Recent works have demonstrated how Linear Parameter Varying Model Predictive Control (LPV MPC) algorithms are able to control nonlinear systems with precision and reduced computational load. Specifically, these schemes achieve comparable performances to state-of-the-art nonlinear MPCs, while requiring the solution of only one quadratic programming problem (thus being real-time capable). In this tutorial paper, we provide a step-by-step overview of how to implement such LPV MPC algorithms, covering from modelling to stability aspects. For illustration purposes, we consider a realistic implementation for a gas-lift petroleoum extraction process, comparing the LPV approach with the becnhmark nonlinear MPC software CasADi.
In this paper, an offset-free bilinear model predictive control approach for wind turbines is presented. State-of-the-art controllers employ different control loops for pitch angle and generator torque which switch depending on wind conditions. In contrast, the presented controller is based on one unified control law that works for all wind conditions. The inherent nonlinearity of wind turbines is addressed through a piecewise-affine approximation of the power coefficient, which is modelled in a mixed-integer fashion. The presented controller is compared to a state-of-the-art baseline controller in a numerical case study using OpenFAST. Simulation results show that the presented controller ensures accurate reference power tracking. Additionally, damage equivalent loads are reduced for higher wind speeds.
The increasing penetration of renewable energy resources has transformed the energy system from traditional hierarchical energy delivery paradigm to a distributed structure. Such development is accompanied with continuous liberalization in the energy sector, giving rise to possible energy trading among networked local energy hub. Joint operation of such hubs can improve energy efficiency and support the integration of renewable energy resource. Acknowledging peer-to-peer trading between hubs, their optimal operation within the network can maximize consumption of locally produced energy. However, for such complex systems involving multiple stakeholders, both computational tractability and privacy concerns need to be accounted for. We investigate both decentralized and centralized model predictive control (MPC) approaches for a network of energy hubs. While the centralized control strategy offers superior performance to the decentralized method, its implementation is computationally prohibitive and raises privacy concerns, as the information of each hub has to be shared extensively. On the other hand, a classical decentralized control approach can ease the implementation at the expense of sub-optimal performance of the overall system. In this work, a distributed scheme based on a consensus alternating direction method of multipliers (ADMM) algorithm is proposed. It combines the performance of the centralized approach with the privacy preservation of decentralized approach. A novel multi-horizon MPC framework is also introduced to increase the prediction horizon without compromising the time discretization or making the problem computationally intractable. A benchmark three-hub network is used to compare the performance of the mentioned methods. The results show superior performance in terms of total cost, computational time, robustness to demand and prices variations.
Modern power systems are characterized by low inertia and fast voltage dynamics due to the increase of sources connecting via power electronics and the removal of large traditional thermal generators. Power electronics are commonly equipped with fast controllers that are able to reach a desired voltage setpoint within seconds. In this paper, we propose and compare two approaches using Model Predictive Control (MPC) to compute optimal voltage references for the power electronic devices in order to minimize the losses in a DC microgrid: i) a traditional setpoint-tracking MPC which receives a previously computed optimal setpoint; ii) an economic MPC which does not require a priori computed setpoints. We show that the economic MPC outperforms the setpoint-tracking MPC in simulations with the CIGRE benchmark system when multiple load disturbances occur. Some insights and discussions related to the stability of the closed-loop system using its dissipativity properties are highlighted for both approaches.
This research paper compares two neural-network-based adaptive controllers, namely the Hybrid Deep Learning Neural Network Controller (HDLNNC) and the Adaptive Model Predictive Control with Nonlinear Prediction and Linearization along the Predicted Trajectory (AMPC-NPLPT), for controlling a nonlinear object with delay. Specifically, the study investigates the effect of delay on the accuracy of the two controllers. The experimental results demonstrate that the AMPC-NPLPT approach outperforms HDLNNC regarding control accuracy for the given nonlinear object control problem.
