N4SID method applied to obtain a discrete-time linear state space system as a mathematical model of a jaw crusher prototype

2017 ◽  
Author(s):  
Ademar G. Costa ◽  
Jose Leonardo B. Maldonado ◽  
Fabricio A. Romero ◽  
Jhon C. Sanmartin ◽  
Michael Valarezo ◽  
...  
Keyword(s):  
Mathematical Model ◽  
State Space ◽  
Discrete Time ◽  
Space System ◽  
Jaw Crusher ◽  
State Space System ◽  
Linear State ◽  
Time Linear

THE LINEAR QUADRATIC DYNAMIC GAME FOR DISCRETE-TIME DESCRIPTOR SYSTEMS

2003 ◽  
Vol 05 (04) ◽  
pp. 361-374
Author(s):  
HUA XU ◽  
HIROAKI MUKAIDANI
Keyword(s):  
State Space ◽  
Discrete Time ◽  
Dynamic Game ◽  
Descriptor Systems ◽  
Linear Feedback ◽  
Space System ◽  
Linear Quadratic ◽  
Reduced Order ◽  
State Space System ◽  
Zero Sum

The linear quadratic zero-sum dynamic game for discrete time descriptor systems is considered. A method, which involves solving a linear quadratic zero-sum dynamic game for a reduced-order discrete time state space system, is developed to find the linear feedback saddle-point solutions of the problem. Checkable conditions, which are described in terms of two dual algebraic Riccati equations and a Hamiltonian matrix, are given such that the linear quadratic zero-sum dynamic game for the reduced-order discrete time state space system is available. Sufficient conditions for the existence of the solutions are obtained. In contrast with the dynamic game in state space systems, the dynamic game in descriptor systems admits uncountably many linear feedback saddle-point solutions. All these solutions have the same existence conditions and achieve the same value of the dynamic game.

scholarly journals Stability Analysis of the Bat Algorithm Described as a Stochastic Discrete-Time State-Space System

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-10
Author(s):  
Janusz Piotr Paplinski
Keyword(s):  
Stability Analysis ◽  
State Space ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Bat Algorithm ◽  
Discrete Time System ◽  
Space System ◽  
State Matrix ◽  
State Space System

The main problem with the soft-computing algorithms is a determination of their parameters. The tuning rules are very general and need experiments during a trial and error method. The equations describing the bat algorithm have the form of difference equations, and the algorithm can be treated as a stochastic discrete-time system. The behaviour of this system depends on its dynamic and preservation stability conditions. The paper presents the stability analysis of the bat algorithm described as a stochastic discrete-time state-space system. The observability and controllability analyses were made in order to verify the correctness of the model describing the dynamic of BA. Sufficient conditions for stability are derived based on the Lyapunov stability theory. They indicate the recommended areas of the location of the parameters. The analysis of the position of eigenvalues of the state matrix shows how the different values of parameters affect the behaviour of the algorithm. They indicate the recommended area of the location of the parameters. Simulation results confirm the theory-based analysis.

Model-Based Discrete Linear State Estimator for Nonlinearizable Systems With State-Dependent Noise

1990 ◽  
Vol 112 (4) ◽  
pp. 774-781 ◽  
Author(s):  
R. J. Chang
Keyword(s):  
Discrete Time ◽  
Continuous Model ◽  
Equivalent Model ◽  
State Estimator ◽  
Time Model ◽  
State Dependent ◽  
Present Technique ◽  
Linear State ◽  
Noisy Measurement ◽  
Time Linear

A practical technique to derive a discrete-time linear state estimator for estimating the states of a nonlinearizable stochastic system involving both state-dependent and external noises through a linear noisy measurement system is presented. The present technique for synthesizing a discrete-time linear state estimator is first to construct an equivalent reference linear model for the nonlinearizable system such that the equivalent model will provide the same stationary covariance response as that of the nonlinear system. From the linear continuous model, a discrete-time state estimator can be directly derived from the corresponding discrete-time model. The synthesizing technique and filtering performance are illustrated and simulated by selecting linear, linearizable, and nonlinearizable systems with state-dependent noise.

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