Based on our recent research on neural heuristic quantization systems, we propose an emulation problem consistent with the neuromimetic paradigm. This optimal quantization problem can be solved with model predictive control (MPC) by deriving the conditions under which the quantized system can guarantee (asymptotic) stability during emulation by optimizing a Lyapunov-like objective function. The neuromimetic model features large numbers of discrete inputs, and the optimization involves integer variables. The approach in the paper begins by solving an optimization using model predictive control (MPC) and then using a neural network to train the data generated in this process and applying Fincke and Pohst's sphere decoding algorithm to narrow down the search for the optimal solution.
Conventional control of fluid systems does not consider system-wide knowledge for optimising energy efficient operation. Distributed control of fluid systems combines reliable local control of components while using system-wide cooperation to ensure energy efficient operation. The presented work compares three approaches to distributed control based on multi-agent systems, distributed model predictive control (DMPC), multi-agent deep reinforcement learning (MADRL) and market mechanism design. These approaches were applied to a generic fluid system and evaluated with regard to functionality, energy efficient operation, modeling effort, reliability in the face of disruptions, and transparency of control decisions. All approaches were shown to fulfil the functionality, though a trade-off between functional quality and energy efficiency was identified. Increased modeling effort was shown to improve the performance slightly while a strong interdependence of information caused by excessive information sharing has proven to be disadvantageous. DMPC and partially observable MADRL were less sensitive to disruptions than market mechanism. In conclusion, agent-based control of fluid systems achieves greater energy efficiency than conventional methods, with values similar to centralized optimal control and thus represent a viable design approach of fluid system control.
We propose an optimal operation control strategy for an electro-thermal microgrid. Compared to existing work, our approach increases flexibility by operating the thermal network with variable flow temperatures and in that way explicitly exploits its inherent storage capacities. To this end, the microgrid is represented by a multi-layer network composed of an electrical and a thermal layer. We show that the system behavior can be represented by a discrete-time state model derived from DC power flow approximations and 1d incompressible Euler equations. Both layers are interconnected via heat pumps. By combining this model with desired operating objectives and constraints, we obtain a constrained convex optimization problem. This is used to derive a model predictive control scheme for the optimal operation of electro-thermal microgrids. The performance of the proposed operation control algorithm is demonstrated in a numerical case study.
Model predictive control (MPC) is a promising approach for the lateral and longitudinal control of autonomous vehicles. However, the parameterization of the MPC with respect to high-level requirements such as passenger comfort as well as lateral and longitudinal tracking is a challenging task. Numerous tuning parameters as well as conflicting requirements need to be considered. This contribution formulates the MPC tuning task as a multi-objective optimization problem. Solving it is challenging for two reasons: First, MPC-parameterizations are evaluated on an computationally expensive simulation environment. As a result, the used optimization algorithm needs to be as sampleefficient as possible. Second, for some poor parameterizations the simulation cannot be completed and therefore useful objective function values are not available (learning with crash constraints). In this contribution, we compare the sample efficiency of multi-objective particle swarm optimization (MOPSO), a genetic algorithm (NSGA-II) and multiple versions of Bayesian optimization (BO). We extend BO, by introducing an adaptive batch size to limit the computational overhead and by a method on how to deal with crash constraints. Results show, that BO works best for a small budget, NSGA-II is best for medium budgets and for large budgets none of the evaluated optimizers is superior to random search. Both proposed BO extensions are shown to be beneficial.
We compare the performance of proportional-integral-derivative (PID) control, linear model predictive control (LMPC), and nonlinear model predictive control (NMPC) for a physical setup of the quadruple tank system (QTS). We estimate the parameters in a continuous-discrete time stochastic nonlinear model for the QTS using a prediction-error-method based on the measured process data and a maximum likelihood (ML) criterion. In the NMPC algorithm, we use this identified continuous-discrete time stochastic nonlinear model. The LMPC algorithm is based on a linearization of this nonlinear model. We tune the PID controller using Skogestad's IMC tuning rules using a transfer function representation of the linearized model. Norms of the observed tracking errors and the rate of change of the manipulated variables are used to compare the performance of the control algorithms. The LMPC and NMPC perform better than the PID controller for a predefined time-varying setpoint trajectory. The LMPC and NMPC algorithms have similar performance.
