Multi-stage nonlinear model predictive control applied to a semi-batch polymerization reactor under uncertainty
TL;DR: In this paper, the authors present a robust non-conservative nonlinear model predictive control (MPC) approach based on the representation of the evolution of the uncertainty by a scenario tree, and leads to a non-ervative robust control of the uncertain plant because the adaptation of future inputs to new information is taken into account.
About: This article is published in Journal of Process Control.The article was published on 2013-10-01. It has received 291 citations till now. The article focuses on the topics: Model predictive control & Robust control.
Citations
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24 Oct 2013
TL;DR: CasADi is presented, an open-source software framework for numerical optimization and algorithmic differentiation that offers a level of abstraction which is lower than algebraic modeling languages, but higher than conventional AD tools.
283 citations
Cites methods from "Multi-stage nonlinear model predict..."
...[139,140] proposed a less conservative approach to robust NMPC, which we shall employ here....
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01 Jan 2013
TL;DR: CasADi as mentioned in this paper is an open-source software framework for numerical optimization and algorithmic differentiation that offers a level of abstraction which is lower than algebraic modeling languages, but higher than conventional AD tools.
Abstract: Methods and software for derivative-based numerical optimization in general and simulation-based optimization in particular have seen a large rise in popularity over the past 30 years. Still, due to practical difficulties in implementing many of the methods in a fast and reliable manner, it remains an underused technology both in academia and in industry. To address this, we present a set of methods and tools with the aim of making techniques for dynamic optimization more accessible. In particular, we present CasADi, an open-source software framework for numerical optimization and algorithmic differentiation (AD) that offers a level of abstraction which is lower than algebraic modeling languages, but higher than conventional AD tools. We also discuss several of the many application problems which have already been addressed with CasADi by researchers from diverse fields.
272 citations
TL;DR: In this paper, the authors propose a constraint tightening approach to non-conservatively guarantee recursive feasibility and stability in Stochastic Model Predictive Control (SMPC), and prove asymptotic stability in probability of the minimal robust positively invariant set obtained by the unconstrained LQ-optimal controller.
Abstract: Constraint tightening to non-conservatively guarantee recursive feasibility and stability in Stochastic Model Predictive Control is addressed. Stability and feasibility requirements are considered separately, highlighting the difference between existence of a solution and feasibility of a suitable, a priori known candidate solution. Subsequently, a Stochastic Model Predictive Control algorithm which unifies previous results is derived, leaving the designer the option to balance an increased feasible region against guaranteed bounds on the asymptotic average performance and convergence time. Besides typical performance bounds, under mild assumptions, we prove asymptotic stability in probability of the minimal robust positively invariant set obtained by the unconstrained LQ-optimal controller. A numerical example, demonstrating the efficacy of the proposed approach in comparison with classical, recursively feasible Stochastic MPC and Robust MPC, is provided.
145 citations
TL;DR: In this paper, a multi-stage scenario-based nonlinear model predictive control (MPC) approach is proposed to deal with uncertainties in the context of economic NMPC, and a novel algorithm inspired by tube-based MPC is proposed in order to achieve a trade-off between the variability of the controlled system and the economic performance under uncertainty.
142 citations
TL;DR: In this paper, the authors propose a modularization of the NMPC implementations that facilitates the comparison of different solutions and the transition from simulation to online application, and the proposed platform supports the multi-stage robust NMPC approach to deal with uncertainty.
104 citations
References
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TL;DR: The flexible constraint handling capabilities of MPC are shown to be a significant advantage in the context of the overall operating objectives of the process industries and the 1-, 2-, and ∞-norm formulations of the performance objective are discussed.
5,188 citations
TL;DR: An SQP algorithm that uses a smooth augmented Lagrangian merit function and makes explicit provision for infeasibility in the original problem and the QP subproblems is discussed and a reduced-Hessian semidefinite QP solver (SQOPT) is discussed.
Abstract: Sequential quadratic programming (SQP) methods have proved highly effective for solving constrained optimization problems with smooth nonlinear functions in the objective and constraints. Here we consider problems with general inequality constraints (linear and nonlinear). We assume that first derivatives are available and that the constraint gradients are sparse. Second derivatives are assumed to be unavailable or too expensive to calculate.
We discuss an SQP algorithm that uses a smooth augmented Lagrangian merit function and makes explicit provision for infeasibility in the original problem and the QP subproblems. The Hessian of the Lagrangian is approximated using a limited-memory quasi-Newton method.
SNOPT is a particular implementation that uses a reduced-Hessian semidefinite QP solver (SQOPT) for the QP subproblems. It is designed for problems with many thousands of constraints and variables but is best suited for problems with a moderate number of degrees of freedom (say, up to 2000). Numerical results are given for most of the CUTEr and COPS test collections (about 1020 examples of all sizes up to 40000 constraints and variables, and up to 20000 degrees of freedom).
2,205 citations
TL;DR: This paper provides a novel solution to the problem of robust model predictive control of constrained, linear, discrete-time systems in the presence of bounded disturbances by solving the optimal control problem that is solved online.
1,357 citations
"Multi-stage nonlinear model predict..." refers methods in this paper
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...Tube-based MPC, presented for linear systems in [5] and xtended to the nonlinear case in [6], has recently received attenion as an alternative to min–max approaches for the formulation f a robust NMPC scheme with guaranteed stability and recursive easibility....
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TL;DR: A condensing algorithm for the solution of the approximating linearly constrained quadratic subproblems, and high rank update procedures are introduced, which are especially suited for optimal control problems and lead to significant improvements of the convergence behaviour and reductions of computing time and storage requirements.
1,326 citations
TL;DR: This paper develops for the first time a rigorous algorithmic procedure for determining a robust decision policy in response to any weighting of the scenarios.
Abstract: A common approach in coping with multiperiod optimization problems under uncertainty where statistical information is not really enough to support a stochastic programming model, has been to set up and analyze a number of scenarios. The aim then is to identify trends and essential features on which a robust decision policy can be based. This paper develops for the first time a rigorous algorithmic procedure for determining such a policy in response to any weighting of the scenarios. The scenarios are bundled at various levels to reflect the availability of information, and iterative adjustments are made to the decision policy to adapt to this structure and remove the dependence on hindsight.
1,321 citations