Explicit non-linear model predictive control for autonomous helicopters

This thesis is concerned with different topics in multi-parametric programming and explicit model predictive control, with particular emphasis on hybrid systems. The main goal is to extend the applicability of these concepts to a wider range of problems of practical interest, and to propose algorithmic solutions to challenging problems such as constrained dynamic programming of hybrid linear systems and nonlinear explicit model predictive control. The concepts of multi-parametric programming and explicit model predictive control are presented in detail, and it is shown how the solution to explicit model predictive control may be efficiently computed using a combination of multi-parametric programming and dynamic programming. A novel algorithm for constrained dynamic programming of mixed-integer linear problems is proposed and illustrated with a numerical example that arises in the context of inventory scheduling. Based on the developments on constrained dynamic programming of mixed-integer linear problems, an algorithm for explicit model predictive control of hybrid systems with linear cost function is presented. This method is further extended to the design of robust explicit controllers for hybrid linear systems for the case when uncertainty is present in the model. The final part of the thesis is concerned with developments in nonlinear explicit model predictive control. By using suitable model reduction techniques, the model captures the essential nonlinear dynamics of the system, while the achieved reduction in dimensionality allows the use of nonlinear multi-parametric programming methods.

Fast explicit nonlinear model predictive control via multiresolution function approximation with guaranteed stability

The objective is to evaluate the performance of an explicit model predictive control for controlling the room temperature actuated by the on-off air conditioner to minimize the energy usage by reducing the working time of a compressor. There are a lot of on-off air conditioners already installed in the educational building in Thailand. To replace all of those by the inverter air conditioner or HVAC system, the high investment cost is required. Therefore, the on-off air conditioners continue to work in such building. The effective solution may be the low cost control unit which is simple like a remote control. The method is to design the remote control embedded by the temperature sensor and the explicit model predictive control that is based on the off-line optimization. The experiment is performed in the laboratory room with dimension 4×7×3.5 m (WxLxH) actuated by Saijo Denki 18,320 Btu on-off air conditioner. The experimental results reveal that the temperature reaches the desired value 25 degree Celsius within 10 minute and keeps fluctuating between 23 and 26 degree Celsius. The working time of compressor is reduced 33.33 %. The result shows that the explicit model predictive control is effective for the remote control application in terms of the implementation and energy saving.

A nonlinear fault tolerant station keeping controller for a multi‐vectored propeller airship without velocity and angular velocity sensors is developed, which is composed of three modules: nonlinear model predictive controller (NMPC), sliding mode observer (SMO), and linear programming (LP) based control allocation. The kinematics and dynamics model of the airship are introduced. Based on the nonlinear model, with the assumption that the velocity and angular velocity sensors are damaged, a sliding mode observer is designed to estimate the velocity and angular velocity of the airship. To achieve good performance in the station keeping mission, an explicit nonlinear model predictive control is derived. A linear programming base control allocation method is proposed to solve both amplitude and rate constraint of the propulsion forces and deflection angles. Stability analysis is carried out to prove that the system can be stabilized in finite time. Simulation results for the station keeping control are illustrated to prove the effectiveness of the proposed method.

Data-driven modeling and stability control for industrial zinc roaster and its edge controller implementation

This paper introduces a quasi‐linear parameter‐varying model predictive control (qLPV MPC) framework for robust trajectory tracking of fully actuated unmanned underwater vehicles (UUVs), explicitly considering external disturbances and input constraints. To address the challenges of nonlinear dynamics, actuator limitations, and external disturbances, the UUV system is formulated as a qLPV model to balance the computational efficiency and the control accuracy. Then, a qLPV MPC method is designed for UUVs by incorporating an auxiliary feedback control law and a terminal constraint set, which ensures iterative feasibility and asymptotic stability. The input‐to‐state stability (ISS) is mathematically proven through Lyapunov‐based analysis, so that the proposed framework could stabilize bounded tracking errors despite system disturbances. Finally, an iterative solution method based on sequential quadratic programming (SQP) is introduced to obtain efficient solutions of the optimal control sequence while reducing the computational complexity. Simulation studies are conducted to validate the effectiveness of the proposed controller. The results show that the proposed method exhibits smaller tracking errors and faster convergence speeds compared to traditional robust nonlinear model predictive control (NMPC).

