Distributed nonlinear model predictive control for a quadrotor UAV

Highly dynamic systems such as Micro Multirotor Aerial Vehicles (Micro-MAVs) require control approaches that enable safe operation where extreme limitations in embedded systems, such as energy, processing capability and memory, are present. Nonlinear model predictive control (NMPC) approaches can respect operational constraints in a safe manner. However, they are typically challenging to implement using embedded computers on-board of Micro-MAVs. Implementations of classic NMPC approaches rely on high-performance computers. In this work, we propose a fast nonlinear model predictive control approach that ensures the stabilization and control of Micro Multirotor Aerial Vehicles (Micro-MAVs). This aerial robotic system uses a low processing power board that relies solely on on-board sensors to localize itself, which makes it suitable for experiments in GPS-denied environments. The proposed approach has been verified in numerical simulations using processing capabilities that are available on Micro-MAVs.

This study reveals endogenous instability in the financial market based on the dynamic interaction between endogenous investment behavior and debt in a nonlinear framework, by using a nonlinear model predictive control (NMPC) approach. It is found that when the debt ratio is below a critical threshold, increased debt has a positive effect on investment. On the other hand, when the debt ratio is above that threshold, growing financial stress and greater debt become a drag on investment, leading to an economic downturn and an outbreak of financial crisis. The paper provides theoretical support for Minsky’s financial instability hypothesis.

This paper discusses path-following control for robotics, moving a manipulator along a path in Cartesian space, making a trade-off between tracking accuracy and the speed at which the path is followed. We present and validate a nonlinear model predictive control (NMPC) approach suitable for this nonlinear control task. This approach entails a method to model the position of the robot end-effector with respect to the path and, in addition, a reformulation of the robot prediction model in terms of an independent path parameter instead of time. This way, we obtain a convenient parameterization of path properties in the optimal control formulation and many geometric constraints, such as tracking tolerance, transform into simple linear or vector-norm constraints. Numerical simulations illustrate the benefits of this novel NMPC approach in an implementation that employs a direct multiple shooting discretization strategy and the real-time iteration scheme for fast computation of the control law. We show results of closed-loop simulations for a 6-DOF industrial robot executing a writing task, with computation times close to enabling real-time implementation.

Although intrinsically marine craft are known to exhibit non-linear dynamic characteristics, modern marine autopilot system designs continue to be developed based on both linear and non-linear control approaches. This article evaluates two novel non-linear autopilot designs based on non-linear local control network and non-linear model predictive control approaches to establish their effectiveness in terms of control activity expenditure, power consumption and mission duration length under similar operating conditions. From practical point of view, autopilot with less energy consumption would in reality provide the battery-powered vehicle with longer mission duration. The autopilot systems are used to control the non-linear yaw dynamics of an unmanned surface vehicle named Springer. The yaw dynamics of the vehicle being modelled using a multi-layer perceptron-type neural network. Simulation results showed that the autopilot based on local control network method performed better for Springer. Furthermore, on the whole, the local control network methodology can be regarded as a plausible paradigm for marine control system design.

Advanced control strategies, together with state-estimation methods, are frequently applied to nonlinear and complex systems. It is crucial to understand which of these are the most efficient methods for the best use of these approaches in a chemical process. In the current work, nonlinear model predictive control (NMPC) approaches were developed that considered three numerical methods: single shooting (SS), multiple shooting (MS), and orthogonal collocation (OC). Their performance was compared against the Van de Vusse reactor benchmark while considering set-point changes, unreachable set-point, disturbances, and mismatches. The results showed that the NMPC based on OC presented less computational cost than the other approaches. The extended Kalman filter (EKF), constrained extended Kalman filter (CEKF), and the moving horizon estimator (MHE) were also developed. The estimators’ performance was compared for the same benchmark by considering the computational cost and the mean squared error (MSE) for the estimated variables, thereby verifying the CEKF as the best option. Finally, the performance of the nine combinations of estimators and control approaches was compared to consider the Van de Vusse reactor and the same scenarios, thereby verifying the best performance of the CEKF with the OC. The present work can help with choosing the numerical method and the estimator for controlling chemical processes.