This contribution deals with multi-objective model-predictive control (MPC) of a wave energy converter (WEC) device concept, which can harvest energy from sea waves using a dielectric elastomer generator (DEG) power take-off system. We aim to maximise the extracted energy through control while minimising the accumulated damage to the DEG. With reference to system operation in stochastic waves, we first generate ground truth solutions by solving an optimal control problem, and we analyse the MPC performance to determine a prediction horizon that trades off accuracy and efficiency for computation. Fixed weights in the MPC scheme can produce unpredictable costs for variable sea condition, meaning the average rate of cost accumulation can vary vastly. To steer this cost growth, we propose a heuristic to adapt the algorithm by changing the weighting of the cost functions using for fulfilling the long-time goal of accumulating a small enough damage in a fixed time. A simulated case-study is presented in order to evaluate the performance of the proposed MPC framework and the weight-adaptation algorithm. The proposed heuristic proves to be able to limit the amount of accumulated damage while remaining close to (or even improving) the energy yield obtained with a comparable fixed-weight MPC.
Flexible robots may overcome some of the industry's major challenges, such as enabling intrinsically safe human-robot collaboration and achieving a higher payload-to-mass ratio. However, controlling flexible robots is complicated due to their complex dynamics, which include oscillatory behavior and a high-dimensional state space. Nonlinear model predictive control (NMPC) offers an effective means to control such robots, but its significant computational demand often limits its application in real-time scenarios. To enable fast control of flexible robots, we propose a framework for a safe approximation of NMPC using imitation learning and a predictive safety filter. Our framework significantly reduces computation time while incurring a slight loss in performance. Compared to NMPC, our framework shows more than an eightfold improvement in computation time when controlling a three-dimensional flexible robot arm in simulation, all while guaranteeing safety constraints. Notably, our approach outperforms state-of-the-art reinforcement learning methods. The development of fast and safe approximate NMPC holds the potential to accelerate the adoption of flexible robots in industry. The project code is available at: tinyurl.com/anmpc4fr
Sampling-based Model Predictive Control (MPC) is a flexible control framework that can reason about non-smooth dynamics and cost functions. Recently, significant work has focused on the use of machine learning to improve the performance of MPC, often through learning or fine-tuning the dynamics or cost function. In contrast, we focus on learning to optimize more effectively. In other words, to improve the update rule within MPC. We show that this can be particularly useful in sampling-based MPC, where we often wish to minimize the number of samples for computational reasons. Unfortunately, the cost of computational efficiency is a reduction in performance; fewer samples results in noisier updates. We show that we can contend with this noise by learning how to update the control distribution more effectively and make better use of the few samples that we have. Our learned controllers are trained via imitation learning to mimic an expert which has access to substantially more samples. We test the efficacy of our approach on multiple simulated robotics tasks in sample-constrained regimes and demonstrate that our approach can outperform a MPC controller with the same number of samples.
Sampling-based methods have become a cornerstone of contemporary approaches to Model Predictive Control (MPC), as they make no restrictions on the differentiability of the dynamics or cost function and are straightforward to parallelize. However, their efficacy is highly dependent on the quality of the sampling distribution itself, which is often assumed to be simple, like a Gaussian. This restriction can result in samples which are far from optimal, leading to poor performance. Recent work has explored improving the performance of MPC by sampling in a learned latent space of controls. However, these methods ultimately perform all MPC parameter updates and warm-starting between time steps in the control space. This requires us to rely on a number of heuristics for generating samples and updating the distribution and may lead to sub-optimal performance. Instead, we propose to carry out all operations in the latent space, allowing us to take full advantage of the learned distribution. Specifically, we frame the learning problem as bi-level optimization and show how to train the controller with backpropagation-through-time. By using a normalizing flow parameterization of the distribution, we can leverage its tractable density to avoid requiring differentiability of the dynamics and cost function. Finally, we evaluate the proposed approach on simulated robotics tasks and demonstrate its ability to surpass the performance of prior methods and scale better with a reduced number of samples.
