scholarly journals Optimal control methods for nonlinear parameter estimation in biophysical neuron models

2022 ◽  
Author(s):  
Nirag Kadakia
Keyword(s):  
Optimal Control ◽  
State Space ◽  
Measurement Noise ◽  
State Variables ◽  
Neuron Models ◽  
Unknown Parameters ◽  
Space Modeling ◽  
Wide Range ◽  
Functional Forms ◽  
Realistic Neuron

Functional forms of biophysically-realistic neuron models are constrained by neurobiological and anatomical considerations, such as cell morphologies and the presence of known ion channels. Despite these constraints, neurons models still contain unknown static parameters which must be inferred from experiment. This inference task is most readily cast into the framework of state-space models, which systematically takes into account partial observability and measurement noise. Inferring only dynamical state variables such as membrane voltages is a well-studied problem, and has been approached with a wide range of techniques beginning with the well-known Kalman filter. Inferring both states and fixed parameters, on the other hand, is less straightforward. Here, we develop a method for joint parameter and state inference that combines traditional state space modeling with chaotic synchronization and optimal control. Our methods are tailored particularly to situations with considerable measurement noise, sparse observability, very nonlinear or chaotic dynamics, and highly uninformed priors. We illustrate our approach both in a canonical chaotic model and in a phenomenological neuron model, showing that many unknown parameters can be uncovered reliably and accurately from short and noisy observed time traces. Our method holds promise for estimation in larger-scale systems, given ongoing improvements in calcium reporters and genetically-encoded voltage indicators.

Active Control of Viscoelastic Systems by the Method of Receptance

2017 ◽  
Vol 140 (2) ◽  
Author(s):  
Kumar V. Singh ◽  
Xiaoxuan Ling
Keyword(s):  
State Space ◽  
Active Control ◽  
Transfer Functions ◽  
Controller Design ◽  
Internal State ◽  
State Variables ◽  
Approximation Techniques ◽  
Linear System Of Equations ◽  
Space Modeling ◽  
Wide Range

Viscoelastic materials have frequency and temperature-dependent properties and they can be used as passive controlling devices in wide range of vibration applications. In order to design active control for viscoelastic systems, an accurate mathematical modeling is needed. In practice, various material models and approximation techniques are used to model the dynamic behavior of viscoelastic systems. These models are then transformed into approximating state-space models, which introduces several challenges such as introduction of nonphysical internal state variables and requirement of observer/state estimator design. In this paper, it is shown that the active control for viscoelastic structures can be designed accurately by only utilizing the available receptance transfer functions (RTF) and hence eliminating the need for state-space modeling for control design. By using the recently developed receptance method, it is shown that active control for poles and zeros assignment of the viscoelastic systems can be achieved. It is also shown that a nested active controller can also be designed for continuous structures (beams/rods) supported by viscoelastic elements. It is highlighted that such a controller design requires modest size of RTF and solution of the set of linear system of equations.

Furnace Modelling Using State Space Representation

2006 ◽  
Vol 3 (1) ◽  
pp. 37
Author(s):  
Razidah Ismail
Keyword(s):  
State Space ◽  
Power Plants ◽  
Controller Design ◽  
Cost Savings ◽  
Combined Cycle ◽  
The State ◽  
Space Representation ◽  
State Variables ◽  
State Space Representation ◽  
Space Modeling

The state space modeling approach was developed to cope with the demand and performance due to the increase in system complexity, which may have multiple inputs and multiple outputs (MIMO). This approach is based on time-domain analysis and synthesis using state variables. This paper describes the development of a state space representation of a furnace system of a combined cycle power plant. Power plants will need to operate optimally so as to stay competitive, as even a small improvement in energy efficiency would involve substantial cost savings. Both the quantitative and qualitative analyses of the state space representation of the furnace system are discussed. These include the responses of systems excited by certain inputs and the structural properties of the system. The analysis on the furnace system showed that the system is bounded input and bounded output stable, controllable and observable. In practice, the state space formulation is very important for numerical computation and controller design, and can be extended for time-varying systems.

