Towards parallelizable sampling-based Nonlinear Model Predictive Control

This paper proposes a new sampling-based nonlinear model predictive control (MPC) algorithm, with a bound on complexity quadratic in the prediction horizon N and linear in the number of samples. The idea of the proposed algorithm is to use the sequence of predicted inputs from the previous time step as a warm start, and to iteratively update this sequence by changing its elements one by one, starting from the last predicted input and ending with the first predicted input. This strategy, which resembles the dynamic programming principle, allows for parallelization up to a certain level and yields a suboptimal nonlinear MPC algorithm with guaranteed recursive feasibility, stability and improved cost function at every iteration, which is suitable for real-time implementation. The complexity of the algorithm per each time step in the prediction horizon depends only on the horizon, the number of samples and parallel threads, and it is independent of the measured system state. Comparisons with the fmincon nonlinear optimization solver on benchmark examples indicate that as the simulation time progresses, the proposed algorithm converges rapidly to the "optimal" solution, even when using a small number of samples.Comment: 9 pages, 9 pictures, submitted to IFAC World Congress 201

Dual Maxwellian-Kappa modelling of the solar wind electrons: new clues on the temperature of Kappa populations

Context. Recent studies on Kappa distribution functions invoked in space plasma applications have emphasized two alternative approaches which may assume the temperature parameter either dependent or independent of the power-index $\kappa$. Each of them can obtain justification in different scenarios involving Kappa-distributed plasmas, but direct evidences supporting any of these two alternatives with measurements from laboratory or natural plasmas are not available yet. Aims. This paper aims to provide more facts on this intriguing issue from direct fitting measurements of suprathermal electron populations present in the solar wind, as well as from their destabilizing effects predicted by these two alternating approaches. Methods. Two fitting models are contrasted, namely, the global Kappa and the dual Maxwellian-Kappa models, which are currently invoked in theory and observations. The destabilizing effects of suprathermal electrons are characterized on the basis of a kinetic approach which accounts for the microscopic details of the velocity distribution. Results. In order to be relevant, the model is chosen to accurately reproduce the observed distributions and this is achieved by a dual Maxwellian-Kappa distribution function. A statistical survey indicates a $\kappa$-dependent temperature of the suprathermal (halo) electrons for any heliocentric distance. Only for this approach the instabilities driven by the temperature anisotropy are found to be systematically stimulated by the abundance of suprathermal populations, i.e., lowering the values of $\kappa$-index.Comment: Submitted to A&

Electromagnetic cyclotron instabilities in bi-Kappa distributed plasmas : a quasilinear approach

Anisotropic bi-Kappa distributed plasmas, as encountered in the solar wind and planetary magnetospheres,are susceptible to a variety of kinetic instabilities including the cyclotron instabilities driven by an excess ofperpendicular temperature T⊥ > T∥ (where ∥, ⊥ denote directions relative to the mean magnetic field). Theseinstabilities have been extensively investigated in the past, mainly limiting to a linear stability analysis. Abouttheir quasilinear (weakly nonlinear) development some insights have been revealed by numerical simulationsusing PIC and Vlasov solvers. This paper presents a self-consistent analytical approach, which provides forboth the electron and proton cyclotron instabilities an extended picture of the quasilinear time evolution ofthe anisotropic temperatures as well as the wave energy densities

Handbook of linear data-driven predictive control:Theory, implementation and design

Data-driven predictive control (DPC) has gained an increased interest as an alternative to model predictive control in recent years, since it requires less system knowledge for implementation and reliable data is commonly available in smart engineering systems. Several data-driven predictive control algorithms have been developed recently, which largely follow similar approaches, but with specific formulations and tuning parameters. This review aims to provide a structured and accessible guide on linear data-driven predictive control methods and practices for people in both academia and the industry seeking to approach and explore this field. To do so, we first discuss standard methods, such as subspace predictive control (SPC), and data-enabled predictive control (DeePC), but we also include newer hybrid approaches to DPC, such as γ–data-driven predictive control and generalized data-driven predictive control. For all presented data-driven predictive controllers we provide a detailed analysis regarding the underlying theory, implementation details and design guidelines, including an overview of methods to guarantee closed-loop stability and promising extensions towards handling nonlinear systems. The performance of the reviewed DPC approaches is compared via simulations on two benchmark examples from the literature, allowing us to provide a comprehensive overview of the different techniques in the presence of noisy data.</p

Handbook of linear data-driven predictive control:Theory, implementation and design

Data-driven predictive control (DPC) has gained an increased interest as an alternative to model predictive control in recent years, since it requires less system knowledge for implementation and reliable data is commonly available in smart engineering systems. Several data-driven predictive control algorithms have been developed recently, which largely follow similar approaches, but with specific formulations and tuning parameters. This review aims to provide a structured and accessible guide on linear data-driven predictive control methods and practices for people in both academia and the industry seeking to approach and explore this field. To do so, we first discuss standard methods, such as subspace predictive control (SPC), and data-enabled predictive control (DeePC), but we also include newer hybrid approaches to DPC, such as γ–data-driven predictive control and generalized data-driven predictive control. For all presented data-driven predictive controllers we provide a detailed analysis regarding the underlying theory, implementation details and design guidelines, including an overview of methods to guarantee closed-loop stability and promising extensions towards handling nonlinear systems. The performance of the reviewed DPC approaches is compared via simulations on two benchmark examples from the literature, allowing us to provide a comprehensive overview of the different techniques in the presence of noisy data.</p

Safety and effectiveness of bariatric surgery: Roux-en-y gastric bypass is superior to gastric banding in the management of morbidly obese patients: a reply to the response by Bhoyrul et al

<p>Abstract</p> <p>Background</p> <p>We have read the letter by Bhoyrul et al. in response to our recently published article "<it>Safety and effectiveness of bariatric surgery: Roux-en-Y gastric bypass is superior to gastric banding in the management of morbidly obese patients"</it>. We strongly disagree with the content of the letter.</p> <p>Results and discussion</p> <p>Bhoyrul et al. base their letter mostly on low level evidence such as single-institutional case series (level IV evidence) and expert opinion (level V evidence). Surprisingly, they do not comment on the randomized controlled trial, which clearly favours gastric bypass over gastric banding.</p> <p>Conclusion</p> <p>The letter by Bhoyrul et al. is based on low level evidence and is itself biased, unsubstantiated, and not supported by the current literature.</p