This paper presents a parallel Monte Carlo simulation based performance quantification method for nonlinear model predictive control (NMPC) in closed-loop. The method provides distributions for the controller performance in stochastic systems enabling performance quantification. We perform high-performance Monte Carlo simulations in C enabled by a new thread-safe NMPC implementation in combination with an existing high-performance Monte Carlo simulation toolbox in C. We express the NMPC regulator as an optimal control problem (OCP), which we solve with the new thread-safe sequential quadratic programming software NLPSQP. Our results show almost linear scale-up for the NMPC closed-loop on a 32 core CPU. In particular, we get approximately 27 times speed-up on 32 cores. We demonstrate the performance quantification method on a simple continuous stirred tank reactor (CSTR), where we perform 30,000 closed-loop simulations with both an NMPC and a reference proportional-integral (PI) controller. Performance quantification of the stochastic closed-loop system shows that the NMPC outperforms the PI controller in both mean and variance.
This paper presents a systematic method for the selection of the Model Predictive Control (MPC) stage cost. We match the MPC feedback law to a proportional-integral (PI) controller, which we efficiently tune by high-performance Monte Carlo (MC) simulation. The PI tuning offers a wide range of tuning possibilities that is then inherited by the MPC design. The MC simulation tuning of the PI controller is based on the minimization of two different objectives; 1) the 2-norm tracking error, and 2) a bi-objective consisting of the 2-norm tracking error and a 2-norm input rate of movement penalty. We apply the method to design MPC for an exothermic chemical reaction conducted in an adiabatic continuous stirred tank reactor (CSTR). The process is of interest as the nonlinear dynamics result in a desired operating point very close to a constraint. Our MPC design includes stage costs automatically designed to match the tuned PI controllers, hard input constraints, and a soft output constraint. Stochastic simulation results show that both the PI controller and the MPC can track the desired operating point. However, the MPC shows reduced output constraint violation compared to the PI controller. As such, the MPC design method successfully combines the efficient tuning of the PI controller with the constraint handling properties of MPC.
Autonomous driving has a natural bi-level structure. The goal of the upper behavioural layer is to provide appropriate lane change, speeding up, and braking decisions to optimize a given driving task. However, this layer can only indirectly influence the driving efficiency through the lower-level trajectory planner, which takes in the behavioural inputs to produce motion commands. Existing sampling-based approaches do not fully exploit the strong coupling between the behavioural and planning layer. On the other hand, end-to-end Reinforcement Learning (RL) can learn a behavioural layer while incorporating feedback from the lower-level planner. However, purely data-driven approaches often fail in safety metrics in unseen environments. This paper presents a novel alternative; a parameterized bi-level optimization that jointly computes the optimal behavioural decisions and the resulting downstream trajectory. Our approach runs in real-time using a custom GPU-accelerated batch optimizer, and a Conditional Variational Autoencoder learnt warm-start strategy. Extensive simulations show that our approach outperforms state-of-the-art model predictive control and RL approaches in terms of collision rate while being competitive in driving efficiency.
In this paper, we propose a data-driven economic model predictive control (EMPC) scheme with generalized terminal constraint to control an unknown linear time-invariant system. Our scheme is based on the Fundamental Lemma to predict future system trajectories using a persistently exciting input-output trajectory. The control objective is to minimize an economic cost objective. By employing a generalized terminal constraint with artificial equilibrium, the scheme does not require prior knowledge of the optimal equilibrium. We prove that the asymptotic average performance of the closed-loop system can be made arbitrarily close to that of the optimal equilibrium. Moreover, we extend our results to the case of an unknown linear stage cost function, where the Fundamental lemma is used to predict the stage cost directly. The effectiveness of the proposed scheme is shown by a numerical example.
