The development of an efficient optimal control package

Sargent, R. W. H.; Sullivan, G. R.

doi:10.1007/bfb0006520

Cited by 81 publications

(49 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…This gives rise to the so called "sequential" approach to optimal control problems, where in each optimization iteration the two steps, system simulation and optimization, are performed sequentially, one after the other. This approach emerged early in the nonlinear optimal control literature [50]. In contrast to the sequential approach, the so called "simultaneous" approach addresses the full nonlinear program as stated above in (2a)-(2f) directly by a Newton type optimization algorithm, i.e., optimization and simulation are performed simultaneously.…”

Section: Sequential Vs Simultaneous Optimal Controlmentioning

confidence: 99%

Efficient Numerical Methods for Nonlinear MPC and Moving Horizon Estimation

Diehl

Ferreau

Haverbeke

2009

Lecture Notes in Control and Information Sciences

441

273

View full text Add to dashboard Cite

This overview paper reviews numerical methods for solution of optimal control problems in real-time, as they arise in nonlinear model predictive control (NMPC) as well as in moving horizon estimation (MHE). In the first part, we review numerical optimal control solution methods, focussing exclusively on a discrete time setting. We discuss several algorithmic "building blocks" that can be combined to a multitude of algorithms. We start by discussing the sequential and simultaneous approaches, the first leading to smaller, the second to more structured optimization problems. The two big families of Newton type optimization methods, Sequential Quadratic Programming (SQP) and Interior Point (IP) methods, are presented, and we discuss how to exploit the optimal control structure in the solution of the linear-quadratic subproblems, where the two major alternatives are "condensing" and band structure exploiting approaches. The second part of the paper discusses how the algorithms can be adapted to the real-time challenge of NMPC and MHE. We recall an important sensitivity result from parametric optimization, and show that a tangential solution predictor for online data can easily be generated in Newton type algorithms. We point out one important difference between SQP and IP methods: while both methods are able to generate the tangential predictor for fixed active sets, the SQP predictor even works across active set changes. We then classify many proposed real-time optimization approaches from the literature into the developed categories.

show abstract

Section: Sequential Vs Simultaneous Optimal Controlmentioning

confidence: 99%

Efficient Numerical Methods for Nonlinear MPC and Moving Horizon Estimation

Diehl

Ferreau

Haverbeke

2009

Lecture Notes in Control and Information Sciences

441

273

View full text Add to dashboard Cite

show abstract

“…The feasible path approach (Sargent and Sullivan, 1977;Morison, 1984;Jang et al, 1987;Mutjaba and Machietto, 1988) consists of converting the path constraint h into a terminal inequality constraint. The optimal control problem may then be posed as a conventional NLP optimisation problem, where function evaluation implicitly integrates the system f, g to evaluate L, M and the terminal path constraints N. The reformulation is typically of the form:…”

Section: Dynamic Optimisationmentioning

confidence: 99%

Selection of process control structure based on economics

Narraway¹,

Perkins²

1994

Computers & Chemical Engineering

View full text Add to dashboard Cite

It has been recognised that the effect of dynamics on process economics is heavily dependent on the implemented controller, and that the physically attainable controller performance is limited by the choice of controlled and manipulated variables. This work considers the systematic selection of economically optimal square regulatory control structures from the set of all possible measurements and manipulated variables. This is a combinatorial problem, as typical processes have millions of potential control structures, where a control structure consists of a set of variables to be controlled and manipulated, but does not include a control law relating the variables.The solution of such a synthesis problem requires an analysis method. Historical approaches to control structure evaluation consider "controllability indices", and their trade off against steady state economics, whereas the economic indicators described in this thesis allow direct comparison and trade off of control structures against steady state economics.Assuming a method for assessing control structure economics, a hierarchical decomposition of the design problem into steady state and dynamic problems is demonstrated.A method for assessing the effect of dynamics on process economics for a specific control structure without tuning a controller is developed, based on linearised process models, linear systems theory and constraint control concepts. This assessment is extended to consider the control structure selection problem, resulting in a mixed integer linear programming (MILP) outer approximation to a mixed integer nonlinear programming (MINLP) problem.A mixed integer nonlinear optimal control problem is posed for the problem of selecting an optimal multiloop proportional-integral process control structure.The above problems are formulated as standard optimisation problems, and solved by appropriate techniques. Experience with the methods is presented as a set of case studies.Finally the novel features and applications of the work are discussed along with potential areas of further research.

show abstract

“…Furthermore, few options exist (Sargent & Sullivan (1977)), even in this case, for imposing constraints on continuous profiles and for handling discontinuities and/or singular profiles.…”

Section: List Of Figuresmentioning

confidence: 99%