The $\alpha$-Method Direct Transcription in Path Constrained Dynamic Optimization

2009 ◽  
Vol 31 (3) ◽  
pp. 2386-2417 ◽  
Author(s):  
Nigam Chandra Parida ◽  
Soumyendu Raha
Keyword(s):  
Dynamic Optimization ◽  
Direct Transcription

scholarly journals Co-Design of an Active Suspension Using Simultaneous Dynamic Optimization

2011 ◽  
Author(s):  
James T. Allison ◽  
Zhi Han
Keyword(s):  
Dynamic Optimization ◽  
Control Design ◽  
Active Suspension ◽  
Design Methods ◽  
Physical Design ◽  
Optimization Approach ◽  
Computationally Efficient ◽  
Direct Transcription ◽  
Design Component ◽  
Design Variables

Design of physical systems and associated control systems are coupled tasks; design methods that manage this interaction explicitly can produce system-optimal designs, whereas conventional sequential processes may not. Here we explore a new technique for combined physical system and control design (co-design) based on a simultaneous dynamic optimization approach known as direct transcription, which transforms infinite-dimensional control design problems into finite dimensional nonlinear programming problems. While direct transcription problem dimension is often large, sparse problem structures and fine-grained parallelism (among other advantageous properties) can be exploited to yield computationally efficient implementations. Extension of direct transcription to co-design gives rise to a new problem structures and new challenges. Here we illustrate direct transcription for co-design using a new automotive active suspension design example developed specifically for testing co-design methods. This example builds on prior active suspension problems by incorporating a more realistic physical design component that includes independent design variables and a broad set of physical design constraints, while maintaining linearity of the associated differential equations.

scholarly journals Co-Design of an Active Suspension Using Simultaneous Dynamic Optimization

2014 ◽  
Vol 136 (8) ◽  
Author(s):  
James T. Allison ◽  
Tinghao Guo ◽  
Zhi Han
Keyword(s):  
Dynamic Optimization ◽  
Active Suspension ◽  
Design Methods ◽  
Physical Design ◽  
Simultaneous Optimization ◽  
Sequential Optimization ◽  
Optimization Approach ◽  
Active System ◽  
Direct Transcription ◽  
Design Component

Design of physical systems and associated control systems are coupled tasks; design methods that manage this interaction explicitly can produce system-optimal designs, whereas conventional sequential processes may not. Here, we explore a new technique for combined physical and control system design (co-design) based on a simultaneous dynamic optimization approach known as direct transcription, which transforms infinite-dimensional control design problems into finite-dimensional nonlinear programming problems. While direct transcription problem dimension is often large, sparse problem structures and fine-grained parallelism (among other advantageous properties) can be exploited to yield computationally efficient implementations. Extension of direct transcription to co-design gives rise to new problem structures and new challenges. Here, we illustrate direct transcription for co-design using a new automotive active suspension design example developed specifically for testing co-design methods. This example builds on prior active suspension problems by incorporating a more realistic physical design component that includes independent design variables and a broad set of physical design constraints, while maintaining linearity of the associated differential equations. A simultaneous co-design approach was implemented using direct transcription, and numerical results were compared with conventional sequential optimization. The simultaneous optimization approach achieves better performance than sequential design across a range of design studies. The dynamics of the active system were analyzed with varied level of control authority to investigate how dynamic systems should be designed differently when active control is introduced.

scholarly journals A direct transcription-based multiple shooting formulation for dynamic optimization

2020 ◽  
Vol 140 ◽  
pp. 106846 ◽  
Author(s):  
Morgan T. Kelley ◽  
Ross Baldick ◽  
Michael Baldea
Keyword(s):  
Dynamic Optimization ◽  
Multiple Shooting ◽  
Direct Transcription

scholarly journals Direct Transcription for Dynamic Optimization: A Tutorial with a Case Study on Dual-Patient Ventilation During the COVID-19 Pandemic

2020 ◽  
Author(s):  
Eric C. Kerrigan ◽  
Yuanbo Nie ◽  
Omar Faqir ◽  
Caroline H. Kennedy ◽  
Steven A. Niederer ◽  
...  
Keyword(s):  
Dynamic Optimization ◽  
Direct Transcription

On the Uses of Linear-Quadratic Methods in Solving Nonlinear Dynamic Optimization Problems With Direct Transcription

2020 ◽  
Author(s):  
Daniel R. Herber ◽  
Athul K. Sundarrajan
Keyword(s):  
Dynamic Optimization ◽  
Nonlinear Dynamic ◽  
Optimal Control Problems ◽  
Optimization Problems ◽  
Control Problems ◽  
Linear Quadratic ◽  
Direct Transcription ◽  
Solution Strategies ◽  
Engineered Systems ◽  
Direct Incorporation

Abstract Solving nonlinear dynamic optimization (NLDO) and optimal control problems can be quite challenging, but the need for effective methods is ever increasing as more engineered systems become more dynamic and integrated. In this article, we will explore the various uses of linear-quadratic dynamic optimization (LQDO) in the direct transcription-based solution strategies for NLDO. Three general LQDO-based strategies are discussed, including direct incorporation, two-level optimization, and quasi-linearization. Connections are made between a variety of existing approaches, including sequential quadratic programming. The case studies are solved with the various methods using a publicly available, MATLAB-based tool. Results indicate that the LQDO-based strategies can improve existing solvers and be effective solution strategies. However, there are robustness issues and problem derivative requirements that must be considered.

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