The ability to reliably maximize tire force usage would improve the safety of autonomous vehicles, especially in challenging edge cases. However, vehicle control near the limits of handling has many challenges, including robustly contending with tire force saturation, balancing model fidelity and computational efficiency, and coordinating inputs with the lower level chassis control system. This work studies Nonlinear Model Predictive Control for limit handling, specifically adapting to changing tire-road conditions and maximally allocating tire force utilization. We present a novel hierarchical framework that combines a single-track model with longitudinal weight transfer dynamics in the predictive control layer, with lateral brake distribution occurring at the chassis control layer. This vehicle model is simultaneously used in an Unscented Kalman Filter for online friction estimation. Comparative experiments on a full-scale vehicle operating on a race track at up to 95% of maximum tire force usage demonstrate the overall practical effectiveness of this approach.
In this paper, a real time implementable load coordination strategy is developed for the optimization of electric demands in a smart home. The strategy minimizes the electricity cost to the home owner, while limiting the disruptions associated with the deferring of flexible power loads. A multi-objective nonlinear mixed integer programming is formulated as a sequential model predictive control, which is then solved using genetic algorithm. The load shifting benefits obtained by deploying an advanced coordination strategy are compared against a baseline controller for various home characteristics, such as location, size and equipment. The simulation study shows that the deployment of the smart home energy management strategy achieves approximately 5% reduction in grid cost compared to a baseline strategy. This is achieved by deferring approximately 50\% of the flexible loads, which is possible due to the use of the stationary energy storage.
We propose the first method that determines the exact worst-case execution time (WCET) for implicit linear model predictive control (MPC). Such WCET bounds are imperative when MPC is used in real time to control safety-critical systems. The proposed method applies when the quadratic programming solver in the MPC controller belongs to a family of well-established active-set solvers. For such solvers, we leverage a previously proposed complexity certification framework to generate a finite set of archetypal optimization problems; we prove that these archetypal problems form an execution-time equivalent cover of all possible problems; that is, that they capture the execution time for solving any possible optimization problem that can be encountered online. Hence, by solving just these archetypal problems on the hardware on which the MPC is to be deployed, and by recording the execution times, we obtain the exact WCET. In addition to providing formal proofs of the methods efficacy, we validate the method on an MPC example where an inverted pendulum on a cart is stabilized. The experiments highlight the following advantages compared with classical WCET methods: (i) in contrast to classical static methods, our method gives the exact WCET; (ii) in contrast to classical measurement-based methods, our method guarantees a correct WCET estimate and requires fewer measurements on the hardware.
This paper presents a deep learning based model predictive control (MPC) algorithm for systems with unmatched and bounded state-action dependent uncertainties of unknown structure. We utilize a deep neural network (DNN) as an oracle in the underlying optimization problem of learning based MPC (LBMPC) to estimate unmatched uncertainties. Generally, non-parametric oracles such as DNN are considered difficult to employ with LBMPC due to the technical difficulties associated with estimation of their coefficients in real time. We employ a dual-timescale adaptation mechanism, where the weights of the last layer of the neural network are updated in real time while the inner layers are trained on a slower timescale using the training data collected online and selectively stored in a buffer. Our results are validated through a numerical experiment on the compression system model of jet engine. These results indicate that the proposed approach is implementable in real time and carries the theoretical guarantees of LBMPC.
Partially-observable problems pose a trade-off between reducing costs and gathering information. They can be solved optimally by planning in belief space, but that is often prohibitively expensive. Model-predictive control (MPC) takes the alternative approach of using a state estimator to form a belief over the state, and then plan in state space. This ignores potential future observations during planning and, as a result, cannot actively increase or preserve the certainty of its own state estimate. We find a middle-ground between planning in belief space and completely ignoring its dynamics by only reasoning about its future accuracy. Our approach, filter-aware MPC, penalises the loss of information by what we call "trackability", the expected error of the state estimator. We show that model-based simulation allows condensing trackability into a neural network, which allows fast planning. In experiments involving visual navigation, realistic every-day environments and a two-link robot arm, we show that filter-aware MPC vastly improves regular MPC.
