Nonlinear Model Predictive Control for Constrained Output Path Following

We consider the tracking of geometric paths in output spaces of nonlinear systems subject to input and state constraints without pre-specified timing requirements. Such problems are commonly referred to as constrained output path-following problems. Specifically, we propose a predictive control approach to constrained path-following problems with and without velocity assignments and provide sufficient convergence conditions based on terminal regions and end penalties. Furthermore, we analyze the geometric nature of constrained output path-following problems and thereby provide insight into the computation of suitable terminal control laws and terminal regions. We draw upon an example from robotics to illustrate our findings.Comment: 12 pages, 4 figure

Implementation of Nonlinear Model Predictive Path-Following Control for an Industrial Robot

Many robotic applications, such as milling, gluing, or high precision measurements, require the exact following of a pre-defined geometric path. In this paper, we investigate the real-time feasible implementation of model predictive path-following control for an industrial robot. We consider constrained output path following with and without reference speed assignment. We present results from an implementation of the proposed model predictive path-following controller on a KUKA LWR IV robot.Comment: 8 pages, 3 figures; final revised versio

Towards Distributed OPF using ALADIN

The present paper discusses the application of the recently proposed Augmented Lagrangian Alternating Direction Inexact Newton (ALADIN) method to non-convex AC Optimal Power Flow Problems (OPF) in a distributed fashion. In contrast to the often used Alternating Direction of Multipliers Method (ADMM), ALADIN guarantees locally quadratic convergence for AC OPF. Numerical results for 5 to 300 bus test cases indicate that ALADIN is able to outperform ADMM and to reduce the number of iterations by about one order of magnitude. We compare ALADIN to numerical results for ADMM documented in the literature. The improved convergence speed comes at the cost of increasing the communication effort per iteration. Therefore, we propose a variant of ALADIN that uses inexact Hessians to reduce communication. Additionally, we provide a detailed comparison of these ALADIN variants to ADMM from an algorithmic and communication perspective. Moreover, we prove that ALADIN converges locally at quadratic rate even for the relevant case of suboptimally solved local NLPs

Optimal Power Flow: An Introduction to Predictive, Distributed and Stochastic Control Challenges

The Energiewende is a paradigm change that can be witnessed at latest since the political decision to step out of nuclear energy. Moreover, despite common roots in Electrical Engineering, the control community and the power systems community face a lack of common vocabulary. In this context, this paper aims at providing a systems-and-control specific introduction to optimal power flow problems which are pivotal in the operation of energy systems. Based on a concise problem statement, we introduce a common description of optimal power flow variants including multi-stage-problems and predictive control, stochastic uncertainties, and issues of distributed optimization. Moreover, we sketch open questions that might be of interest for the systems and control community

A Parallel Decomposition Scheme for Solving Long-Horizon Optimal Control Problems

We present a temporal decomposition scheme for solving long-horizon optimal control problems. In the proposed scheme, the time domain is decomposed into a set of subdomains with partially overlapping regions. Subproblems associated with the subdomains are solved in parallel to obtain local primal-dual trajectories that are assembled to obtain the global trajectories. We provide a sufficient condition that guarantees convergence of the proposed scheme. This condition states that the effect of perturbations on the boundary conditions (i.e., initial state and terminal dual/adjoint variable) should decay asymptotically as one moves away from the boundaries. This condition also reveals that the scheme converges if the size of the overlap is sufficiently large and that the convergence rate improves with the size of the overlap. We prove that linear quadratic problems satisfy the asymptotic decay condition, and we discuss numerical strategies to determine if the condition holds in more general cases. We draw upon a non-convex optimal control problem to illustrate the performance of the proposed scheme

Distributed State Estimation for AC Power Systems using Gauss-Newton ALADIN

This paper proposes a structure exploiting algorithm for solving non-convex power system state estimation problems in distributed fashion. Because the power flow equations in large electrical grid networks are non-convex equality constraints, we develop a tailored state estimator based on Augmented Lagrangian Alternating Direction Inexact Newton (ALADIN) method, which can handle the nonlinearities efficiently. Here, our focus is on using Gauss-Newton Hessian approximations within ALADIN in order to arrive at at an efficient (computationally and communicationally) variant of ALADIN for network maximum likelihood estimation problems. Analyzing the IEEE 30-Bus system we illustrate how the proposed algorithm can be used to solve highly non-trivial network state estimation problems. We also compare the method with existing distributed parameter estimation codes in order to illustrate its performance

A model for brain life history evolution

This work was funded by Swiss NSF grant PP00P3-146340 to LL http://www.snf.ch/en/Pages/default.aspx.Complex cognition and relatively large brains are distributed across various taxa, and many primarily verbal hypotheses exist to explain such diversity. Yet, mathematical approaches formalizing verbal hypotheses would help deepen the understanding of brain and cognition evolution. With this aim, we combine elements of life history and metabolic theories to formulate a metabolically explicit mathematical model for brain life history evolution. We assume that some of the brain’s energetic expense is due to production (learning) and maintenance (memory) of energy-extraction skills (or cognitive abilities, knowledge, information, etc.). We also assume that individuals use such skills to extract energy from the environment, and can allocate this energy to grow and maintain the body, including brain and reproductive tissues. The model can be used to ask what fraction of growth energy should be allocated at each age, given natural selection, to growing brain and other tissues under various biological settings. We apply the model to find uninvadable allocation strategies under a baseline setting (“me vs nature”), namely when energy-extraction challenges are environmentally determined and are overcome individually but possibly with maternal help, and use modern-human data to estimate model’s parameter values. The resulting uninvadable strategies yield predictions for brain and body mass throughout ontogeny and for the ages at maturity, adulthood, and brain growth arrest. We find that: (1) a me-vs-nature setting is enough to generate adult brain and body mass of ancient human scale and a sequence of childhood, adolescence, and adulthood stages; (2) large brains are favored by intermediately challenging environments, moderately effective skills, and metabolically expensive memory; and (3) adult skill is proportional to brain mass when metabolic costs of memory saturate the brain metabolic rate allocated to skills.Publisher PDFPeer reviewe

Economic Nonlinear Model Predictive Control

In recent years, Economic Model Predictive Control (empc) has received considerable attention of many research groups. The present tutorial survey summarizes state-of-the-art approaches in empc. In this context empc is to be understood as receding-horizon optimal control with a stage cost that does not simply penalize the distance to a desired equilibrium but encodes more sophisticated economic objectives. This survey provides a comprehensive overview of empc stability results: with and without terminal constraints, with and without dissipativtiy assumptions, with averaged constraints, formulations with multiple objectives and generalized terminal constraints as well as Lyapunov-based approaches. Moreover, we compare different performance criteria for some of the considered approaches and comment on the connections to recent research on dissipativity of optimal control problems. We consider a discrete-time setting and point towards continuous-time variants. We illustrate the different empc schemes with several examples

Maximal Islanding Time For Microgrids via Distributed Predictive Control

Motivated by a specific application in electricity distribution networks, we present a hierarchical model predictive control algorithm for scheduling energy storage devices. We demonstrate that, for the proposed optimization problem, the alternating direction method of multipliers can be implemented in a distributed fashion. Numerical experiments supporting the theoretical results are provided