Keywords: Electrical Power Systems, Energy Efficient Buildings, Distributed Model Predictive Control
Abstract: This paper presents a distributed predictive control framework coordinating battery energy storage systems and Heating, Ventilation and Air Conditioning (HVAC) systems in the distribution network for the provision of ancillary services to the power grid, whilst keeping both the indoor thermal comfort and the voltage within acceptable limits. The HVAC systems are modeled as virtual storage devices and aggregated with battery energy storage systems to form virtual storage plants (VSPs). An optimization problem over a given prediction horizon is formulated for coordinating an arbitrary number of such VSPs so as to deliver the required regulation reserve whilst maintaining an acceptable voltage profile of the distribution network. The formulated optimization problem is incorporated into a Model Predictive Control (MPC) scheme. The nonlinear HVAC system model makes the resulted MPC problem nonlinear, which is then convexified and solved in a distributed manner by using the alternating direction method of multipliers (ADMM). Simulation results using realistic data demonstrate the effectiveness of the proposed approach, which delivers the required services by satisfying the system constraints.

Keywords: Energy Efficient Buildings, Economic Predictive Control
Abstract: Buildings are responsible for about a quarter of global energy-related CO_2 emissions. Consequently, the decarbonisation of the housing stock is essential in achieving net-zero carbon emissions. Global decarbonisation targets can be achieved through increased efficiency in using energy generated by intermittent resources. The paper presents a co-design framework for simultaneous optimal design and operation of residential buildings using Model Predictive Control (MPC). The framework is capable of explicitly taking into account operational constraints and pushing the system to its efficiency and performance limits in an integrated fashion. The optimality criterion minimises system cost considering time-varying electricity prices and battery degradation. A case study illustrates the potential of co-design in enhancing flexibility and self-sufficiency of a system operating under different conditions. Specifically, numerical results from a low-fidelity model show substantial carbon emission reduction and bill savings compared to an a-priori sizing approach.

Keywords: Learning and Predictive Control, Explicit Model Predictive Control, Energy Efficient Buildings
Abstract: We present a differentiable predictive control (DPC) methodology for learning constrained control laws for unknown nonlinear systems. DPC poses an approximate solution to multiparametric programming problems emerging from explicit nonlinear model predictive control (MPC). Contrary to approximate MPC, DPC does not require supervision by an expert controller. Instead, a system dynamics model is learned from the observed system's dynamics, and the neural control law is optimized offline by leveraging the differentiable closed-loop system model. The combination of a differentiable closed-loop system and penalty methods for constraint handling of system outputs and inputs allows us to optimize the control law's parameters directly by backpropagating economic MPC loss through the learned system model. The control performance of the proposed DPC method is demonstrated in simulation using a multi-zone building emulator. Without considering plant-model mismatch, the presented DPC is capable of learning complex constrained control policies for a learned system dynamics model.

Keywords: Cyber-Physical Systems, IoT/IoE, Robust Model Predictive Control
Abstract: We consider the control of constrained, uncertain systems over wireless communication networks with varying capabilities. We consider the case that a radio resource manager, which manages the wireless network, provides guaranteed minimum communication at fixed time instants while offering more frequent communication depending on the current load of the shared network, available network capacity or other conditions. We present a robust model predictive control strategy exploiting ideas of tube MPC. It takes the varying communication possibilities directly into account and utilizes possibly additionally available communication to improve the closed loop performance. Conditions to guarantee closed loop properties of the overall system are presented. Simulations illustrate the proposed approach and its benefits.

Keywords: Economic Predictive Control, Robust Model Predictive Control
Abstract: In this paper, we provide non-averaged and transient performance guarantees for recently developed, tube-based robust economic model predictive control (MPC) schemes. In particular, we consider both tube-based MPC schemes with and without terminal conditions. We show that the closed-loop performance obtained by applying such MPC schemes is approximately optimal when evaluated both on finite and infinite time horizons. These performance bounds are similar to those derived previously for nominal economic MPC. The theoretical results are discussed in a numerical example.

