3D mesh generation from aerial LiDAR point cloud data

Three dimensional urban scene modelling became important issue in the last few years. Beside visual experience, 3D city modelling has gained a significant function in diverse analysing tasks, however the amount of data requires a high level of automation of model generation. In this work, we introduce an automatic and robust algorithm which produces detailed 3D virtual city models by analysing high resolution airborne LiDAR point clouds. Using the idea of the surface normal based roof segmentation we have designed a procedure, which takes into account the boundaries of each roof segment, so that the adjacent segments connect without gaps. We have developed an algorithm to detect 3D edge lines of the rooftops. Since the applied triangulation methods operate on the whole convex hull of the input points, hollow outer parts of the roof segments are filled in with false triangles. To solve this problem, we have proposed a method using a Markov Random Field, in which we filter out the incorrect triangles lying on the concave parts

Reconstruction of Epidemiological Data in Hungary Using Stochastic Model Predictive Control

In this paper, we propose a model-based method for the reconstruction of not directly measured epidemiological data. To solve this task, we developed a generic optimization-based approach to compute unknown time-dependent quantities (such as states, inputs, and parameters) of discrete-time stochastic nonlinear models using a sequence of output measurements. The problem was reformulated as a stochastic nonlinear model predictive control computation, where the unknown inputs and parameters were searched as functions of the uncertain states, such that the model output followed the observations. The unknown data were approximated by Gaussian distributions. The predictive control problem was solved over a relatively long time window in three steps. First, we approximated the expected trajectories of the unknown quantities through a nonlinear deterministic problem. In the next step, we fixed the expected trajectories and computed the corresponding variances using closed-form expressions. Finally, the obtained mean and variance values were used as an initial guess to solve the stochastic problem. To reduce the estimated uncertainty of the computed states, a closed-loop input policy was considered during the optimization, where the state-dependent gain values were determined heuristically. The applicability of the approach is illustrated through the estimation of the epidemiological data of the COVID-19 pandemic in Hungary. To describe the epidemic spread, we used a slightly modified version of a previously published and validated compartmental model, in which the vaccination process was taken into account. The mean and the variance of the unknown data (e.g., the number of susceptible, infected, or recovered people) were estimated using only the daily number of hospitalized patients. The problem was reformulated as a finite-horizon predictive control problem, where the unknown time-dependent parameter, the daily transmission rate of the disease, was computed such that the expected value of the computed number of hospitalized patients fit the truly observed data as much as possible

Optimal Solar Panel Area Computation and Temperature Tracking for a CubeSat System using Model Predictive Control

Recently, there has been a rising interest in small satellites such as CubeSats in the aerospace community due to their small size and cost-effective operation. It is challenging to ensure precision performance for satellites with minimum cost and energy consumption. To support maneuverability, the CubeSat is equipped with a propellant tank, in which the fuel must be maintained in the appropriate temperature range. Simultaneously, the energy production should be maximized, such that the other components of the satellite are not overheated. To meet the technological requirements, we propose a multicriteria optimal control design using a nonlinear dynamical thermal model of the CubeSat system. First, a PID control scheme with an anti-windup compensation is employed to evaluate the minimum heat flux necessary to keep the propellant tank at a given reference temperature. Secondly, a linearization-based controller is designed for temperature control. Thirdly, the optimization of the solar cell area and constrained temperature control is solved as an integrated nonlinear model predictive control problem using the quasilinear parameter varying form of the state equations. Several simulation scenarios for different power limits and solar cell coverage cases are shown to illustrate the trade-offs in control design and to show the applicability of the approach

Computational Stability Analysis of Lotka-Volterra Systems

This paper concerns the computational stability analysis of locally stable Lotka-Volterra (LV) systems by searching for appropriate Lyapunov functions in a general quadratic form composed of higher order monomial terms. The Lyapunov conditions are ensured through the solution of linear matrix inequalities. The stability region is estimated by determining the level set of the Lyapunov function within a suitable convex domain. The paper includes interesting computational results and discussion on the stability regions of higher (3,4) dimensional LV models as well as on the monomial selection for constructing the Lyapunov functions. Finally, the stability region is estimated of an uncertain 2D LV system with an uncertain interior locally stable equilibrium point

Efficient implementation of Gaussian process–based predictive control by quadratic programming

Abstract The paper addresses the problem of accelerating predictive control of non‐linear system models augmented with Gaussian processes (GP‐MPC). Due to the non‐linear and stochastic prediction model, predictive control of GP‐based models requires to solve a stochastic optimization problem. Different model simplification methods have to be applied to reformulate this problem to a deterministic, non‐linear optimization task that can be handled by a numerical solver. As these problems are still complex, especially with exact moment calculations, real‐time implementation of GP‐MPC is extremely challenging. The existing solutions accelerate the computations at the solver level by linearizing the non‐linear optimization problem and applying sequential convexification. In contrast, this paper proposes a novel GP‐MPC solution approach that without linearization formulates a series of surrogate quadratic programs (QP‐s) to iteratively obtain the solution of the original non‐linear optimization problem. The first step is embedding the non‐linear mean‐variance dynamics of the GP‐MPC prediction model in a linear parameter‐varying (LPV) structure and rewriting the constraints in parameter‐varying form. By fixing the scheduling trajectory at a known variation (based on previously computed or initial state‐input trajectories), optimization of the input sequence for the remaining varying linear model reduces to a linearly constrained quadratic program. After solving the QP, the non‐linear prediction model is simulated for the new control input sequence and new scheduling trajectories are updated. The procedure is iterated until the convergence of the scheduling, that is, the solution of the QP converges to the solution of the original non‐linear optimization problem. By designing a reference tracking controller for a 4DOF robot arm, we illustrate that the convergence is remarkably fast and the approach is computationally advantageous compared to current solutions. The proposed method enables the application of GP‐MPC algorithms even with exact moment matching on fast dynamical systems and requires only a QP solver

Computational method for estimating the domain of attraction of discrete-time uncertain rational systems

Using linear matrix inequality (LMI) conditions, we propose a computational method to generate Lya- punov functions and to estimate the domain of attraction (DOA) of uncertain nonlinear (rational) discrete- time systems. The presented method is a discrete-time extension of the approach first presented in [39], where the authors used Finsler’s lemma and affine annihilators to give sufficient LMI conditions for sta- bility. The system representation required for DOA computation is generated systematically by using the linear fractional transformation (LFT). Then a model simplification step not affecting the computed Lya- punov function (LF) is executed on the obtained linear fractional representation (LFR). The LF is computed in a general quadratic form of a state and parameter dependent vector of rational functions, which are generated from the obtained LFR model. The proposed method is compared to the numeric n-dimensional order reduction technique proposed in [11]. Finally, additional tuning knobs are proposed to obtain more degrees of freedom in the LMI conditions. The method is illustrated on two benchmark examples