Sergio Lucia

A new Robust NMPC Scheme and its Application to a Semi-batch Reactor Example

Abstract In this paper, a non-conservative robust nonlinear model predictive control scheme that can guarantee satisfaction of the constraints and optimal expected performance under uncertainty is introduced. The proposed control scheme is evaluated by simulations using a well known benchmark problem where the operation of a semi-batch polymerization reactors is optimized under very tight temperature tolerance limits. The simulation results show that the proposed scheme is capable of optimizing the process operation and, at the same time, it ensures robust operation within the whole range of uncertainties.

An environment for the efficient testing and implementation of robust NMPC

In the last years many research studies have presented simulation or experimental results using Nonlinear Model Predictive Control (NMPC). The computation times needed for the solution of the resulting nonlinear optimization problems are in many cases no longer an obstacle due to the advances in algorithms and computational power. However, NMPC is not yet an industrial reality as its linear counterpart is. Two reasons for this are the lack of good tool support for the development of NMPC solutions and the fact that it is difficult to ensure the robustness of NMPC to plant-model mismatch. In this paper, we address both these issues. The main contribution is the development of an environment for the efficient implementation and testing of NMPC solutions, offering flexibility to test different algorithms and formulations without the need to re-encode the model or the algorithm. In addition, we present and discuss the approach of multi-stage robust NMPC to systematically deal with the robustness issue. The benefits of our approach are illustrated by experimental results on a laboratory plant.

Robust Nonlinear Model Predictive Control with Reduction of Uncertainty Via Robust Optimal Experiment Design

Abstract This paper studies the reduction of the conservativeness of robust nonlinear model predictive control (NMPC) via the reduction of the uncertainty range using guaranteed parameter estimation. Optimal dynamic experiment design is formulated in the framework of robust NMPC in order to obtain probing inputs that maximize the information content of the feedback and simultaneously to guarantee the satisfaction of the process constraints. We propose a criterion for optimal experiment design which provides a minimization of parameter uncertainty in the direction of improved performance of the process under robust economic NMPC. A case study from the chemical engineering domain is studied to show the benefits of the proposed approach.

Efficient Robust Economic Nonlinear Model Predictive Control of an Industrial Batch Reactor

Abstract In this paper we present a systematic and efficient approach to deal with uncertainty in Nonlinear Model Predictive Control (NMPC). The main idea of the approach is to represent the NMPC setting as a real-time decision problem under uncertainty that is formulated as a multi-stage stochastic problem with recourse, based on a description of the uncertainty by a scenario tree. This formulation explicitly takes into account the fact that new information will be available in the future and thus reduces the conservativeness compared to open-loop worst-case approaches. We show that the proposed multistage NMPC formulation can deal with significant plant-model mismatch as it is usually encountered in the process industry and still satisfies tight constraints for the different values of the uncertain parameters, in contrast to standard NMPC. The use of an economic cost function leads to a superior performance compared to the standard tracking formulation. The potential of the approach is demonstrated for an industrial case study provided by BASF SE in the context of the European Project EMBOCON. The numerical solution of the resulting large optimization problems is implemented using the optimization framework CasADi.

Multi-stage Nonlinear Model Predictive Control with verified robust constraint satisfaction

This paper presents an approach to verify robust constraint satisfaction using dynamic state bounding techniques in the framework of multi-stage Nonlinear Model Predictive Control (NMPC). In multi-stage NMPC, the uncertainty is described by a tree of discrete scenarios, and the future control inputs depend on the previous realizations of the uncertainty, constituting a closed-loop approach which has been shown to provide significantly better performance than an open-loop approach. While the approach has demonstrated very promising results in practice, one of the problems of multi-stage NMPC is the fact that no guarantees can be given for the uncertainty values that are not explicitly considered in the scenario tree. In this work, we address this problem by updating the resulting optimization problem in an iterative fashion such that the constraints satisfaction is guaranteed based on the rigorous bounding of the state variables over the set of possible uncertainty realizations. We illustrate that the approach can deal in real time with challenging problems by presenting simulation results of an industrial batch polymerization reactor.