Keywords: Optimization and Model Predictive Control, Robust Model Predictive Control, Automotive
Abstract: A new polynomial systems method is defined for the restricted structure nonlinear predictive controllers design. The control algorithm is established for a discrete-time nonlinear system, described in the polynomial matrix linear parameter varying form. The low-order restricted structure controller is parameterized in terms of discrete transfer operators set that the designer chooses multiplied by a set of optimized gains. The controller within the feedback loop can have a general linear parameter varying form or something as simple as a PI structure. The predictive control multi-step cost-index, which is minimized, comprises weighted error, control signal costing, and gain magnitude terms. A simulation of an automotive example is used to evaluate the nonlinear restricted structure controller performance.

Keywords: Optimization and Model Predictive Control, Tracking and Path Following Predictive Control, Economic Predictive Control
Abstract: This paper proposes a feedback-optimizing model predictive control (FOMPC) algorithm to regulate a disturbed linear time-invariant system to an equilibrium point that is the solution to a steady-state optimization problem. This regulation is achieved without knowledge of the optimal steady-state set-points or explicit solution of the steady-state optimization problem. We develop the FOMPC algorithm by indirectly formulating the residuals of the Karush--Kuhn--Tucker (KKT) optimality conditions associated with the steady-state optimization into the transient performance objective of the MPC controller. By solving the steady-state optimization problem implicitly, via feedback, the proposed algorithm allows the optimal steady-states to be reached despite unknown disturbances and/or set-point changes, and in the presence of linear inequality constraints. We establish recursive feasibility and stability of the approach, and show that FOMPC is a generalization of conventional tracking model predictive control.

Keywords: Robust Model Predictive Control, Dedicated Optimization Solvers for Model Predictive Control, Real-Time Implementation of Model Predictive Control
Abstract: In this paper, we propose an efficient zero-order algorithm that can be used to compute an approximate solution to robust optimal control problems (OCP) and robustified nonconvex programs in general. In particular, we focus on robustified OCPs that make use of ellipsoidal uncertainty sets and show that, with the proposed zero-order method, we can efficiently obtain suboptimal, but robustly feasible solutions. The main idea lies in leveraging an inexact sequential quadratic programming (SQP) algorithm in which an advantageous sparsity structure is enforced. The obtained sparsity allows one to eliminate the variables associated with the propagation of the ellipsoidal uncertainty sets and to solve a reduced problem with the same dimensionality and sparsity structure of a nominal OCP. The inexact algorithm can drastically reduce the computational complexity of the SQP iterations (e.g., in the case where a structure exploiting interior-point method is used to solve the underlying quadratic programs (QPs), from O(N cdot (n_x^6 + n_u^3)) to O(N cdot (n_x^3 + n_u^3))). Moreover, standard embedded QP solvers for nominal problems can be leveraged to solve the reduced QP.

Keywords: Robust Model Predictive Control, Optimization and Model Predictive Control
Abstract: Recently, a regional MPC approach has been proposed that exploits the piecewise affine structure of the optimal solution (without computing the entire explicit solution beforehand). Here, "regional" refers to the idea of using the affine feedback law that is optimal in a vicinity of the current state of operation, and therefore provides the optimal input signal without requiring to solve a QP. In the present paper, we apply the idea of regional MPC to min-max MPC problems. We show that the new robust approach can significantly reduce the number of QPs to be solved within min-max MPC resulting in a reduced overall computational effort. Moreover, we compare the performance of the new approach to an existing robust regional MPC approach using a numerical example with varying horizon. Finally, we provide a rule for choosing a suitable robust regional MPC approach based on the horizon.

Keywords: Stability and Recursive Feasibility, Scheduling and Manufacturing
Abstract: In recent years, theoretical results for model predictive control (MPC) have been expanded to address discrete actuators (decisions) and high-level planning and scheduling problems. The application of MPC-style methods to scheduling problems has been driven, in part, by the robustness afforded by feedback. The ability of MPC, and feedback methods in general, to reject small persistent disturbances is well-recognized. In many planning and scheduling applications, however, we must also consider an additional class of discrete and infrequent disturbances, such as breakdowns and unplanned maintenance. In this paper, we establish that nominal MPC is robust, in a stochastic context, to this class of discrete and infrequent disturbances. We illustrate these results with a nonlinear blending example.

