The building sector accounts for almost 40 percent of the global energy consumption. This reveals a great opportunity to exploit renewable energy resources in buildings to achieve the climate target. In this context, this paper offers a building energy system embracing a heat pump, a thermal energy storage system along with grid-connected photovoltaic thermal (PVT) collectors to supply both electric and thermal energy demands of the building with minimum operating cost. To this end, the paper develops a stochastic model predictive control (MPC) strategy to optimally determine the set-point of the whole building energy system while accounting for the uncertainties associated with the PVT energy generation. This system enables the building to 1-shift its electric demand from high-peak to off-peak hours and 2- sell electricity to the grid to make energy arbitrage.
Featuring the fast response and flexibility in control allocation, an electric vehicle with in-wheel motors is a good platform for implementing advanced vehicle dynamics control. Among many active safety functions of an in-wheel motor driven vehicle (IMDV), lateral stability control is a key technology, which can be realized through torque vectoring. To further advance the lateral stabilization performance of the IMDV, in this paper a novel data-driven nonlinear model predictive control (NMPC) is proposed based the recurrent high-order neural network (RHONN) modelling method. First, the new RHONN model is developed to represent vehicle's nonlinear dynamic behaviors. Different from the conventional physics-based modelling method, the RHONN model only needs data and forms high-order polynomials. Based on the RHONN model, the steady-state responses of vehicle's yaw rate and sideslip angle are iteratively optimized and set as the control objectives for low-level controller, aiming to improve the system robustness. Besides, a nonlinear model predictive controller is designed based on the RHONN, which is expected to improve the prediction accuracy during the receding horizon control. Further, a constrained optimization problem is formulated to derive the required yaw moment for vehicle lateral dynamics stabilization. Finally, the performance of the developed RHONN-based nonlinear MPC is validated on an IMDV in the CarSim/Simulink simulation environment. The validation results show that the developed approach outperforms the conventional method, and further improves the stable margin of the system. It is able to enhance the lateral stabilization performance of the IMDV under various driving scenarios, demonstrating the feasibility and effectiveness of the proposed approach.
In this paper, we design a stochastic Model Predictive Control (MPC) traffic signal control method for an urban traffic network when the uncertainties in the estimation of the exogenous (in/out)-flows and the turning ratios of downstream traffic flows are taken into account. Assuming that the traffic model parameters are random variables with known expectations and variance, the traffic signal control and coordination problem is formulated as a quadratic program with linear and second-order cone constraints. In order to reduce computational complexity, we suggest a way to decompose the optimization problem corresponding to the whole traffic network into multiple subproblems. By applying Alternating Direction Method of Multipliers (ADMM), the optimal stochastic traffic signal splits are found in distributed manner. The effectiveness of the designed control method is validated via some simulations using VISSIM and MATLAB.
We present a safe-by-design trajectory planning and tracking framework for nonlinear dynamical systems using a hierarchy of system models. The planning layer uses a low-fidelity model to plan a feasible trajectory satisfying the planning constraints, and the tracking layer utilizes the high-fidelity model to design a controller that restricts the error states between the low- and high-fidelity models to a bounded set. The low-fidelity model enables the planning to be performed online (e.g. using Model Predictive Control) and the tracking controller and error bound are derived offline (e.g. using sum-of-squares programming). To provide freedom in the choice of the low-fidelity model, we allow the tracking error to depend on both the states and inputs of the planner. The goal of this article is to provide a tutorial review of this hierarchical framework and to illustrate it with examples, including a design for vehicle obstacle avoidance.
Model predictive control (MPC) has become a hot cake technology for various applications due to its ability to handle multi-input multi-output systems with physical constraints. The optimization solvers require considerable time, limiting their embedded implementation for real-time control. To overcome the bottleneck of traditional quadratic programming (QP) solvers, this paper proposes a robust penalty method (RPM) to solve an optimization problem in a linear MPC. The main idea of RPM is to solve an unconstrained QP problem using Broyden Fletcher Goldfarb Shannon (BFGS) algorithm. The beauty of this method is that it can find optimal solutions even if initial conditions are in an infeasible region, which makes it robust. Moreover, the RPM is computationally inexpensive as compared to the traditional QP solvers. The proposed RPM is implemented on resource-limited embedded hardware (STM32 microcontroller), and its performance is validated with a case study of a citation aircraft control problem. We show the hardware-in-the-loop co-simulation results of the proposed RPM and compared them with the active set method (ASM) and interior point method (IPM) QP solvers. The performance of MPC with the aforementioned solvers is compared by considering the optimality, time complexity, and ease of hardware implementation. Presented results show that the proposed RPM gives the same optimality as ASM and IPM, and outperforms them in terms of speed.