Model predictive control (MPC) is a popular optimal control approach that can explicitly deal with system constraints. However, its high computational cost motivates researches on various approximation methods that make the MPC more practically viable for systems with fast dynamics and/or limited on-board computing power. Neighboring extremal (NE) is one such method that can be used to adapt to a nominal open-loop MPC sequence based on state perturbations so that it alleviates the online computational burden and extends the applicability of the MPC. In this paper, a cloud-based nonlinear MPC (NMPC) framework is considered where the NMPC is first performed on the cloud by taking advantage of its powerful computation and storage capabilities. To save the computational power, instead of solving the NMPC problem at every time step, the open-loop control sequence is downloaded for on-board implementation, then the NE is employed to systematically update the control sequence based on the deviation of the measured/estimated state from the nominal state obtained by the cloud-based NMPC. However, due to unknown disturbances and request-response communication delays between the plant and the cloud, the cloud-based NMPC may not show a reasonable performance for the plant even with the NE adaptations when the deviation is large. Therefore, we develop an event-triggered scheme based on a cost criteria to strike a balance between performance and cost. Finally, the efficacy of the proposed control synthesis is demonstrated with simulations on the application of the cart inverted pendulum.

In this paper a hierarchical model predictive control framework for the energy management of a hybrid electric vehicle is extended by replacing the supervisory linear model predictive controller with a nonlinear model predictive controller. The nonlinear system dynamics of a parallel hybrid electric vehicle are incorporated into a nonlinear optimal control problem which is solved at each time instance. The discretization of the continuous time system dynamics is realized via direct multiple shooting. The low-level linear model predictive controller considers the actuator dynamics for optimal tracking of the driver's torque demand while the high-level controller considers the slow dynamics of the vehicle and the battery. The proposed strategy is validated in simulation with the worldwide harmonized light vehicles test cycle and compared to a hierarchical model predictive control framework with linearized system dynamics.

SUMMARYA multistep nonlinear model predictive control (MPC) framework is developed to achieve steady‐state offset‐free control in the presence of plant–model mismatch. Our formulation explicitly accounts for the effect of plant–model mismatch by involving the output feedback error, which is expressed as the difference between the measured process output and the predicted model output at the previous sampling instance, in the multistep model recursive prediction. The proposed scheme is capable of improving the performance of nonlinear MPC, because the plant–model mismatch is effectively compensated through the recursive prediction propagation. We prove that this formulation is able to remove the steady‐state error to achieve offset‐free control. The proposed nonlinear MPC framework is applied to a highly nonlinear two‐input two‐output continuous stirred tank reactor, in comparison with other MPC implementations. The results obtained demonstrate that the proposed technique outperforms some existing popular MPC schemes and can realise offset‐free control even under significant plant–model mismatch and unmeasured disturbances. Copyright © 2012 John Wiley & Sons, Ltd.

In this article, we present a quasi-infinite horizon nonlinear model predictive control (MPC) scheme for tracking of generic reference trajectories. This scheme is applicable to nonlinear systems, which are locally incrementally stabilizable. For such systems, we provide a reference generic offline procedure to compute an incrementally stabilizing feedback with a continuously parameterized quadratic quasi-infinite horizon terminal cost. As a result, we get a nonlinear reference tracking MPC scheme with a valid terminal cost for general reachable reference trajectories without increasing the online computational complexity. The practicality of this approach is demonstrated with a benchmark example.