Predictive control, embedded cyberphysical systems and systems of systems – A perspective☆

Today’s world is changing rapidly due to advancements in information technology, computation and communication. Actuation, communication, sensing, and control are becoming ubiquitous. These technological advancements have led to the widespread availability of information and the possibility to connect systems in unforeseen manner. There is a strong desire for smart(er) cities, buildings, devices, factories, health monitoring – a smarter world. However, designing such a smarter world requires addressing also many challenges resulting from the emerging complex interactions and interoperation of systems. How is it possible to handle the increasing complexity during design and maintenance of such systems? How can one guarantee safety and performance of systems operating over networks which are subject to erroneous communication, delays, and failures of sensors and actuators? Is it possible to design control systems which allow for easy reconfiguration or even self-organization, for example by letting subsystems join and leave larger systems via plug and play strategies? Can one guarantee privacy of the controlled subsystems while exchanging information, which is necessary for maintaining overall system performance? We believe that predictive control is a well suited control approach to tackle some of these challenges due to its flexibility with respect to the formulation of the problem and the possibility to directly take constraints, preview information, as well as models of different complexity of the physical world into account. In this perspective we limit our attention to three areas we believe predictive control methods can provide a basis to tackle the appearing challenges: the efficient and easy implementation of predictive control on omnipresent embedded computation hardware, the question of resource and network aware control, as well as control on the network level of systems of systems. We briefly summarize results from these fields and outline some ideas on challenges, which arise.

Economic multi-stage output nonlinear model predictive control

Nonlinear Model Predictive control is one of the most promising control strategies in the field of advanced control. It can be used to optimize economic cost functions online satisfying all constraints which makes it very appealing in the context of industrial applications. In the last years, several robust NMPC methods have been presented. Among them, multi-stage stochastic NMPC has been proven to provide very promising results and to be computationally feasible by the use of advanced optimization tools. In this paper, we present an extension of the multi-stage approach that takes into account explicitly not only plant-model mismatch but also state estimation error through innovation sampling. We accommodate these errors into the resulting optimization problem by including them in the scenario tree formulation. We use a multiple-model estimation algorithm that fits to the multi-stage approach. The results are illustrated by simulation results of a chemical reactor.

Efficient stochastic model predictive control based on polynomial chaos expansions for embedded applications

Assuming the probability distributions of the uncertainties to be known, we use polynomial chaos theory to propagate the uncertainty through the dynamics of a linear system in order to obtain explicit expressions of the mean and variance of the future states. These expressions can then be used to formulate an stochastic MPC problem with chance constraints. We formulate the described method as a tractable optimization problem that can be solved very efficiently using fast optimization methods which are suitable for embedded applications. The methods are validated considering an uncertain aircraft system. The resulting optimization problems are verified on a low-cost microcontroller underlining the real-time feasibility and the potential of the approach.

Towards dual robust nonlinear model predictive control: A multi-stage approach

This paper presents an approach to dual robust nonlinear model predictive control (NMPC). Dual control is traditionally formulated as a technique that seeks to solve the trade-off between probing actions, which result in a better estimation of the unknown parameters, and the optimal operation of the uncertain dynamic system. We propose a dual robust NMPC method based on the multi-stage approach that represents the uncertainty as a scenario tree of its possible realizations. We achieve a dual control formulation by taking explicitly into account the reduction of the uncertainty that future probing actions would provide over the prediction horizon. Using such formulation, our approach does not require any a priori decision on the relative importance of the probing actions with respect to the optimal operation of the system, as proposed in some recent approaches. The results obtained for a chemical engineering example show the advantages of using a dual NMPC approach based on multi-stage NMPC over the sequential use of parameter estimation with a posteriori approximation of the covariance of the parameter estimates.

Improving scenario decomposition algorithms for robust nonlinear model predictive control

Abstract This paper deals with the efficient computation of solutions of robust nonlinear model predictive control problems that are formulated using multi-stage stochastic programming via the generation of a scenario tree. Such a formulation makes it possible to consider explicitly the concept of recourse, which is inherent to any receding horizon approach, but it results in large-scale optimization problems. One possibility to solve these problems in an efficient manner is to decompose the large-scale optimization problem into several subproblems that are iteratively modified and repeatedly solved until a solution to the original problem is achieved. In this paper we review the most common methods used for such decomposition and apply them to solve robust nonlinear model predictive control problems in a distributed fashion. We also propose a novel method to reduce the number of iterations of the coordination algorithm needed for the decomposition methods to converge. The performance of the different approaches is evaluated in extensive simulation studies of two nonlinear case studies.