We propose a learning-based robust predictive control algorithm that compensates for significant uncertainty in the dynamics for a class of discrete-time systems that are nominally linear with an additive nonlinear component. Such systems commonly model the nonlinear effects of an unknown environment on a nominal system. We optimize over a class of nonlinear feedback policies inspired by certainty equivalent "estimate-and-cancel" control laws pioneered in classical adaptive control to achieve significant performance improvements in the presence of uncertainties of large magnitude, a setting in which existing learning-based predictive control algorithms often struggle to guarantee safety. In contrast to previous work in robust adaptive MPC, our approach allows us to take advantage of structure (i.e., the numerical predictions) in the a priori unknown dynamics learned online through function approximation. Our approach also extends typical nonlinear adaptive control methods to systems with state and input constraints even when we cannot directly cancel the additive uncertain function from the dynamics. We apply contemporary statistical estimation techniques to certify the system's safety through persistent constraint satisfaction with high probability. Moreover, we propose using Bayesian meta-learning algorithms that learn calibrated model priors to help satisfy the assumptions of the control design in challenging settings. Finally, we show in simulation that our method can accommodate more significant unknown dynamics terms than existing methods and that the use of Bayesian meta-learning allows us to adapt to the test environments more rapidly.
Cloud computing holds the promise of reduced costs through economies of scale. To realize this promise, cloud computing vendors typically solve sequential resource allocation problems, where customer workloads are packed on shared hardware. Virtual machines (VM) form the foundation of modern cloud computing as they help logically abstract user compute from shared physical infrastructure. Traditionally, VM packing problems are solved by predicting demand, followed by a Model Predictive Control (MPC) optimization over a future horizon. We introduce an approximate formulation of an industrial VM packing problem as an MILP with soft-constraints parameterized by the predictions. Recently, predict-and-optimize (PnO) was proposed for end-to-end training of prediction models by back-propagating the cost of decisions through the optimization problem. But, PnO is unable to scale to the large prediction horizons prevalent in cloud computing. To tackle this issue, we propose the Predict-and-Critic (PnC) framework that outperforms PnO with just a two-step horizon by leveraging reinforcement learning. PnC jointly trains a prediction model and a terminal Q function that approximates cost-to-go over a long horizon, by back-propagating the cost of decisions through the optimization problem \emph{and from the future}. The terminal Q function allows us to solve a much smaller two-step horizon optimization problem than the multi-step horizon necessary in PnO. We evaluate PnO and the PnC framework on two datasets, three workloads, and with disturbances not modeled in the optimization problem. We find that PnC significantly improves decision quality over PnO, even when the optimization problem is not a perfect representation of reality. We also find that hardening the soft constraints of the MILP and back-propagating through the constraints improves decision quality for both PnO and PnC.
Stability under model predictive control (MPC) schemes is frequently ensured by terminal ingredients. Employing a (control) Lyapunov function as the terminal cost constitutes a common choice. Learning-based methods may be used to construct the terminal cost by relating it to, for instance, an infinite-horizon optimal control problem in which the optimal cost is a Lyapunov function. Value iteration, an approximate dynamic programming (ADP) approach, refers to one particular cost approximation technique. In this work, we merge the results of terminally unconstrained predictive control and approximate value iteration to draw benefits from both fields. A prediction horizon is derived in dependence on different factors such as approximation-related errors to render the closed-loop asymptotically stable further allowing a suboptimality estimate in comparison to an infinite horizon optimal cost. The result extends recent studies on predictive control with ADP-based terminal costs, not requiring a local initial stabilizing controller. We compare this controller in simulation with other terminal cost options to show that the proposed approach leads to a shorter minimal horizon in comparison to previous results.
