Direct transcription solution of optimal control problems with higher order state constraints: theory vs practice

Betts, John T.; Campbell, Stephen L.; Engelsone, A.

doi:10.1007/s11081-007-9000-8

Cited by 25 publications

(20 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Third, we will discuss the well known benchmark problem by Betts and Campbell from [6,7] that originally motivated our research on parabolic boundary control problems, and, as a first step, the work in [30] on elliptic boundary control problems, and suggest a framework for its analysis. We will use an approximation to this model problem, which has also been investigated in the context of direct transcription methods by Kameswaran and Biegler [16] or Betts et al in [8], for our numerical experiments.…”

Section: Introductionmentioning

confidence: 99%

On regularization methods for the numerical solution of parabolic control problems with pointwise state constraints

Neitzel¹,

Tröltzsch²

2008

ESAIM: COCV

View full text Add to dashboard Cite

Abstract. In this paper we study Lavrentiev-type regularization concepts for linear-quadratic parabolic control problems with pointwise state constraints. In the first part, we apply classical Lavrentiev regularization to a problem with distributed control, whereas in the second part, a Lavrentiev-type regularization method based on the adjoint operator is applied to boundary control problems with state constraints in the whole domain. The analysis for both classes of control problems is investigated and numerical tests are conducted. Moreover the method is compared with other numerical techniques.Mathematics Subject Classification. 49K20, 49N10, 49M05.

show abstract

Section: Introductionmentioning

confidence: 99%

On regularization methods for the numerical solution of parabolic control problems with pointwise state constraints

Neitzel¹,

Tröltzsch²

2008

ESAIM: COCV

View full text Add to dashboard Cite

show abstract

“…Even if the mathematical analysis of an optimal control problem says that the inequality constraint is or is not an equality along the numerically optimum solution, the optimizer may choose to adjust the residual to improve the overall performance of the NLP. This ability to perturb the numerical solution can be very desirable as shown in [3,4] and is one of the issues that will be re-examined in this paper in the context of GPOPS II. It should be noted carefully what our interests are here.…”

Section: Common Featuresmentioning

confidence: 99%

“…It has been noted with DTS that DT can also serve as a type of regularization in that theoretical difficulties can be ignored if they happen on small enough scale [4]. This was subsequently analyzed in more detail in [22].…”

Section: Regularizationmentioning

confidence: 99%

See 1 more Smart Citation

Comments on direct transcription solution of DAE constrained optimal control problems with two discretization approaches

Campbell

Betts

2016

Numer Algor

View full text Add to dashboard Cite

There have been a number of results in the literature showing that a direct transcription numerical approach to optimal control problems could have a number of surprising and desirable behaviors that were not always predicted by the existing theory especially when differential algebraic equations are involved. Most of these results were developed with an implicit Runge-Kutta (IRK) discretization being used. It is important to know which of these observations hold for direct transcription software using different types of discretizations and which are discretization specific. This paper reexamines several of these questions but using an hp-pseudospectral code. It is seen that while philosophically the results are often similar to the IRK results, there are some differences that should be understood by users solving constrained optimal control problems. This paper also discusses a type of regularization for higher index problems that does not reduce the index.

show abstract

“…Due to the many connections, some researchers in the numerical DAE community have begun to consider control/optimization issues while at the same time some from the control/optimization community have begun to examine DAE issues [7,8,10,13,14,15,22,23,34,36].…”

Section: Recent Developments and Open Problemsmentioning

confidence: 99%

Control and Optimization with Differential-Algebraic Constraints

Biegler¹,

Campbell²,

Mehrmann³

2012

View full text Add to dashboard Cite

Differential Algebraic Equations (DAEs) are mixed systems of differential and algebraic equations. It has been recognized for some time now that they have great potential both theoretically and in applications. DAEs form one of the most elegant and simple ways to model a physical system because they allow for the creation of separate models for subcomponents that can then be pasted together via a network. As a consequence, this concept is used in many modern CAD/modeling systems like SIMULINK, Scicos and DYMOLA, although most software packages cannot fully exploit the full potential of DAE models.But this nice feature of DAEs for modeling has also a disadvantage, since it shifts all of the difficulties of a system onto the analysis and the numerical methods. For this reason in recent years much effort has been spent to analyze general DAEs and to derive suitable numerical methods either for general DAEs, see e.g. [9,19,18,20,29,38] or for special DAEs arising in applications, see e.g. [6,12,28,37].This analytical and numerical work so far has been primarily driven by the simulation community, where the desire was to simulate the behavior of a complex system which could be electrical, mechanical, chemical, or all three. Due to the ever growing complexity of models which pose new challenges, the field is developing rather rapidly including now also hybrid [2,3,4,11,21,31,39] and delay systems [16,17,25,26,27].Once a system can be modeled and simulated, there arises the need to control the process or optimize its performance. The control of physical processes is an important task in many applications and over the last two decades there have been tremendous advances in the theory and applications of control in almost all disciplines of science and technologies. Note that this includes not only the obvious applications such as designing a more efficient process, but also determining what are the control mechanisms inherent in complex biological systems and fitting models to data. Recent Developments and Open ProblemsAs the two topics, simulation of DAEs and control/optimization, have evolved in recent years, there has been a growing awareness of interconnections which arise in a number of ways. One obvious way is the control of DAE modeled systems. Optimality conditions and a maximum principle for general DAEs have only recently been obtained [30] and the results are far from complete. But there are other more subtle connections in that the necessary conditions for an optimal control problem typically form a DAE and the solution of some control problems in the presence of constraints or invariants also involve DAEs. An open problem is in 1

show abstract

Direct transcription solution of optimal control problems with higher order state constraints: theory vs practice

Cited by 25 publications

References 13 publications

On regularization methods for the numerical solution of parabolic control problems with pointwise state constraints

On regularization methods for the numerical solution of parabolic control problems with pointwise state constraints

Comments on direct transcription solution of DAE constrained optimal control problems with two discretization approaches

Control and Optimization with Differential-Algebraic Constraints

Contact Info

Product

Resources

About