Fast and Exact Simulation Methods Applied on a Broad Range of Neuron Models

2010 ◽  
Vol 22 (6) ◽  
pp. 1468-1472 ◽  
Author(s):  
Michiel D'Haene ◽  
Benjamin Schrauwen
Keyword(s):  
Linear Models ◽  
Iteration Scheme ◽  
Integration Scheme ◽  
State Variables ◽  
Neuron Models ◽  
Time Constants ◽  
Highly Nonlinear ◽  
Wide Range ◽  
Computation Scheme ◽  
Event Based

Recently van Elburg and van Ooyen ( 2009 ) published a generalization of the event-based integration scheme for an integrate-and-fire neuron model with exponentially decaying excitatory currents and double exponential inhibitory synaptic currents, introduced by Carnevale and Hines. In the paper, it was shown that the constraints on the synaptic time constants imposed by the Newton-Raphson iteration scheme, can be relaxed. In this note, we show that according to the results published in D'Haene, Schrauwen, Van Campenhout, and Stroobandt ( 2009 ), a further generalization is possible, eliminating any constraint on the time constants. We also demonstrate that in fact, a wide range of linear neuron models can be efficiently simulated with this computation scheme, including neuron models mimicking complex neuronal behavior. These results can change the way complex neuronal spiking behavior is modeled: instead of highly nonlinear neuron models with few state variables, it is possible to efficiently simulate linear models with a large number of state variables.

Optimal Control Deconvolution for Velocity Meter Signals

1988 ◽  
Vol 110 (1) ◽  
pp. 17-23
Author(s):  
P. M. Clarkson ◽  
J. K. Hammond
Keyword(s):  
Experimental Data ◽  
Optimal Control ◽  
State Space ◽  
State Space Model ◽  
The State ◽  
Measurement Noise ◽  
Deconvolution Method ◽  
System Parameters ◽  
Space Model ◽  
Inaccurate Estimation

A method of deconvolution has been developed which uses the techniques of optimal control. The application of the technique to velocity meter signals is presented. It is shown that provided a state-space model of the transducer dynamics can be obtained the method can provide effective deconvolution even when the data are corrupted by measurement noise. As well as the deconvolution method and the control of the measurement noise the formation of the state-space model and the effects of inaccurate estimation of system parameters are considered. Results are presented using both simulated and experimental data.

scholarly journals Furnace Modelling Using State Space Representation

2006 ◽  
Vol 3 (1) ◽  
pp. 37 ◽  
Author(s):  
Razidah Ismail
Keyword(s):  
State Space ◽  
Power Plants ◽  
Controller Design ◽  
Cost Savings ◽  
Combined Cycle ◽  
The State ◽  
Space Representation ◽  
State Variables ◽  
State Space Representation ◽  
Space Modeling

The state space modeling approach was developed to cope with the demand and performance due to the increase in system complexity, which may have multiple inputs and multiple outputs (MIMO). This approach is based on time-domain analysis and synthesis using state variables. This paper describes the development of a state space representation of a furnace system of a combined cycle power plant. Power plants will need to operate optimally so as to stay competitive, as even a small improvement in energy efficiency would involve substantial cost savings. Both the quantitative and qualitative analyses of the state space representation of the furnace system are discussed. These include the responses of systems excited by certain inputs and the structural properties of the system. The analysis on the furnace system showed that the system is bounded input and bounded output stable, controllable and observable. In practice, the state space formulation is very important for numerical computation and controller design, and can be extended for time-varying systems.

Active Control of Viscoelastic Systems by the Method of Receptance

2016 ◽  
Author(s):  
Kumar V. Singh ◽  
Xiaoxuan Ling
Keyword(s):  
Feedback Control ◽  
State Space ◽  
Active Control ◽  
Eigenvalue Problems ◽  
Transfer Functions ◽  
Internal State ◽  
State Variables ◽  
Viscoelastic System ◽  
Approximation Techniques ◽  
Wide Range