Keywords: Stochastic Model Predictive Control, Optimization and Model Predictive Control, Stability and Recursive Feasibility
Abstract: Stochastic Model Predictive Control (MPC) has established itself as a simple method to approximate stochastically disturbed optimal control problems, yet it comes with significant computational effort. In particular, taking into account all information of stochastic disturbances---if at all possible---can be expensive. However, due to the continuous re-optimization, MPC schemes also have a certain inherent robustness. Hence, we ask the question, which part of the perturbation is absorbed by the MPC-inherent robustness, and which needs to be explicitly taken into account in the optimization.

In this paper, we compare several stochastic MPC algorithms taking into account a growing amount of the stochastic information: starting with deterministic schemes of certainty equivalence type, we use the noise's distribution's quantiles and finally we take, potentially, all stochastic information into account when performing Monte Carlo simulations in the MPC scheme. We carry out a numerical case study for the inverted pendulum, in which we observe that for short prediction horizons Monte Carlo does not pay off while for large prediction horizon it has slight advantages. Further, we discuss possible explanations for this behavior.

Keywords: Optimization and Model Predictive Control

Keywords: Optimization and Model Predictive Control, Stochastic Model Predictive Control

Keywords: Stochastic Model Predictive Control, Dedicated Optimization Solvers for Model Predictive Control, Automotive
Abstract: Stochastic nonlinear model predictive control (SNMPC) allows to directly take model uncertainty into account, e.g., by including probabilistic chance constraints. This paper proposes linear-regression Kalman filtering to perform high-accuracy propagation of mean and covariance information for the nonlinear system dynamics in a tractable approximation of the stochastic optimal control problem. In addition, a tailored adjoint-based sequential quadratic programming (SQP) algorithm is presented to considerably reduce the computational cost and allow a real-time implementation of the resulting SNMPC. The prediction accuracy and control performance of the proposed approach are illustrated on a vehicle control application subject to external disturbances, while highlighting a worst-case computation time of 10 ms for SNMPC which is close to that of deterministic NMPC for this particular case study.

Keywords: Tracking and Path Following Predictive Control
Abstract: Offset-free action of model predictive control (MPC) for nonlinear systems with the number of measured outputs greater than controlled outputs is a nontrivial problem. Motivated by investigating the possible application of MPC for the control system of magnetic levitation (Maglev) vehicles -- tracking only the gap while measuring the gap, acceleration, and current -- for higher speeds than hitherto travelled, different possible offset-free nonlinear MPC strategies are reviewed and discussed. Moreover, a novel approach based on a two-stage observer is introduced, requiring less effort to design an offset-free MPC. The different strategies are applied and analyzed in detail for a realistic model of the control system of the latest Transrapid vehicle, called TR09. Unlike usual offset-free MPC studies, the controller performance is also studied in a typical dynamic scenario, revealing the conflict and trade-off between the requirements for speed of command response and the robustness of closed-loop stability.

Keywords: Optimization and Model Predictive Control

Keywords: Aerospace, Dedicated Hardware Implementation of Model Predictive Control, Formation control: mobile robots, UAVs
Abstract: We propose the design of a nonlinear model predictive controller (NMPC) for the attitude and speed control problem of fixed-wing unmanned aerial vehicles (UAVs). The controller is designed to stabilize to a set point in the output space that allows for a globally unique minimum of a quadratic cost for either roll-pitch or pitch-yaw control. The applicability of the proposed method is illustrated with numerical results where we show that even for initial conditions far from the reference, high update rates are feasible on off-the-shelf single-board computers which can be embedded in the UAVs flight stack.

Keywords: Automotive, Motion Control, Tracking and Path Following Predictive Control
Abstract: Trajectory planning with the consideration of obstacles is a classical task in autonomous driving and robotics applications. This paper introduces a novel solution approach for the subclass of autonomous racing problems which is additionally capable of dealing with reward objects. This special type of objects is representing particular regions in state space, whose optional reaching is somehow beneficial (e.g. results in bonus points during a race). First, a homotopy class is selected which represents the left/right and catch/ignore decisions related to obstacle avoidance and reward collection, respectively. For this purpose, a linear mixed-integer problem is posed such that an approximated combinatorial problem is solved and repetitive switching decisions between solver calls are avoided. Secondly, an optimal control problem (OCP) based on a single-track vehicle model is solved within this homotopy class. In the corresponding nonlinear program, homotopy iterations are performed on the race track boundaries which correspond to the previously chosen homotopy class. This leads to an improved convergence of the solver compared to the direct approach. The mixed-integer method's effectiveness is demonstrated within a real-world test scenario during the autonomous racing competition Roborace. Furthermore, its combination with the OCP as well as the performance gain resulting from the homotopy iterations are shown in simulation.

