On the state equations of nonlinear networks and the uniqueness of their solutions

1986 ◽  
Vol 74 (3) ◽  
pp. 513-514 ◽  
Author(s):  
M. Koksal
Keyword(s):  
The State ◽  
State Equations ◽  
Nonlinear Networks

scholarly journals Combinatory Attitude Determination Method for High Rotational Speed Rigid-Body Aircraft

2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Liangliang An ◽  
Liangming Wang ◽  
Ning Liu ◽  
Jian Fu
Keyword(s):  
Rigid Body ◽  
Rotational Speed ◽  
Attitude Determination ◽  
Unscented Kalman Filter ◽  
The State ◽  
Determination Method ◽  
State Equations ◽  
High Rotational Speed ◽  
Motion Equations ◽  
Accuracy Measurement

In this paper, we present a novel multisensor combinatory attitude determination method that enables high-accuracy measurement of the attitude of a high rotational speed rigid-body aircraft. We analyze the external moments of the aircraft during flight and develop the method using theoretical deductions based on the motion equations of a rigid body rotating around the centroid. The proposed method fuses the data measured from GPS, gyrometer, and magnetometer and uses the improved unscented Kalman filter (UKF) algorithm to perform filtering. First, appropriate assumptions and simplifying approximations are made for around-centroid motion equations of a rigid body according to the motion characteristics of the high rotational speed aircraft. Using these assumptions and approximations, the constraint equations between the Euler attitude angles and flight-path angle, trajectory deflection angle are derived to serve as the state equation. Second, the roll angle with error is calculated using the geomagnetic field model and the geomagnetic intensity measured by a three-axis magnetometer and then fused with the angular velocity information obtained from the gyroscope for constructing the measurement equations. Finally, the state equations are discretized using the Runge–Kutta method during the UKF prediction stage, improving the prediction accuracy. Simulation results show that the proposed method can effectively determine the attitude information of the high rotational speed aircraft, achieving high level of reliability and accuracy thanks to the combination of information from GPS, gyroscope, and magnetometer.

scholarly journals Development of a New Research Platform for Electrical Drive System Modelling for Real-Time Digital Simulation Applications

2013 ◽  
Vol 2013 ◽  
pp. 1-10
Author(s):  
S. Umashankar ◽  
Mandar Bhalekar ◽  
Surabhi Chandra ◽  
D. Vijayakumar ◽  
D. P. Kothari
Keyword(s):  
Real Time ◽  
Digital Simulation ◽  
The State ◽  
Order System ◽  
System Modelling ◽  
Step Size ◽  
State Equations ◽  
Real Time System ◽  
Zero Crossing ◽  
Research Platform

This paper presents the research platform for real-time digital simulation applications which replaces the requirement for full-scale or partial-scale validation of physical systems. To illustrate this, a three-phase AC-DC-AC converter topology has been used consists of diode rectifier, DC link, and an IGBT inverter with inductive load. In this topology, rectifier as well as inverter decoupled and solved separately using decoupled method, which results in the reduced order system so that it is easy to solve the state equation. This method utilizes an analytical approach to formulate the state equations, and interpolation methods have been implemented to rectify the zero-crossing errors, with fixed step size of 100 μsec is used. The proposed algorithm and the model have been validated using MATLAB simulation as m-file program and also in real-time DSP controller domain. The performance of the real-time system model is evaluated based on accuracy, zero crossing, and step size.

scholarly journals Optimal Control of Diffusions with Hard Terminal State Restrictions

2012 ◽  
Vol 2012 ◽  
pp. 1-38
Author(s):  
Atle Seierstad
Keyword(s):  
Optimal Control ◽  
Maximum Principle ◽  
Terminal State ◽  
The State ◽  
State Equations ◽  
Brownian Motions ◽  
Terminal Time ◽  
State Restrictions

A maximum principle is proved for certain problems of optimal control of diffusions where hard end constraints occur. The results apply to several dimensional problems, where some of the state equations involve Brownian motions, but not the equations corresponding to states being hard restricted at the terminal time.

scholarly journals Adaptive Mesh Iteration Method for Trajectory Optimization Based on Hermite-Pseudospectral Direct Transcription

2017 ◽  
Vol 2017 ◽  
pp. 1-7
Author(s):  
Humin Lei ◽  
Tao Liu ◽  
Deng Li ◽  
Jikun Ye ◽  
Lei Shao
Keyword(s):  
Error Estimate ◽  
Relative Error ◽  
Iteration Method ◽  
Trajectory Optimization ◽  
Simulation Experiment ◽  
Adaptive Mesh ◽  
The State ◽  
State Equations ◽  
Direct Transcription ◽  
Interpolating Polynomials

An adaptive mesh iteration method based on Hermite-Pseudospectral is described for trajectory optimization. The method uses the Legendre-Gauss-Lobatto points as interpolation points; then the state equations are approximated by Hermite interpolating polynomials. The method allows for changes in both number of mesh points and the number of mesh intervals and produces significantly smaller mesh sizes with a higher accuracy tolerance solution. The derived relative error estimate is then used to trade the number of mesh points with the number of mesh intervals. The adaptive mesh iteration method is applied successfully to the examples of trajectory optimization of Maneuverable Reentry Research Vehicle, and the simulation experiment results show that the adaptive mesh iteration method has many advantages.

The Optimum Design of Spatial Frames Using the Method of Constrained Steepest Descent With State Equations

1971 ◽  
Vol 93 (4) ◽  
pp. 1261-1267 ◽  
Author(s):  
D. L. Bartel ◽  
E. J. Haug ◽  
Kwan Rim
Keyword(s):  
Nonlinear Programming ◽  
Mechanical Design ◽  
The State ◽  
Steepest Descent ◽  
Mathematical Programming Problem ◽  
State Variables ◽  
State Equations ◽  
Design Problems ◽  
Out Of Plane ◽  
Plane Frames

This paper considers the design of a class of spatial frames which occur frequently in mechanical systems: plane frames with out-of-plane loads. The design objective is to minimize the weight subject to constraints on stress and geometry. The method of constrained steepest descent with state equations is introduced to solve the resulting mathematical programming problem. This method differs from the usual methods of nonlinear programming in that the state variables and the state equations are used explicitly in the formulation. This results in a natural matching of the essential features of the design problem and the method used to obtain its solution. The method is effective and general in that it can be readily applied to a wide variety of design problems which occur in mechanical design.

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