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Personne# Harsh Ambarishkumar Shukla

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Jean-Hubert Hours, Colin Neil Jones, Harsh Ambarishkumar Shukla

In this paper, a novel optimality-tracking algorithm for solving Economic Nonlinear Model Predictive Control (ENMPC) problems in real-time is presented. Developing online schemes for ENMPC is challenging, since it is unclear how convexity of the Quadratic Programming (QP) problem, which is obtained by linearisation of the NMPC program around the current iterate, can be enforced efficiently. Therefore, we propose addressing the problem by means of an augmented Lagrangian formulation. Our tracking scheme consists of a fixed number of inexact Newton steps computed on an augmented Lagrangian subproblem followed by a dual update per time step. Under mild assumptions on the number of iterations and the penalty parameter, it can be proven that the sub-optimality error provided by the parametric algorithm remains bounded over time. This result extends the authors' previous works from a theoretical and a computational perspective. Efficacy of the approach is demonstrated on an ENMPC example consisting of a bioreactor.

The research community has been making significant progress in hardware implementation, numerical computing and algorithm development for optimization-based control. However, there are two key challenges that still have to be overcome for optimization-based control to be a viable option in the context of advanced industrial applications. First, the large existing gap between algorithm development and its deployment on platforms used by practitioners in industry. Second, from a more theoretical viewpoint, the lack of robustness of certain approaches, which are based on the unreasonable assumption that the model at hand perfectly represents the object under investigation. This thesis addresses the aforementioned challenges by establishing software toolboxes for automatic code generation, and proposing a data-driven methodology to enhance the performance of real-time optimization strategies during operation.
The first part of this thesis focuses on the efficient implementation of Model Predictive Control (MPC) based on first-order operator splitting methods. Because of the cheap numerical operations associated with them, splitting methods are favorable candidates for applications with limited computing power. We first identify the computational bottlenecks and, subsequently, discuss their efficient deployment on processors, Field Programmable Gate Arrays (FPGA), and heterogeneous platforms. For rapid prototyping and deployment, two code generation toolboxes are developed: SPLIT and LAFF. These possess a high-level parsing interface for MATLAB and yield optimized C code that can be directly used in a variety of FPGA platforms. Features such as pipelining, memory partitioning, and parallelization are automatically incorporated, not requiring users to have in-depth knowledge about computer architecture and low-level programming. We then propose a framework to a priori solve the co-design problem arising in splitting method-based MPC to provide trade-offs between resources and latency. We provide analytical expressions that can avoid the daunting and time-consuming task of exploring the design space manually, thus reducing the final application development time.
The second part of the thesis deals with learning plant-model mismatch using Gaussian processes (GPs) in Real Time Optimization (RTO) schemes. Inaccurate models, the presence of disturbances, and time-varying conditions typically lead to the suboptimal operation of many plants. We use data-driven global surrogate models in the form of GPs to cope with such problems and show better numerical convergence and handling of noise effectively when compared to standard RTO techniques. We moreover prove that GPs can be certified as probabilistic and deterministic fully linear models, a key property to guarantee global convergence of derivative-free trust region (DFT) methods. We then propose a novel DFT methodology to incorporate noise, which requires less plant evaluations than other alternatives. Finally, we conclude this work by performing experiments on a Solid-Oxide Fuel Cell system.

Dominique Bonvin, Timm Faulwasser, Colin Neil Jones, Harsh Ambarishkumar Shukla

In the context of static real-time optimization, the use of measurements allows dealing with uncertainty in the form of plant-model mismatch and disturbances. Modifier adaptation (MA) is a measurement-based scheme that uses first-order corrections to the model cost and constraint functions so as to achieve plant optimality upon convergence. However, first-order corrections rely crucially on the estimation of plant gradients, which typically requires costly plant experiments. The present paper proposes to implement real-time optimization via MA but use recursive Gaussian processes to represent the plant-model mismatch and estimate the plant gradients. This way, one can (i) attenuate the effect of measurement noise, and (ii) avoid plant-gradient estimation by means finite-difference schemes and, often, additional plant experiments. We use steady-state optimization data to build Gaussian-process regression functions. The efficiency of the proposed scheme is illustrated via a constrained variant of the Williams-Otto reactor problem.