In this work, a novel distributed search-planning framework is proposed, where a dynamically varying team of autonomous agents cooperate in order to search multiple objects of interest in three-dimension (3-D). It is assumed that the agents can enter and exit the mission space at any point in time, and as a result the number of agents that actively participate in the mission varies over time. The proposed distributed search-planning framework takes into account the agent dynamical and sensing model, and the dynamically varying number of agents, and utilizes model predictive control (MPC) to generate cooperative search trajectories over a finite rolling planning horizon. This enables the agents to adapt their decisions on-line while considering the plans of their peers, maximizing their search planning performance, and reducing the duplication of work.
Neural network (NN) approximations of model predictive control (MPC) are a versatile approach if the online solution of the underlying optimal control problem (OCP) is too demanding and if an exact computation of the explicit MPC law is intractable. The drawback of such approximations is that they typically do not preserve stability and performance guarantees of the original MPC. However, such guarantees can be recovered if the maximum error with respect to the optimal control law and the Lipschitz constant of that error are known. We show in this work how to compute both values exactly when the control law is approximated by a maxout NN. We build upon related results for ReLU NN approximations and derive mixed-integer (MI) linear constraints that allow a computation of the output and the local gain of a maxout NN by solving an MI feasibility problem. Furthermore, we show theoretically and experimentally that maxout NN exist for which the maximum error is zero.
Model predictive control (MPC) achieves stability and constraint satisfaction for general nonlinear systems, but requires computationally expensive online optimization. This paper studies approximations of such MPC controllers via neural networks (NNs) to achieve fast online evaluation. We propose safety augmentation that yields deterministic guarantees for convergence and constraint satisfaction despite approximation inaccuracies. We approximate the entire input sequence of the MPC with NNs, which allows us to verify online if it is a feasible solution to the MPC problem. We replace the NN solution by a safe candidate based on standard MPC techniques whenever it is infeasible or has worse cost. Our method requires a single evaluation of the NN and forward integration of the input sequence online, which is fast to compute on resource-constrained systems. The proposed control framework is illustrated using two numerical non-linear MPC benchmarks of different complexity, demonstrating computational speedups that are orders of magnitude higher than online optimization. In the examples, we achieve deterministic safety through the safety-augmented NNs, where a naive NN implementation fails.
We present a Stochastic Model Predictive Control (SMPC) framework for linear systems subject to Gaussian disturbances. In order to avoid feasibility issues, we employ a recent initialization strategy, optimizing over an interpolation of the initial state between the current measurement and previous prediction. By also considering the variance in the interpolation, we can employ variable-size tubes, to ensure constraint satisfaction in closed-loop. We show that this novel method improves control performance and enables following the constraint closer, then previous methods. Using a DC-DC converter as numerical example we illustrated the improvement over previous methods.
This paper proposes methods for reachability analysis of nonlinear systems in both open loop and closed loop with advanced controllers. The methods combine hybrid zonotopes, a construct called a state-update set, functional decomposition, and special ordered set approximations to enable linear growth in reachable set memory complexity with time and linear scaling in computational complexity with the system dimension. Facilitating this combination are new identities for constructing nonconvex sets that contain nonlinear functions and for efficiently converting a collection of polytopes from vertex representation to hybrid zonotope representation. Benchmark numerical examples from the literature demonstrate the proposed methods and provide comparison to state-of-the-art techniques.