Nonlinear Hybrid Model Predictive Control for building energy systems

The use of model predictive control for quadro-tor applications requires balancing trajectory tracking performance and constraint satisfaction with fast computation. This paper proposes a Flatness-based Model Predictive Control (FMPC) approach that can be applied to quadrotors, and more generally, differentially flat nonlinear systems. Our proposed FMPC couples feedback model predictive control with feedforward linearization. The proposed approach has the computational advantage that, similar to linear model predictive control, it only requires solving a convex quadratic program instead of a nonlinear program. However, unlike linear model predictive control, we still account for the nonlinearity in the model through the use of an inverse term. In simulation, we demonstrate improved robustness over approaches that couple model predictive control with feedback linearization. In experiments using quadrotor vehicles, we also demonstrate improved trajectory tracking compared to classical linear and nonlinear model predictive control approaches.

Preliminary study for motion sickness reduction in autonomous vehicles: an MPC approach

Stochastic Nonlinear Model Predictive Control with Active Model Discrimination: A Closed-Loop Fault Diagnosis Application

In this paper, we present a prediction-based dynamic programming (DP) control approach, a nonlinear model predictive control (NMPC) approach, and a linear optimal control (LOC) approach to analyze the minimization of the total energy use of a hybrid ground-coupled heat pump (hp) system (incorporating a ground-coupled hp, a gas boiler, a passive cooler, and an active chiller) under operational constraints. A large-scale emulator model (based on finite-volume method and the equivalent-diameter approach) is used for the borehole system and for the assessment of different control algorithms. A nonlinear autoregressive exogenous model is identified from the input-output data generated by the emulator model to be used in a DP-based controller. Since DP is a global optimal control method, it was used as a reference for performance assessment. Next, a state-space reduced-order control-oriented model with a larger sampling time is obtained from the emulator model using the so-called proper orthogonal decomposition model reduction technique. This model is used in an NMPC algorithm to see how much NMPC is suboptimal with respect to the DP in terms of annual energy use minimization. Finally, a series of LOCs based on constant hp coefficients of performance is tested to see how much the system performance deteriorates. The control algorithms are used for the satisfaction of heating-cooling demands of three types of buildings: 1) heating dominated; 2) cooling dominated; and 3) thermally balanced. The effects of constraining thermal buildup/depletion of ground, variable electricity prices, and marginal violation of thermal comfort on the performance of the different controllers applied are also separately analyzed.

In the last years, the development of kites as a new approach to use the wind energy to produce electricity or to pull boats in order to save fuel has received attention from both the industry and academia. In this study, we propose a nonlinear model predictive control (NMPC) approach to control a towing kite based on an economic objective function in contrast to the tracking of a predefined trajectory, as it is usually done. We use a simple model of a kite that has been recently developed. The use of a simple model usually comes at a price of higher model inaccuracy. To cope with the uncertainties in the model as well as with external disturbances we propose the use of multi-stage nonlinear model predictive control. Simulation results show that the use of the multi-stage NMPC approach avoids the violation of constraints and achieves a better performance than standard NMPC under the presence of strong uncertainties.

Dynamic modelling and nonlinear model predictive control of a Fluid Catalytic Cracking Unit

We present a nonlinear model predictive control (NMPC) approach to design optimal feedback controllers for the class of continuous-time input affine polynomial systems subject to state and input constraints. The corresponding feedback law is obtained via the solution of an efficient to solve convex optimization problem subject to sum of squares (SOS) constraints. To serve the conflicting requirements of performance and computational costs in various applications, the approach comes in three different control schemes which differ in how many times the (updated) optimization problem has to be solved, and whether this is done on- or offline. Each of the proposed control schemes minimizes an upper bound on the cost functional while guaranteeing closed-loop stability and satisfaction of input and state constraints. Finally, simulations of an example system show the applicability and the effectiveness of the proposed controllers.

Wind turbine fatigue reduction based on economic-tracking NMPC with direct ANN fatigue estimation

Motivated by the passivity-based nonlinear model predictive control approach (NMPC) in [8], a more general stabilizing NMPC strategy based on passivity and dissipativity is proposed in this paper. We consider model discrepancies and show that the supply rate of the nominal model is always in excess of that of the real system under certain parameter conditions. The stabilizing NMPC scheme proposed for the nominal model also guarantees the stability for the real dynamic system. Compared to the time-triggered NMPC scheme, we further explore the event-triggered NMPC scheme, which can preserve dissipativity under discretization. The L2 stability of the system plant is guaranteed with the provided conditions.