Insect flight is a strongly nonlinear and actuated dynamical system. As such, strategies for understanding its control have typically relied on either model-based methods or linearizations thereof. Here we develop a framework that combines model predictive control on an established flight dynamics model and deep neural networks (DNN) to create an efficient method for solving the inverse problem of flight control. We turn to natural systems for inspiration since they inherently demonstrate network pruning with the consequence of yielding more efficient networks for a specific set of tasks. This bio-inspired approach allows us to leverage network pruning to optimally sparsify a DNN architecture in order to perform flight tasks with as few neural connections as possible, however, there are limits to sparsification. Specifically, as the number of connections falls below a critical threshold, flight performance drops considerably. We develop sparsification paradigms and explore their limits for control tasks. Monte Carlo simulations also quantify the statistical distribution of network weights during pruning given initial random weights of the DNNs. We demonstrate that on average, the network can be pruned to retain approximately 7% of the original network weights, with statistical distributions quantified at each layer of the network. Overall, this work shows that sparsely connected DNNs are capable of predicting the forces required to follow flight trajectories. Additionally, sparsification has sharp performance limits.
Several studies have reported the importance of optimally operating the absorption column in a post-combustion CO2 capture (PCC) plant. It has been demonstrated in our previous work how economic Model Predictive Control (EMPC) has a great potential to improve the operation of the PCC plant. However, the use of a general economic objective such as maximizing the absorption efficiency of the column can cause EMPC to drive the state of the system close to the constraints. This may often than not lead to solvent overcirculation and flooding which are undesirable. In this work, we present an EMPC with zone tracking algorithm as an effective means to address this problem. The proposed control algorithm incorporates a zone tracking objective and an economic objective to form a multi-objective optimal control problem. To ensure that the zone tracking objective is achieved in the presence of model uncertainties and time-varying flue gas flow rate, we propose a method to modify the original target zone with a control invariant set. The zone modification method combines both ellipsoidal control invariant set techniques and a back-off strategy. The use of ellipsoidal control invariant sets ensure that the method is applicable to large scale systems such as the absorption column. We present several simulation case studies that demonstrate the effectiveness and applicability of the proposed control algorithm to the absorption column in a post-combustion CO2 capture plant.
Economic model predictive control and tracking model predictive control are two popular advanced process control strategies used in various of fields. Nevertheless, which one should be chosen to achieve better performance in the presence of noise is uncertain when designing a control system. To this end, a sensitivity-based performance assessment approach is proposed to pre-evaluate the dynamic economic and tracking performance of them in this work. First, their controller gains around the optimal steady state are evaluated by calculating the sensitivities of corresponding constrained dynamic programming problems. Second, the controller gains are substituted into control loops to derive the propagation of process and measurement noise. Subsequently, the Taylor expansion is introduced to simplify the calculation of variance and mean of each variable. Finally, the tracking and economic performance surfaces are plotted and the performance indices are precisely calculated through integrating the objective functions and the probability density functions. Moreover, boundary moving (i.e., back off) and target moving can be pre-configured to guarantee the stability of controlled processes using the proposed approach. Extensive simulations under different cases illustrate the proposed approach can provide useful guidance on performance assessment and controller design.
Robust autonomy stacks require tight integration of perception, motion planning, and control layers, but these layers often inadequately incorporate inherent perception and prediction uncertainties, either ignoring them altogether or making questionable assumptions of Gaussianity. Robots with nonlinear dynamics and complex sensing modalities operating in an uncertain environment demand more careful consideration of how uncertainties propagate across stack layers. We propose a framework to integrate perception, motion planning, and control by explicitly incorporating perception and prediction uncertainties into planning so that risks of constraint violation can be mitigated. Specifically, we use a nonlinear model predictive control based steering law coupled with a decorrelation scheme based Unscented Kalman Filter for state and environment estimation to propagate the robot state and environment uncertainties. Subsequently, we use distributionally robust risk constraints to limit the risk in the presence of these uncertainties. Finally, we present a layered autonomy stack consisting of a nonlinear steering-based distributionally robust motion planning module and a reference trajectory tracking module. Our numerical experiments with nonlinear robot models and an urban driving simulator show the effectiveness of our proposed approaches.
