulate a new cost function using the spike times of the neuron and determine the analytical gradient with respect to the model parameters. The optimal parameters are calculated using gradient based optimization techniques. We first use data generated by models to establish the accuracy of our technique. We also optimize the model to fit an experimental spike train of a biological neuron. We are able to find the optimal parameter set using a hybrid algorithm which is a combination of the gradient descent method and global optimization techniques.

On the numerical approximations for linear functional differential equations with input and output delays

1985 24th IEEE Conference on Decision and Control, 1985

ABSTRACT In this paper we state some new results on the approximations for linear retarded functi... more ABSTRACT In this paper we state some new results on the approximations for linear retarded functional differential equations with delays in control and observation. We consider the finite difference (i.e., averaging) approximation scheme for such systems treated as evolution equations in the state space setup, and we establish several basic properties of the approximation scheme. These results are extensions of recent results of Lasiecka and ManitiusL1 to the case of systems with input and output delays.

On spectral controllability of multi-input time-delay systems

Systems & Control Letters, 1985

ABSTRACT It is proved that under certain verifiable conditions, spectral controllability of a lin... more ABSTRACT It is proved that under certain verifiable conditions, spectral controllability of a linear system with commensurate state delays and with m inputs, m > 1, implies the existence of an n × 1 vector b contained in the image of the control matrix B such that the system with B replaced by b is spectrally controllable. Both the necessity and the sufficiency of these conditions are shown, a procedure to construct b is given, and an example is discussed.

Optimal control of hereditary systems

A systems identification approach to estimating the connectivity in a neuronal population model

Mapping the brain and its complex networked structure has been one of the most researched topics ... more Mapping the brain and its complex networked structure has been one of the most researched topics in the last decade and continues to be the path towards understanding brain diseases. In this paper we present a new approach to estimating the connectivity between neurons in a network model. We use systems identification techniques for nonlinear dynamic models to compute the synaptic connections from other pre-synaptic neurons in the population. We are able to show accurate estimation even in the presence of model error and inaccurate assumption of post-synaptic potential dynamics. This allows to compute the connectivity matrix of the network using a very small time window of membrane potential data of the individual neurons. The specificity and sensitivity measures for randomly generated networks are reported.

The increasing need of knowledge in the treatment of brain diseases has driven a huge interest in... more The increasing need of knowledge in the treatment of brain diseases has driven a huge interest in understanding the phenomenon of neural spiking. Researchers have successfully been able to create mathematical models which, with specific parameters, are able to reproduce the experimental neuronal responses. The spiking activity is characterized using spike trains and it is essential to develop methods for parameter estimation that rely solely on the spike times or interspike intervals (ISI). In this paper we describe a new technique for optimization of a single neuron model using an experimental spike train from a biological neuron. We are able to fit model parameters using the gradient descent method. The optimized model is then used to predict the activity of the biological neuron and the performance is quantified using a spike distance measure.

Estimation of connections in a hybrid neuronal network

Journal | MESA, Feb 28, 2016

The paper describes a new method of reconstructing the connections in a neuronal network based on... more The paper describes a new method of reconstructing the connections in a neuronal network based on a simulation using the Izhikevich hybrid model of a neuron expressed by nonlinear differential equations with jump discontinuities. The estimation of synaptical connections is accomplished by using an Unscented Kalman Filter to first synchronize the spiking in the network model with the observed impulses in membrane potentials and then using the recursive least-squares method to estimate the strength of each connection. The algorithm was tested on data generated by the Hodgkin-Huxley models and Hindmarsh-Rose models. The algorithm produced results for networks of sizes up to 70 neurons, and was able to accurately capture and track the changes in the connectivity.

Dynamical observer for a flexible beam via finite element approximations

ABSTRACT The purpose of this view-graph presentation is a computational investigation of the clos... more ABSTRACT The purpose of this view-graph presentation is a computational investigation of the closed-loop output feedback control of a Euler-Bernoulli beam based on finite element approximation. The observer is part of the classical observer plus state feedback control, but it is finite-dimensional. In the theoretical work on the subject it is assumed (and sometimes proved) that increasing the number of finite elements will improve accuracy of the control. In applications, this may be difficult to achieve because of numerical problems. The main difficulty in computing the observer and simulating its work is the presence of high frequency eigenvalues in the finite-element model and poor numerical conditioning of some of the system matrices (e.g. poor observability properties) when the dimension of the approximating system increases. This work dealt with some of these difficulties.

