A Model Predictive Control Scheme with Additional Performance Index for Transient Behavior

This paper presents a Model Predictive Control (MPC) scheme for nonlinear continuous time systems where an extra performance index, which is not a measure of the distance to the set point, is introduced to influence the transient behavior of the controlled system. The scheme is based on the following fact, proven in the paper: Given a stabilizing MPC controller, adding a function, integrable in the interval [t;+1), to the stage cost does not change the asymptotic convergence property of the closed loop state trajectory. As a numerical example, this result is applied to solve a simple visual servo control problem where an MPC controller drives the state to the origin while penalizing weakly observable trajectories

A Model Predictive Control scheme with Ultimate Bound for Economic Optimization

This paper presents a Model Predictive Control (MPC) scheme for nonlinear continuous-time systems where an economic stage cost, which is not a measure of the distance to a desired set point, is combined with a classic stabilizing stage cost. The associated control strategy leads to a closed-loop behavior that compromises, in a seamless way, between the convergence of the closed-loop state trajectory to a given steady-state and the minimization of the economic cost. More precisely, we derive a set of sufficient conditions under which the closed-loop state trajectory is ultimately bounded around the desired steady-state, with the size of the bound being proportional to the strength of the economic cost. Numerical results show the effectiveness of the proposed scheme on a target estimation and tracking control problem

A virtual vehicle approach to distributed control for formation keeping of underactuated vehicles

This paper addresses the control problem of formation keeping of a fleet of underactuated vehicles under communication constraints, where each agent is allowed to communicate with only a subset of the agents of the fleet. We adopt a virtual vehicle approach where every underactuated agent tracks a virtual vehicle, described by a single integrator model, driven by a consensus-based distributed controller. This approach results in a distributed dynamic controller for formation keeping of underactuated vehicles with exponential convergence guarantee of the formation error to zero. Simulation results are presented for both wheeled-like vehicles (2-D case) and UAV-like vehicles (3-D case)

A Nonlinear Adaptive Controller for Airborne Wind Energy Systems

A nonlinear adaptive path following controller for a kite based airborne wind energy system is presented. For a given desired geometric path, we provide necessary conditions for closed-loop convergence of the kite to a tube centered around the desired path. The proposed controller adapts for the case of unknown wind vector and kite parameters. The effectiveness of the approach is demonstrated via numerical simulations for multiple desired shapes of the geometric path and for varying desired tether length references

A Minimum Energy solution to Monocular Simultaneous Localization and Mapping

In this paper we propose an alternative solution to the Monocular Simultaneous Localization and Mapping (SLAM) problem. This approach uses a Minimum-Energy Observer for Systems with Perspective Outputs and provides an optimal solution. Contrarily to the most famous EKF-SLAM algorithm, this method yields a global solution and no linearization procedures are required. Furthermore, we show that the estimation error converges exponentially fast toward a neighborhood of zero, where this region increases gracefully with the magnitude of the input disturbance, output noise and initial camera position uncertainty. For practical purposes, we present also the filter in both continuous and discrete time form. Moreover, to show how to integrate a new landmark in the state estimation, a simple initialization procedure is presented. The filter performances are illustrated via simulations

Multi-scale spatio-temporal analysis of human mobility

The recent availability of digital traces generated by phone calls and online logins has significantly increased the scientific understanding of human mobility. Until now, however, limited data resolution and coverage have hindered a coherent description of human displacements across different spatial and temporal scales. Here, we characterise mobility behaviour across several orders of magnitude by analysing ∼850 individuals' digital traces sampled every ∼16 seconds for 25 months with ∼10 meters spatial resolution. We show that the distributions of distances and waiting times between consecutive locations are best described by log-normal and gamma distributions, respectively, and that natural time-scales emerge from the regularity of human mobility. We point out that log-normal distributions also characterise the patterns of discovery of new places, implying that they are not a simple consequence of the routine of modern life

Continuous-time Model Predictive Control for Economic Optimization:Theory, Design, and Applications to Motion Control of Underactuated Vehicles

This thesis addresses the design of optimization-based control laws for the case where convergence to a desired set-point, minimization of an arbitrary performance index, or a combination of the two, is the desired objective. The results are developed within the sample-data Model Predictive Control (MPC) framework considering constrained nonlinear continuous-time time-varying dynamical systems. For a given time sampling, a sample-data MPC control strategy consists of i) choosing among all future finite horizon predictions of state and input trajectories of the system the one that minimizes the given performance index, ii) applying the optimal input trajectory to the system until a new time sample is reached, and iii) iterating this process. The performance index is chosen to describe the specific control problem under consideration. In a classic Tracking-MPC framework, where the main goal is to steer the state of the system to a desired steady-state, the performance index is properly chosen to penalize the distance from the current state to a desired one. In order to capture more complex control objectives, in recent years a growing attention has been dedicated to a new class of controllers that goes under the name of Economic-MPC. Here, the term economic is used to stress the fact that the performance index is a general index of interest that we wish to minimize, e.g., economic, which does not denote the distance to a desired set point. This setting makes full use of the potentialities of optimization-based control strategies. Although, it comes with disadvantages. In fact, by choosing an arbitrary performance index, it is difficult to predict, and therefore certify, the evolution of the closed-loop system, which could potentially manifest undersirable behaviors. This thesis provides analysis and certification of a variety of closed-loop behaviors stemming from the use Economic-MPC controllers. A set of tools for design of provably correct MPC controllers is provided for the case where the performance index is of the Tracking-MPC type, purely economic, or a combination of the two. The results focus the certification of both closed-loop economic performance and closed-loop state evolution. The proposed strategies are applied to a range of motion control problems for underactuated vehicles. An MPC controller for Trajectory-Tracking and Path-Following with convergence guarantees is first proposed and then extended, using the results presented on Economic-MPC, to address the control problems of distributed formation keeping, energy efficient trajectory-tracking, and target-following through highly observable trajectories