An approach to resilient planning and control of autonomous vehicles in multi-vehicle traffic scenarios is proposed. The proposed method is based on model predictive control (MPC), where alternative predictions of the surrounding traffic are determined automatically such that they are intentionally adversarial to the ego vehicle. This provides robustness against the inherent uncertainty in traffic predictions. To reduce conservatism, an assumption that other agents are of no ill intent is formalized. Simulation results from highway driving scenarios show that the proposed method in real-time negotiates traffic situations out of scope for a nominal MPC approach and performs favorably to state-of-the-art reinforcement-learning approaches without requiring prior training. The results also show that the proposed method performs effectively, with the ability to prune disturbance sequences with a lower risk for the ego vehicle.
This paper proposes a deep learning-based optimal battery management scheme for frequency regulation (FR) by integrating model predictive control (MPC), supervised learning (SL), reinforcement learning (RL), and high-fidelity battery models. By taking advantage of deep neural networks (DNNs), the derived DNN-approximated policy is computationally efficient in online implementation. The design procedure of the proposed scheme consists of two sequential processes: (1) the SL process, in which we first run a simulation with an MPC embedding a low-fidelity battery model to generate a training data set, and then, based on the generated data set, we optimize a DNN-approximated policy using SL algorithms; and (2) the RL process, in which we utilize RL algorithms to improve the performance of the DNN-approximated policy by balancing short-term economic incentives and long-term battery degradation. The SL process speeds up the subsequent RL process by providing a good initialization. By utilizing RL algorithms, one prominent property of the proposed scheme is that it can learn from the data generated by simulating the FR policy on the high-fidelity battery simulator to adjust the DNN-approximated policy, which is originally based on low-fidelity battery model. A case study using real-world data of FR signals and prices is performed. Simulation results show that, compared to conventional MPC schemes, the proposed deep learning-based scheme can effectively achieve higher economic benefits of FR participation while maintaining lower online computational cost.
In this paper, a control algorithm for guiding a two wheeled mobile robot with unknown inertia to a desired point and orientation using an Adaptive Model Predictive Control (AMPC) framework is presented. The two wheeled mobile robot is modeled as a knife edge or a skate with nonholonomic kinematic constraints and the dynamical equations are derived using the Lagrangian approach. The inputs at every time instant are obtained from Model Predictive Control (MPC) with a set of nominal parameters which are updated using a recursive least squares algorithm. The efficacy of the algorithm is demonstrated through numerical simulations at the end of the paper.
Motivated by large-scale but computationally constrained settings, e.g., the Internet of Things, we present a novel data-driven distributed control algorithm that is synthesized directly from trajectory data. Our method, data-driven Distributed and Localized Model Predictive Control (D$^3$LMPC), builds upon the data-driven System Level Synthesis (SLS) framework, which allows one to parameterize \emph{closed-loop} system responses directly from collected open-loop trajectories. The resulting model-predictive controller can be implemented with distributed computation and only local information sharing. By imposing locality constraints on the system response, we show that the amount of data needed for our synthesis problem is independent of the size of the global system. Moreover, we show that our algorithm enjoys theoretical guarantees for recursive feasibility and asymptotic stability. Finally, we also demonstrate the optimality and scalability of our algorithm in a simulation experiment.
An important issue in quadcopter control is that an accurate dynamic model of the system is nonlinear, complex, and costly to obtain. This limits achievable control performance in practice. Gaussian process (GP) based estimation is an effective tool to learn unknown dynamics from input/output data. However, conventional GP-based control methods often ignore the computational cost associated with accumulating data during the operation of the system and how to handle forgetting in continuous adaption. In this paper, we present a novel Dual Gaussian Process (DGP) based model predictive control strategy that improves the performance of a quadcopter during trajectory tracking. The bio-inspired DGP structure is a combination of a long-term GP and a short-term GP, where the long-term GP is used to keep the learned knowledge in memory and the short-term GP is employed to rapidly compensate unknown dynamics during online operation. Furthermore, a novel recursive online update strategy for the short-term GP is proposed to successively improve the learnt model during online operation in an efficient way. Numerical simulations are used to demonstrate the effectiveness of the proposed strategy.