Viscoelastic materials both stores and dissipate energies and have frequency and temperature dependent properties and hence by tuning and optimizing their damping (viscous) and stiffness (elastic) properties they can be used as passive controlling devices in wide range of vibration applications. If the control of viscoelastic systems (viscoelastic structures or structures composed of viscoelastic elements) to be realized by active means, then an accurate mathematical modeling of the viscoelastic system is needed. In practice, various material models and approximation techniques such as Biot model, Golla-Hughes-McTavish (GHM) model and Anelastic Displacement Field (ADF) methods are used to model the dynamic behavior of viscoelastic systems. These models are then transformed into approximating state space models which introduces several challenges: (i) they increase the size of the related eigenvalue problems, (ii) state space realization introduces non-physical internal state variables, and, (iii) the feedback control implementation poses practical challenges such as observer and state estimator design. In this research it is shown that the active control for viscoelastic structures can be designed accurately by only utilizing the available transfer functions. These transfer functions can be obtained from dynamic experiments and the active feedback control is designed without having the knowledge of approximated state-space system matrices. The problem associated with the active control for viscoelastic system is formulated as feedback control problems in frequency domain by using the receptance method. Active control for poles and zeros assignment of the viscoelastic systems is demonstrated using numerical examples associated with the multi-degree-degree of freedom systems. It is also shown that a nested active controller can also be designed for continuous structures (beams/rods) supported by viscoelastic elements. It is highlighted that such a controller design requires modest size of transfer functions and solution of the set of linear system of equations.

scholarly journals A Kalman particle filter for online parameter estimation with applications to affine models

2021 ◽  
Author(s):  
Jian He ◽  
Asma Khedher ◽  
Peter Spreij
Keyword(s):  
Kalman Filter ◽  
Particle Filter ◽  
State Space ◽  
Outer Layer ◽  
Posterior Distribution ◽  
State Space Model ◽  
The State ◽  
State Variables ◽  
Unknown Parameters ◽  
Space Model

AbstractIn this paper we address the problem of estimating the posterior distribution of the static parameters of a continuous-time state space model with discrete-time observations by an algorithm that combines the Kalman filter and a particle filter. The proposed algorithm is semi-recursive and has a two layer structure, in which the outer layer provides the estimation of the posterior distribution of the unknown parameters and the inner layer provides the estimation of the posterior distribution of the state variables. This algorithm has a similar structure as the so-called recursive nested particle filter, but unlike the latter filter, in which both layers use a particle filter, our algorithm introduces a dynamic kernel to sample the parameter particles in the outer layer to obtain a higher convergence speed. Moreover, this algorithm also implements the Kalman filter in the inner layer to reduce the computational time. This algorithm can also be used to estimate the parameters that suddenly change value. We prove that, for a state space model with a certain structure, the estimated posterior distribution of the unknown parameters and the state variables converge to the actual distribution in $$L^p$$ L p with rate of order $${\mathcal {O}}(N^{-\frac{1}{2}}+\varDelta ^{\frac{1}{2}})$$ O ( N - 1 2 + Δ 1 2 ) , where N is the number of particles for the parameters in the outer layer and $$\varDelta $$ Δ is the maximum time step between two consecutive observations. We present numerical results of the implementation of this algorithm, in particularly we implement this algorithm for affine interest models, possibly with stochastic volatility, although the algorithm can be applied to a much broader class of models.

Vibration Control of a Flexible Beam Using Model Predictive Control

2012 ◽  
Vol 457-458 ◽  
pp. 1299-1304
Author(s):  
Jun Feng Hu ◽  
Da Chang Zhu ◽  
Qiang Chen
Keyword(s):  
Model Predictive Control ◽  
State Space ◽  
Predictive Control ◽  
Optimization Problem ◽  
External Disturbance ◽  
The State ◽  
Measurement Noise ◽  
Flexible Beam ◽  
Control Input ◽  
State Variables

Model predictive control is applied to suppress the vibration of a flexible link with piezoelectric actuators and strain gage transducer. The state-space dynamic model of the system was derived by using finite element method and experimental modal test. On the basis of the model, model predictive controller is designed taking into account the uncertain disturbance and measurement noise. The discrete prediction model is derived from the state-space equation of the system, and the future output is obtained from the model. The uncertain external disturbance and measurement noise are white noise signal, the Kalman filter estimator is designed to estimate the state variables of the system. A standard quadratic programming optimization problem is formed where the performance index function minimizes a quadratic performance function that trades off controller performance and control effort. The constraints are the control input voltage and its change rate. Finally, the optimization problem is solved to obtain the optimal control output. A MIMO control system is built using dSPACE DS1103 platform, and experimental tests are performed. The performances of the controller are verified experimentally. The results of experiment show the effectiveness of the controller.

Sign in / Sign up

Export Citation Format

Share Document