A novel traffic signal split approach based on Explicit Model Predictive Control

The computational cost of implementing Model Predictive Control (MPC) restricts its use in robotic systems with fast dynamics. The use of optimization algorithms to find a control solution is responsible for most of the computational cost. Explicit MPC (eMPC) solutions aim to overcome the computational cost problem by performing the optimization process before runtime. The main contribution of this work is to compare the computational cost of the conventional MPC to the computational cost of eMPC, in the quadrotor stabilization task. The controllers are evaluated in two different scenarios, one in a Model-in-Loop (MIL) environment and the other using the Robot Operating System (ROS) in a Processor-in-Loop (PIL) setup. The results show that eMPC is an alternative to implement predictive controllers with determinism in computational time execution, due to the use of only algebraic operations at runtime, without any numerical tools, but, with the disadvantage of using a significant amount of memory.

The article studies the trajectory tracking control problem of underactuated marine vehicles via the nonlinear model predictive control (NMPC) strategy, where practical control and state constraints present. It is a well-known challenging issue that the conventional NMPC is not applicable for underactuated marine vehicles, due to the fact that there does not exist a local static continuous state-feedback controller to stabilize the underactuated dynamics. To resolve this issue, this article proposes to construct an auxiliary time-varying tracking controller to aid terminal constraint design in the NMPC framework, where the time-varying tracking controller borrows the ideas from Lyapunov's direct method and backstepping approach. Based on this, a novel NMPC algorithm is designed to ensure trajectory tracking control of underactuated marine vehicles. Furthermore, a systematic parameter design approach is developed. Under the designed parameters, we show that the tracking error system is input-to-state stable (ISS). Finally, the effectiveness of the designed algorithm is verified by thorough simulation and hardware experiments.

Model predictive control (MPC) is a powerful control method that handles dynamical systems with constraints. However, solving MPC iteratively in real time, i.e., implicit MPC, remains a computational challenge. To address this, common solutions include explicit MPC and function approximation. Both methods, whenever applicable, may improve the computational efficiency of the implicit MPC by several orders of magnitude. Nevertheless, explicit MPC often requires expensive pre-computation and does not easily apply to higher-dimensional problems. Meanwhile, function approximation, although scales better with dimension, still requires pre-training on a large dataset and generally cannot guarantee to find an accurate surrogate policy, the failure of which often leads to closed-loop instability. To address these issues, we propose a triple-mode hybrid control scheme, named Memory-Augmented MPC, by combining a linear quadratic regulator, a neural network, and an MPC. From its standard form, we derive two variants of such hybrid control scheme: one customized for chaotic systems and the other for slow systems. The proposed scheme does not require pre-computation and is capable of improving the amortized running time of the composed MPC with a well-trained neural network. In addition, the scheme maintains closed-loop stability with any neural networks of proper input and output dimensions, alleviating the need for certifying optimality of the neural network in safety-critical applications. Note to Practitioners—This article was motivated by the need to reduce the amortized cost of MPC in repetitive industrial robotic applications, where long-term operational cost is important and safety is critical. Examples of such applications include factory robotic arm manipulation and fixed-route quadcopter payload transport. Unlike explicit MPC or function approximation, our approach does not require any pre-computation or pre-training. Rather, it attains task proficiency over time by learning a surrogate neural network on the spot and by gradually replacing the costly MPC with the more efficient surrogate model so long as safety permits. Consequently, the proposed scheme incurs a learning cost during the initial phase of the deployment but usually becomes more adept on the task afterwards, leading to amortized efficiency.

In this paper, a model predictive control (MPC) framework for building energy system setpoint optimization is developed and tested. The performance of the MPC framework is presented in comparison to a baseline case, where a fixed setpoint schedule is used. To simulate the MPC procedure, an EnergyPlus building model is used to represent the actual building that the optimal setpoints are applied to, and a Gaussian process (GP) regression meta-model is used in the MPC procedure that generates the optimal setpoints. The performance outputs that are used for evaluation are total heating, ventilation and air conditioning (HVAC) energy usage and the Fanger predicted mean vote (PMV) thermal comfort measure. The inputs for the GP regression meta-models are selected to be representative of data points that could be obtained by modern supervisory control and data acquisition (SCADA) systems to support data-driven building models. The supervisory MPC framework is capable of reducing the total energy usage with minor adjustments in thermal comfort.