Real-world reinforcement learning (RL) problems often demand that agents behave safely by obeying a set of designed constraints. We address the challenge of safe RL by coupling a safety guide based on model predictive control (MPC) with a modified policy gradient framework in a linear setting with continuous actions. The guide enforces safe operation of the system by embedding safety requirements as chance constraints in the MPC formulation. The policy gradient training step then includes a safety penalty which trains the base policy to behave safely. We show theoretically that this penalty allows for a provably safe optimal base policy and illustrate our method with a simulated linearized quadrotor experiment.
With the advent of 5G technology that presents enhanced communication reliability and ultra low latency, there is renewed interest in employing cloud computing to perform high performance but computationally expensive control schemes like nonlinear model predictive control (MPC). Such a cloud-based control scheme, however, requires data sharing between the plant (agent) and the cloud, which raises privacy concerns. This is because privacy-sensitive information such as system states and control inputs has to be sent to/from the cloud and thus can be leaked to attackers for various malicious activities. In this paper, we develop a simple yet effective affine masking strategy for privacy-preserving nonlinear MPC. Specifically, we consider external eavesdroppers or honest-but-curious cloud servers that wiretap the communication channel and intend to infer the plant's information including state information and control inputs. An affine transformation-based privacy-preservation mechanism is designed to mask the true states and control signals while reformulating the original MPC problem into a different but equivalent form. We show that the proposed privacy scheme does not affect the MPC performance and it preserves the privacy of the plant such that the eavesdropper is unable to identify the actual value or even estimate a rough range of the private state and input signals. The proposed method is further extended to achieve privacy preservation in cloud-based output-feedback MPC. Simulations are performed to demonstrate the efficacy of the developed approaches.
Optimal experimental design for parameter precision attempts to maximize the information content in experimental data for a most effective identification of parametric model. With the recent developments in miniaturization and parallelization of cultivation platforms for high-throughput screening of optimal growth conditions massive amounts of informative data can be generated with few experiments. Increasing the quantity of the data means to increase the number of parameters and experimental design variables which might deteriorate the identifiability and hamper the online computation of optimal inputs. To reduce the problem complexity, in this work, we introduce an auxiliary controller at a lower level that tracks the optimal feeding strategy computed by a high-level optimizer in an online fashion. The hierarchical framework is especially interesting for the operation under constraints. The key aspect of this method are discussed together with an in silico study considering parallel glucose limited bacterial fed batch cultivations.
Merging is, in general, a challenging task for both human drivers and autonomous vehicles, especially in dense traffic, because the merging vehicle typically needs to interact with other vehicles to identify or create a gap and safely merge into. In this paper, we consider the problem of autonomous vehicle control for forced merge scenarios. We propose a novel game-theoretic controller, called the Leader-Follower Game Controller (LFGC), in which the interactions between the autonomous ego vehicle and other vehicles with a priori uncertain driving intentions is modeled as a partially observable leader-follower game. The LFGC estimates the other vehicles' intentions online based on observed trajectories, and then predicts their future trajectories and plans the ego vehicle's own trajectory using Model Predictive Control (MPC) to simultaneously achieve probabilistically guaranteed safety and merging objectives. To verify the performance of LFGC, we test it in simulations and with the NGSIM data, where the LFGC demonstrates a high success rate of 97.5% in merging.
Herein we report a multi-zone, heating, ventilation and air-conditioning (HVAC) control case study of an industrial plant responsible for cooling a hospital surgery center. The adopted approach to guaranteeing thermal comfort and reducing electrical energy consumption is based on a statistical non-parametric, non-linear regression technique named Gaussian processes. Our study aimed at assessing the suitability of the aforementioned technique to learning the building dynamics and yielding models for our model predictive control (MPC) scheme. Experimental results gathered while the building was under regular use showcase the final controller performance while subject to a number of measured and unmeasured disturbances. Finally, we provide readers with practical details and recommendations on how to manage the computational complexity of the on-line optimization problem and obtain high-quality solutions from solvers.
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 further 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 can improve 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.