Optimal control of nonlinear systems represented by differential algebraic equations

2000 ◽  
Author(s):  
P.D. Roberts ◽  
V.M. Becerra
Keyword(s):  
Optimal Control ◽  
Nonlinear Systems ◽  
Differential Algebraic Equations ◽  
Algebraic Equations

scholarly journals GEKKO Optimization Suite

Processes ◽  
2018 ◽  
Vol 6 (8) ◽  
pp. 106 ◽  
Author(s):  
Logan Beal ◽  
Daniel Hill ◽  
R. Martin ◽  
John Hedengren
Keyword(s):  
Optimal Control ◽  
Optimization Problems ◽  
Object Oriented ◽  
Differential Algebraic Equations ◽  
Mixed Integer ◽  
Modeling Languages ◽  
Algebraic Equations ◽  
Simulation And Optimization ◽  
Algebraic Modeling Languages ◽  
Real Time Optimization

This paper introduces GEKKO as an optimization suite for Python. GEKKO specializes in dynamic optimization problems for mixed-integer, nonlinear, and differential algebraic equations (DAE) problems. By blending the approaches of typical algebraic modeling languages (AML) and optimal control packages, GEKKO greatly facilitates the development and application of tools such as nonlinear model predicative control (NMPC), real-time optimization (RTO), moving horizon estimation (MHE), and dynamic simulation. GEKKO is an object-oriented Python library that offers model construction, analysis tools, and visualization of simulation and optimization. In a single package, GEKKO provides model reduction, an object-oriented library for data reconciliation/model predictive control, and integrated problem construction/solution/visualization. This paper introduces the GEKKO Optimization Suite, presents GEKKO’s approach and unique place among AMLs and optimal control packages, and cites several examples of problems that are enabled by the GEKKO library.

Pointwise Optimal Control of Dynamical Systems Described by Constrained Coordinates

1999 ◽  
Vol 121 (4) ◽  
pp. 594-598 ◽  
Author(s):  
V. Radisavljevic ◽  
H. Baruh
Keyword(s):  
Optimal Control ◽  
Dynamical Systems ◽  
Feedback Control ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Differential Algebraic Equations ◽  
Control Law ◽  
Algebraic Equations ◽  
The Stability ◽  
The Mathematical Model

A feedback control law is developed for dynamical systems described by constrained generalized coordinates. For certain complex dynamical systems, it is more desirable to develop the mathematical model using more general coordinates then degrees of freedom which leads to differential-algebraic equations of motion. Research in the last few decades has led to several advances in the treatment and in obtaining the solution of differential-algebraic equations. We take advantage of these advances and introduce the differential-algebraic equations and dependent generalized coordinate formulation to control. A tracking feedback control law is designed based on a pointwise-optimal formulation. The stability of pointwise optimal control law is examined.

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