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

Global Sensitivity Analysis of Biochemical Reaction Networks via Semidefinite Programming

We study the problem of computing outer bounds for the region of steady states of biochemical reaction networks modelled by ordinary differential equations, with respect to parameters that are allowed to vary within a predefined region. Using a relaxed version of the corresponding feasibility problem and its Lagrangian dual, we show how to compute certificates for regions in state space not containing any steady states. Based on these results, we develop an algorithm to compute outer bounds for the region of all feasible steady states. We apply our algorithm to the sensitivity analysis of a Goldbeter--Koshland enzymatic cycle, which is a frequent motif in reaction networks for regulation of metabolism and signal transduction.Comment: Proceedings of the 17th IFAC World Congress, Seoul, Korea, 200

Online learning-based model predictive control with Gaussian process models and stability guarantees

Model predictive control allows to provide high performance and safety guarantees in the form of constraint satisfaction. These properties, however, can be satisfied only if the underlying model, used for prediction, of the controlled process is sufficiently accurate. One way to address this challenge is by data-driven and machine learning approaches, such as Gaussian processes, that allow to refine the model online during operation. We present a combination of an output feedback model predictive control scheme and a Gaussian process-based prediction model that is capable of efficient online learning. To this end, the concept of evolving Gaussian processes is combined with recursive posterior prediction updates. The presented approach guarantees recursive constraint satisfaction and input-to-state stability with respect to the model–plant mismatch. Simulation studies underline that the Gaussian process prediction model can be successfully and efficiently learned online. The resulting computational load is significantly reduced via the combination of the recursive update procedure and by limiting the number of training data points while maintaining good performance.Ministerio de Economía y Competitividad ( España) DPI2016-76493-C3-1-

Robustness of Prediction Based Delay Compensation for Nonlinear Systems

Control of systems where the information between the controller, actuator, and sensor can be lost or delayed can be challenging with respect to stability and performance. One way to overcome the resulting problems is the use of prediction based compensation schemes. Instead of a single input, a sequence of (predicted) future controls is submitted and implemented at the actuator. If suitable, so-called prediction consistent compensation and control schemes, such as certain predictive control approaches, are used, stability of the closed loop in the presence of delays and packet losses can be guaranteed. In this paper, we show that control schemes employing prediction based delay compensation approaches do posses inherent robustness properties. Specifically, if the nominal closed loop system without delay compensation is ISS with respect to perturbation and measurement errors, then the closed loop system employing prediction based delay compensation techniques is robustly stable. We analyze the influence of the prediction horizon on the robustness gains and illustrate the results in simulation.Comment: 6 pages, 3 figure

A Model Predictive Control Approach to Trajectory Tracking Problems via Time-Varying Level Sets of Lyapunov Functions

We discuss a model predictive control approach to trajectory tracking problems of constrained nonlinear con- tinuous time systems, where the reference trajectory is a priori known and asymptotically constant. The proposed NMPC scheme is able to explicitly consider input and state constraints while guaranteeing recursive feasibility. To handle the time- varying nature of the tracking problem we advocate the use of time-varying level sets of Lyapunov functions as terminal regions. We prove a necessary and suf?cient condition for positive invariance of these sets and show how these sets can be efficiently computed, if a quadratic Lyapunov function is available. As an example we consider a nonlinear CSTR reactor