Mario Zanon

A Lyapunov function for periodic economic optimizing Model Predictive Control

Model Predictive Control (MPC) schemes are commonly using reference-tracking cost functions, which have attractive properties in terms of stability and numerical implementation. However, many control applications have clear economic objectives that can be used directly as the NMPC cost function. Such NMPC schemes are labelled Economic NMPC. Unfortunately, Economic NMPC schemes suffer from some drawbacks. In particular, stability results for economic NMPC are still very sparse. A Lyapunov function for Economic NMPC was first proposed in [1] for problems having a steady-state optimum. The present paper develops a further generalization and clarification of these results for periodic systems.

Nonlinear MPC and MHE for Mechanical Multi-Body Systems with Application to Fast Tethered Airplanes

Mechanical applications often require a high control frequency to cope with fast dynamics. The control frequency of a nonlinear model predictive controller depends strongly on the symbolic complexity of the equations modeling the system. The symbolic complexity of the model equations for multi-body mechanical systems can often be dramatically reduced by using representations based on non-minimal coordinates, which result in index-3 differential-algebraic equations (DAEs). This paper proposes a general procedure to efficiently treat multi-body mechanical systems in the context of MHE & NMPC using non-minimal coordinate representations, and provides the resulting computational times that can be achieved on a tethered airplane system using code generation.

Periodic Optimal Control, Dissipativity and MPC

Recent research has established the importance of (strict) dissipativity for proving stability of economic MPC in the case of an optimal steady state. In many cases, though, steady-state operation is not economically optimal and periodic operation of the system yields a better performance. In this technical note, we propose ways of extending the notion of (strict) dissipativity for periodic systems. We prove that optimal

Model Predictive Control of Nonholonomic Mobile Robots Without Stabilizing Constraints and Costs

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Towards time-optimal race car driving using nonlinear MPC in real-time

-periodic operation and MPC stability directly follow, similarly to the steady-state case, which can be seen as a special case of the proposed framework. Finally, we illustrate the theoretical results with several simple examples.

Orbit control for a power generating airfoil based on nonlinear MPC

The problem of steering a nonholonomic mobile robot to a desired position and orientation is considered. In this paper, a model predictive control (MPC) scheme based on tailored nonquadratic stage cost is proposed to fulfill this control task. We rigorously prove asymptotic stability while neither stabilizing constraints nor costs are used. To this end, we first design suitable maneuvers to construct bounds on the value function. Second, these bounds are exploited to determine a prediction horizon length such that the asymptotic stability of the MPC closed loop is guaranteed. Finally, numerical simulations are conducted to explain the necessity of having nonquadratic running costs.

Control of dual-airfoil airborne wind energy systems based on nonlinear MPC and MHE

This paper addresses the real-time control of autonomous vehicles under a minimum traveling time objective. Control inputs for the vehicle are computed from a nonlinear model predictive control (MPC) scheme. The time-optimal objective is reformulated such that it can be tackled by existing efficient algorithms for real-time nonlinear MPC that build on the generalized Gauss-Newton method. We numerically validate our approach in simulations and present a real-world hardware setup of miniature race cars that is used for an experimental comparison of different approaches.

Model Predictive Control of Rigid-Airfoil Airborne Wind Energy Systems

The Airborne Wind Energy paradigm proposes to generate energy by flying a tethered airfoil across the wind flow. An essential problem posed by Airborne Wind Energy is the control of the tethered airfoil trajectory during power generation. Tethered flight is a fast, strongly nonlinear, unstable and constrained process, motivating control approaches based on fast Nonlinear Model Predictive Control. In this paper, a computationally efficient 6-DOF control model for a high performance, large-scale, rigid airfoil is proposed. A control scheme based on receding-horizon Nonlinear Model Predictive Control to track reference trajectories is applied to the proposed model. In order to make a real-time application of Nonlinear Model Predictive Control possible, a Real-Time Iteration scheme is proposed and its performance investigated.

From linear to nonlinear MPC: bridging the gap via the real-time iteration

Airborne Wind Energy (AWE) systems generate energy by flying a tethered airfoil across the wind flow at a high velocity. Tethered flight is a fast, strongly nonlinear, unstable and constrained process, motivating control approaches based on fast Nonlinear Model Predictive Control (NMPC) and state estimation approaches based on Moving Horizon Estimation (MHE). Dual-Airfoil AWE systems, i.e. systems with two airfoils attached to a Y-shaped tether have been shown to be more effective than systems based on a single airfoil. This paper proposes a control scheme for a dual-airfoil AWE system based on NMPC and MHE and studies its performance in a realistic scenario based on state-of-the-art turbulence models.

An Experimental Test Setup for Advanced Estimation and Control of an AirborneWind Energy System

In order to allow for a reliable and lasting operation of Airborne Wind Energy systems, several problems need to be addressed. One of the most important challenges regards the control of the tethered airfoil during power generation. Tethered flight of rigid airfoils is a fast, strongly nonlinear, unstable and constrained process, and one promising way to address the control challenge is the use of Nonlinear Model Predictive Control (NMPC) together with online parameter and state estimation based on Moving Horizon Estimation (MHE). In this paper, these techniques are introduced and their performance demonstrated in simulations of a 30 m wingspan tethered airplane with power generation in pumping mode.