We present an output feedback stochastic model predictive control (SMPC) approach for linear systems subject to Gaussian disturbances and measurement noise and probabilistic constraints on system states and inputs. The presented approach combines a linear Kalman filter for state estimation with an indirect feedback SMPC, which is initialized with a predicted nominal state, while feedback of the current state estimate enters through the objective of the SMPC problem. For this combination, we establish recursive feasibility of the SMPC problem due to the chosen initialization, and closed-loop chance constraint satisfaction thanks to an appropriate tightening of the constraints in the SMPC problem also considering the state estimation uncertainty. Additionally, we show that for specific design choices in the SMPC problem, the unconstrained linear-quadratic-Gaussian (LQG) solution is recovered if it is feasible for a given initial condition and the considered constraints. We demonstrate this fact for a numerical example, and show that the resulting output feedback controller can provide non-conservative constraint satisfaction.
In a typical car-following scenario, target vehicle speed fluctuations act as an external disturbance to the host vehicle and in turn affect its energy consumption. To control a host vehicle in an energy-efficient manner using model predictive control (MPC), and moreover, enhance the performance of an ecological adaptive cruise control (EACC) strategy, forecasting the future velocities of a target vehicle is essential. For this purpose, a deep recurrent neural network-based vehicle speed prediction using long-short term memory (LSTM) and gated recurrent units (GRU) is studied in this work. Besides these, the physics-based constant velocity (CV) and constant acceleration (CA) models are discussed. The sequential time series data for training (e.g. speed trajectories of the target and its preceding vehicles obtained through vehicle-to-vehicle (V2V) communication, road speed limits, traffic light current and future phases collected using vehicle-to-infrastructure (V2I) communication) is gathered from both urban and highway networks created in the microscopic traffic simulator SUMO. The proposed speed prediction models are evaluated for long-term predictions (up to 10 s) of target vehicle future velocities. Moreover, the results revealed that the LSTM-based speed predictor outperformed other models in terms of achieving better prediction accuracy on unseen test datasets, and thereby showcasing better generalization ability. Furthermore, the performance of EACC-equipped host car on the predicted velocities is evaluated, and its energy-saving benefits for different prediction horizons are presented.
This paper presents a cloud-based learning model predictive controller that integrates three interacting components: a set of agents, which must learn to perform a finite set of tasks with the minimum possible local cost; a coordinator, which assigns the tasks to the agents; and the cloud, which stores data to facilitate the agents' learning. The tasks consist in traveling repeatedly between a set of target states while satisfying input and state constraints. In turn, the state constraints may change in time for each of the possible tasks. To deal with it, different modes of operation, which establish different restrictions, are defined. The agents' inputs are found by solving local model predictive control (MPC) problems where the terminal set and cost are defined from previous trajectories. The data collected by each agent is uploaded to the cloud and made accessible to all their peers. Likewise, similarity between tasks is exploited to accelerate the learning process. The applicability of the proposed approach is illustrated by simulation results.
Echo State Networks (ESN) are a type of Recurrent Neural Network that yields promising results in representing time series and nonlinear dynamic systems. Although they are equipped with a very efficient training procedure, Reservoir Computing strategies, such as the ESN, require high-order networks, i.e., many neurons, resulting in a large number of states that are magnitudes higher than the number of model inputs and outputs. A large number of states not only makes the time-step computation more costly but also may pose robustness issues, especially when applying ESNs to problems such as Model Predictive Control (MPC) and other optimal control problems. One way to circumvent this complexity issue is through Model Order Reduction strategies such as the Proper Orthogonal Decomposition (POD) and its variants (POD-DEIM), whereby we find an equivalent lower order representation to an already trained high dimension ESN. To this end, this work aims to investigate and analyze the performance of POD methods in Echo State Networks, evaluating their effectiveness through the Memory Capacity (MC) of the POD-reduced network compared to the original (full-order) ESN. We also perform experiments on two numerical case studies: a NARMA10 difference equation and an oil platform containing two wells and one riser. The results show that there is little loss of performance comparing the original ESN to a POD-reduced counterpart and that the performance of a POD-reduced ESN tends to be superior to a normal ESN of the same size. Also, the POD-reduced network achieves speedups of around $80\%$ compared to the original ESN.