A new technique to optimize single neuron models using experimental spike train data

ABSTRACT We propose a new method for fitting model parameters to the neural spike train obtained ... more ABSTRACT We propose a new method for fitting model parameters to the neural spike train obtained from an experimental neuron. Due to the uncertainty associated with measuring the accurate voltage in a noisy environment, it is essential to develop methods that rely solely on the interspike intervals (ISI). Existing techniques do not provide a smooth and continuous cost function and optimal estimation of model parameters is difficult. In this paper we formulate a new cost function using the spike times of the neuron and determine the analytical gradient with respect to the model parameters. The optimal parameters are calculated using gradient based optimization techniques. We first use data generated by models to establish the accuracy of our technique. We also optimize the model to fit an experimental spike train of a biological neuron. We are able to find the optimal parameter set using a hybrid algorithm which is a combination of the gradient descent method and global optimization techniques.

Differentiability and Convergence Rates of Approximating Semigroups for Retarded Functional Differential Equations

SIAM Journal on Numerical Analysis, 1988

In this paper the averaging approximations (i.e., semidiscrete finite-difference scheme) for line... more In this paper the averaging approximations (i.e., semidiscrete finite-difference scheme) for linear retarded functional differential equations are considered in the context of the semigroups on the Hilbert space RntimesL2R^n \times L^2 RntimesL2. It is shown that the approximating semigroups are all differentiable uniformly with respect to the index N determining the mesh size. This fact makes it possible to prove the existence of a uniform exponential decay (or growth) rate for the approximating semigroups, which can be made arbitrarily close to the decay (respectively, growth) rate of the original semigroup. More importantly, the uniform differentiability makes it possible to establish convergence rates that improve with time, and to prove the convergence of the approximating semigroups in the uniform operator topology. The dependence of the convergence rate on the initial conditions and system parameters is also established.

An application of a finite spectrum assignment technique to the design of control laws for a wind tunnel

1982 21st IEEE Conference on Decision and Control, 1982

ABSTRACT An application of a finite spectrum assignment method for time-delay systems to a feedba... more ABSTRACT An application of a finite spectrum assignment method for time-delay systems to a feedback control of Mach number in a wind tunnel is presented. The linearized model of Mach number control is a system of three state equations with a delay in one of the state variables. The proposed feedback is a linear combination of state variables and weighted integrals of some of the state variables over a period equal to time delay. The spectrum of the closed loop system is finite and consists of three eigenvalues that can be placed arbitrarily. Four possible variants of the feedback control law are presented. The calculation of feedback coefficients is very simple. Systems dynamics and feedback laws were simulated numerically.

Computational approach to synthesis of feedback controllers for multivariable systems with delays

1974 IEEE Conference on Decision and Control including the 13th Symposium on Adaptive Processes, 1974

ABSTRACT We shall discuss techniques for the design of feedback controllers for multivariable sys... more ABSTRACT We shall discuss techniques for the design of feedback controllers for multivariable systems with delays. First, techniques for the design of feed-back controllers using the linear-quadratic theory will be presented. Applicability of a new method based on "spectral decomposition" for delay systems will be considered.

Commandabilite des systèmes retardes du point de vue des semi-groupes d’opérateurs

Annales des Sciences Mathematiques du Quebec

Convergence of Projection Series for Functional Differential Equations with Applications to Control Theory

Optimal Control Theory and its Applications, 1974

This paper presents several new results, obtained recently by the authors, for the problem of con... more This paper presents several new results, obtained recently by the authors, for the problem of convergence of projection series for linear retarded functional differential equations (FDE) and for the application of this series to optimal control problems involving FDE’s with boundary conditions in function space.

Joint node H/sub ∞/ control synthesis for connected flexible beams

Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171)

ABSTRACT Describes a method of stabilizing an interconnected system of Timoshenko beams by using ... more ABSTRACT Describes a method of stabilizing an interconnected system of Timoshenko beams by using a finite dimensional model of a Timoshenko beam along with an H∞ control design. The control consists of two types of control: a robust control at the joint nodes (common nodes) of the beams, and local control for each beam after the H ∞ control has been applied at the joint nodes. Based on simulations, we observe that a fast decay rate for vibrations and smooth transients can be achieved. The example shown in the paper is the known “carpenter square” of two beams joined at a common node

Finite dimensional approximations for functional differential equations with input and output delays

29th IEEE Conference on Decision and Control, 1990

ABSTRACT The authors present some results on the numerical approximations for linear retarded fun... more ABSTRACT The authors present some results on the numerical approximations for linear retarded functional differential equations with delays in control and observation. Specifically, they consider the averaging approximation scheme for such systems treated as evolution equations with unbounded input and output operators in the state space set-up developed by A.J. Pritchard and D. Salamon (Technical Report no.2624, Mathematics Research Center, University of Wisconsin, Madison, WI, 1984)