Keywords: Electrical Power Systems, Motion Control, Automotive
Abstract: Brushless DC (BLDC) motor is the first choice for lightweight electric vehicles because of its high torque, high power density, and compatible speed range. The vehicle environment is very dynamic, nonlinear, and noisy. It is challenging to design a BLDC motor control for high-performance operation. Therefore this paper presents Nonlinear Model Predictive Control (NMPC) with online state estimation techniques for speed and torque control. We investigate the performance of three estimation techniques integrated with an NMPC strategy. The estimation techniques include Extended Kalman Filter (EKF), Unscented Kalman Filter (UKF), and Nonlinear Moving Horizon Estimation (NMHE). The comparative study is performed where the state variables are estimated from noisy measurements of output variables. Results of the closed-loop NMPC performance with three estimation techniques are presented and analyzed with different performance indicators. The results show the integration of NMHE with NMPC provides better performance than other estimation techniques. However, the NMHE is computationally expensive as compared to EKF and UKF.

Keywords: Formation control: mobile robots, UAVs, Distributed Model Predictive Control
Abstract: This paper investigates the rendezvous problem for the autonomous cooperative landing of an unmanned aerial vehicle (UAV) on an unmanned surface vehicle (USV). Such heterogeneous agents, with nonlinear dynamics, are dynamically decoupled but share a common cooperative rendezvous task. The underlying control scheme is based on distributed Model Predictive Control (MPC). The main contribution is a rendezvous algorithm with an online update rule of the rendezvous location. The algorithm only requires the agents to exchange information when they can not guarantee to rendezvous. Hence, the exchange of information occurs aperiodically, which reduces the necessary communication between the agents. Furthermore, we prove that the algorithm guarantees recursive feasibility. The simulation results illustrate the effectiveness of the proposed algorithm applied to the problem of autonomous cooperative landing.

Keywords: Robotics, Motion Control
Abstract: Mecanum-wheeled robots have been thoroughly used to automate tasks in many different applications. However, they are usually controlled by neglecting their dynamics and relying only on their kinematic model. In this paper, we model the behaviour of such robots by taking into account both their equations of motion and the electrodynamic response of their actuators, including dry and viscous friction at their shafts. This allows us to design a model predictive controller aimed to minimise the energy consumed by the robot. The controller also satisfies a number of non-linear inequalities modelling motor voltage limits and obstacle avoidance constraints. The result is an agile controller that can quickly adapt to changes in the environment, while generating fast and energy-efficient manoeuvres towards the goal.

Keywords: Robotics, Optimization and Model Predictive Control, Stability and Recursive Feasibility
Abstract: This paper highlights the benefits of a feedback linearization local controller and the associated terminal bound constraints (box-type inequalities) in an NMPC (Nonlinear Model Predictive Control) design for a multicopter system. We replace the standard invariant construction for the terminal region of the NMPC design with two sets: i) a delta-invariant set (with delta the sampling time) which constrains the trajectories to re-enter it periodically, at pre-defined moments of time; ii) a constraint admissible safe set in which the trajectories lie in the remaining time instants. We show that this alternative construction verifies the recursive feasibility and asymptotic stability. Moreover, the additional degrees of freedom and simpler construction show advantages over similar NMPC designs with standard ellipsoidal terminal region.

Keywords: Stability and Recursive Feasibility, Optimization and Model Predictive Control, Motion Control
Abstract: We consider an input-constrained differential-drive robot with actuator dynamics. For this system, we establish asymptotic stability of the origin on arbitrary compact, convex sets using Model Predictive Control (MPC) without stabilizing terminal conditions despite the presence of state constraints and actuator dynamics. We note that the problem without those two additional ingredients was essentially solved beforehand, despite the fact that the linearization is not stabilizable. We propose an approach successfully solving the task at hand by combining the theory of barriers to characterize the viability kernel and an MPC framework based on so-called cost controllability. Moreover, we present a numerical case study to derive quantitative bounds on the required length of the prediction horizon. To this end, we investigate the boundary of the viability kernel and a neighbourhood of the origin, i.e. the most interesting areas.