Energy management systems (EMS) have traditionally been implemented using rule-based control (RBC) and model predictive control (MPC) methods. However, recent research has explored the use of reinforcement learning (RL) as a promising alternative. This paper introduces TreeC, a machine learning method that utilizes the covariance matrix adaptation evolution strategy metaheuristic algorithm to generate an interpretable EMS modeled as a decision tree. Unlike RBC and MPC approaches, TreeC learns the decision strategy of the EMS based on historical data, adapting the control model to the controlled energy grid. The decision strategy is represented as a decision tree, providing interpretability compared to RL methods that often rely on black-box models like neural networks. TreeC is evaluated against MPC with perfect forecast and RL EMSs in two case studies taken from literature: an electric grid case and a household heating case. In the electric grid case, TreeC achieves an average energy loss and constraint violation score of 19.2, which is close to MPC and RL EMSs that achieve scores of 14.4 and 16.2 respectively. All three methods control the electric grid well especially when compared to the random EMS, which obtains an average score of 12 875. In the household heating case, TreeC performs similarly to MPC on the adjusted and averaged electricity cost and total discomfort (0.033 EUR/m$^2$ and 0.42 Kh for TreeC compared to 0.037 EUR/m$^2$ and 2.91 kH for MPC), while outperforming RL (0.266 EUR/m$^2$ and 24.41 Kh).
Over the last few years, we have not seen any major developments in model-free or model-based learning methods that would make one obsolete relative to the other. In most cases, the used technique is heavily dependent on the use case scenario or other attributes, e.g. the environment. Both approaches have their own advantages, for example, sample efficiency or computational efficiency. However, when combining the two, the advantages of each can be combined and hence achieve better performance. The TD-MPC framework is an example of this approach. On the one hand, a world model in combination with model predictive control is used to get a good initial estimate of the value function. On the other hand, a Q function is used to provide a good long-term estimate. Similar to algorithms like MuZero a latent state representation is used, where only task-relevant information is encoded to reduce the complexity. In this paper, we propose the use of a reconstruction function within the TD-MPC framework, so that the agent can reconstruct the original observation given the internal state representation. This allows our agent to have a more stable learning signal during training and also improves sample efficiency. Our proposed addition of another loss term leads to improved performance on both state- and image-based tasks from the DeepMind-Control suite.
Model predictive control allows solving complex control tasks with control and state constraints. However, an optimal control problem must be solved in real-time to predict the future system behavior, which is hardly possible on embedded hardware. To solve this problem, this paper proposes to compute a sequence of one-step optimizations aided by pre-computed inner approximations of reachable sets rather than solving the full-horizon optimal control problem at once. This feature can be used to virtually predict the future system behavior with a low computational footprint. Proofs for recursive feasibility and for the sufficient conditions for asymptotic stability under mild assumptions are given. The presented approach is demonstrated in simulation for functional verification.
One major issue in learning-based model predictive control (MPC) for autonomous driving is the contradiction between the system model's prediction accuracy and computation efficiency. The more situations a system model covers, the more complex it is, along with highly nonlinear and nonconvex properties. These issues make the optimization too complicated to solve and render real-time control impractical.To address these issues, we propose a hierarchical learning residual model which leverages random forests and linear regression.The learned model consists of two levels. The low level uses linear regression to fit the residues, and the high level uses random forests to switch different linear models. Meanwhile, we adopt the linear dynamic bicycle model with error states as the nominal model.The switched linear regression model is added to the nominal model to form the system model. It reformulates the learning-based MPC as a quadratic program (QP) problem and optimization solvers can effectively solve it. Experimental path tracking results show that the driving vehicle's prediction accuracy and tracking accuracy are significantly improved compared with the nominal MPC.Compared with the state-of-the-art Gaussian process-based nonlinear model predictive control (GP-NMPC), our method gets better performance on tracking accuracy while maintaining a lower computation consumption.
We consider multi-agent systems with heterogeneous, nonlinear agents subject to individual constraints that want to achieve a periodic, dynamic cooperative control goal which can be characterised by a set and a suitable cost. We propose a sequential distributed model predictive control (MPC) scheme in which agents sequentially solve an individual optimisation problem to track an artificial periodic output trajectory. The optimisation problems are coupled through these artificial periodic output trajectories, which are communicated and penalised using the cost that characterises the cooperative goal. The agents communicate only their artificial trajectories and only once per time step. We show that under suitable assumptions, the agents can incrementally move their artificial output trajectories towards the cooperative goal, and, hence, their closed-loop output trajectories asymptotically achieve it. We illustrate the scheme with a simulation example.