Control Theory

Encyclopedia of Operations Research and Management Science

Dynamical observer for a flexible beam via finite element approximations

The purpose of this view-graph presentation is a computational investigation of the closed-loop o... more The purpose of this view-graph presentation is a computational investigation of the closed-loop output feedback control of a Euler-Bernoulli beam based on finite element approximation. The observer is part of the classical observer plus state feedback control, but it is finite-dimensional. In the theoretical work on the subject it is assumed (and sometimes proved) that increasing the number of finite elements will improve accuracy of the control. In applications, this may be difficult to achieve because of numerical problems. The main difficulty in computing the observer and simulating its work is the presence of high frequency eigenvalues in the finite-element model and poor numerical conditioning of some of the system matrices (e.g. poor observability properties) when the dimension of the approximating system increases. This work dealt with some of these difficulties.

Conference proceedings : ... Annual International Conference of the IEEE Engineering in Medicine and Biology Society. IEEE Engineering in Medicine and Biology Society. Annual Conference, 2012

The increasing need of knowledge in the treatment of brain diseases has driven a huge interest in... more The increasing need of knowledge in the treatment of brain diseases has driven a huge interest in understanding the phenomenon of neural spiking. Researchers have successfully been able to create mathematical models which, with specific parameters, are able to reproduce the experimental neuronal responses. The spiking activity is characterized using spike trains and it is essential to develop methods for parameter estimation that rely solely on the spike times or interspike intervals (ISI). In this paper we describe a new technique for optimization of a single neuron model using an experimental spike train from a biological neuron. We are able to fit model parameters using the gradient descent method. The optimized model is then used to predict the activity of the biological neuron and the performance is quantified using a spike distance measure.

A systems identification approach to estimating the connectivity in a neuronal population model

2014 36th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, 2014

Mapping the brain and its complex networked structure has been one of the most researched topics ... more Mapping the brain and its complex networked structure has been one of the most researched topics in the last decade and continues to be the path towards understanding brain diseases. In this paper we present a new approach to estimating the connectivity between neurons in a network model. We use systems identification techniques for nonlinear dynamic models to compute the synaptic connections from other pre-synaptic neurons in the population. We are able to show accurate estimation even in the presence of model error and inaccurate assumption of post-synaptic potential dynamics. This allows to compute the connectivity matrix of the network using a very small time window of membrane potential data of the individual neurons. The specificity and sensitivity measures for randomly generated networks are reported.

A new technique to optimize single neuron models using experimental spike train data

2013 American Control Conference, 2013

ABSTRACT We propose a new method for fitting model parameters to the neural spike train obtained ... more ABSTRACT We propose a new method for fitting model parameters to the neural spike train obtained from an experimental neuron. Due to the uncertainty associated with measuring the accurate voltage in a noisy environment, it is essential to develop methods that rely solely on the interspike intervals (ISI). Existing techniques do not provide a smooth and continuous cost function and optimal estimation of model parameters is difficult. In this paper we formulate a new cost function using the spike times of the neuron and determine the analytical gradient with respect to the model parameters. The optimal parameters are calculated using gradient based optimization techniques. We first use data generated by models to establish the accuracy of our technique. We also optimize the model to fit an experimental spike train of a biological neuron. We are able to find the optimal parameter set using a hybrid algorithm which is a combination of the gradient descent method and global optimization techniques.

On the numerical approximations for linear functional differential equations with input and output delays

1985 24th IEEE Conference on Decision and Control, 1985

ABSTRACT In this paper we state some new results on the approximations for linear retarded functi... more ABSTRACT In this paper we state some new results on the approximations for linear retarded functional differential equations with delays in control and observation. We consider the finite difference (i.e., averaging) approximation scheme for such systems treated as evolution equations in the state space setup, and we establish several basic properties of the approximation scheme. These results are extensions of recent results of Lasiecka and ManitiusL1 to the case of systems with input and output delays.

On spectral controllability of multi-input time-delay systems

Systems & Control Letters, 1985

ABSTRACT It is proved that under certain verifiable conditions, spectral controllability of a lin... more ABSTRACT It is proved that under certain verifiable conditions, spectral controllability of a linear system with commensurate state delays and with m inputs, m > 1, implies the existence of an n × 1 vector b contained in the image of the control matrix B such that the system with B replaced by b is spectrally controllable. Both the necessity and the sufficiency of these conditions are shown, a procedure to construct b is given, and an example is discussed.