The optimal operation of water reservoir systems is a challenging task involving multiple conflicting objectives. The main source of complexity is the presence of the water inflow, which acts as an exogenous, highly uncertain disturbance on the system. When model predictive control (MPC) is employed, the optimal water release is usually computed based on the (predicted) trajectory of the inflow. This choice may jeopardize the closed-loop performance when the actual inflow differs from its forecast. In this work, we consider - for the first time - a stochastic MPC approach for water reservoirs, in which the control is optimized based on a set of plausible future inflows directly generated from past data. Such a scenario-based MPC strategy allows the controller to be more cautious, counteracting droughty periods (e.g., the lake level going below the dry limit) while at the same time guaranteeing that the agricultural water demand is satisfied. The method's effectiveness is validated through extensive Monte Carlo tests using actual inflow data from Lake Como, Italy.
Due to the nonlinearities and operational constraints typical to quadcopter missions, Model Predictive Control (MPC) encounters the major challenge of high computational power necessary for the online implementation. This problem may prove impractical, especially for a hardware-limited or small-scale setup. By removing the need for online solvers while keeping the constraint satisfaction and optimality, Explicit MPC (ExMPC) stands out as a strong candidate for this application. Yet, the formulation was usually hindered by the two main problems: nonlinearity and dimensionality. In this paper, we propose an ExMPC solution for the quadcopter position stabilization by analyzing its description (dynamics and constraints) in the flat output space. With the former issue, the system is exactly linearized into a concatenation of three double integrators at a price of cumbersome constraints in the new coordinates. For the latter, with a suitable characterization of these constraints, the stabilizing ExMPC can be computed for each double integrator separately. The controller is then validated via simulations and experimental tests. The proposed scheme achieves similar performance and guarantees to the state-of-the-art solution but with notably less computational effort, allowing scalability in a centralized manner
This article investigates synthetic model-predictive control (MPC) problems to demonstrate that an increased precision of the internal prediction model (PM) automatially entails an improvement of the controller as a whole. In contrast to reinforcement learning (RL), MPC uses the PM to predict subsequent states of the controlled system (CS), instead of directly recommending suitable actions. To assess how the precision of the PM translates into the quality of the model-predictive controller, we compare a DNN-based PM to the optimal baseline PM for three well-known control problems of varying complexity. The baseline PM achieves perfect accuracy by accessing the simulation of the CS itself. Based on the obtained results, we argue that an improvement of the PM will always improve the controller as a whole, without considering the impact of other components such as action selection (which, in this article, relies on evolutionary optimization).
Neural networks (NNs) have emerged as a state-of-the-art method for modeling nonlinear systems in model predictive control (MPC). However, the robustness of NNs, in terms of sensitivity to small input perturbations, remains a critical challenge for practical applications. To address this, we develop Lipschitz-Constrained Neural Networks (LCNNs) for modeling nonlinear systems and derive rigorous theoretical results to demonstrate their effectiveness in approximating Lipschitz functions, reducing input sensitivity, and preventing over-fitting. Specifically, we first prove a universal approximation theorem to show that LCNNs using SpectralDense layers can approximate any 1-Lipschitz target function. Then, we prove a probabilistic generalization error bound for LCNNs using SpectralDense layers by using their empirical Rademacher complexity. Finally, the LCNNs are incorporated into the MPC scheme, and a chemical process example is utilized to show that LCNN-based MPC outperforms MPC using conventional feedforward NNs in the presence of training data noise.
With the rapid growth of wind power penetration, wind farms (WFs) are required to implement frequency regulation that active power control to track a given power reference. Due to the wake interaction of the wind turbines (WTs), there is more than one solution to distributing power reference among the operating WTs, which can be exploited as an optimization problem for the second goal, such as fatigue load alleviation. In this paper, a closed-loop model predictive controller is developed that minimizes the wind farm tracking errors, the dynamical fatigue load, and and the load equalization. The controller is evaluated in a mediumfidelity model. A 64 WTs simulation case study is used to demonstrate the control performance for different penalty factor settings. The results indicated the WF can alleviate dynamical fatigue load and have no significant impact on power tracking. However, the uneven load distribution in the wind turbine system poses challenges for maintenance. By adding a trade-off between the load equalization and dynamical fatigue load, the load differences between WTs are significantly reduced, while the dynamical fatigue load slightly increases when selecting a proper penalty factor.
In this paper we treat optimal trajectory planning for an autonomous vehicle (AV) operating in dense traffic, where vehicles closely interact with each other. To tackle this problem, we present a novel framework that couples trajectory prediction and planning in multi-agent environments, using distributed model predictive control. A demonstration of our framework is presented in simulation, employing a trajectory planner using non-linear model predictive control. We analyze performance and convergence of our framework, subject to different prediction errors. The results indicate that the obtained locally optimal solutions are improved, compared with decoupled prediction and planning.
Thermal-aware workload distribution is a common approach in the literature for power consumption optimization in data centers. However, data centers also have other operational costs such as the cost of equipment maintenance and replacement. It has been shown that server reliability depends on frequency of their temperature variations, arising from workload transitions due to dynamic demands. In this work, we formulate a nonlinear optimization problem that considers the cost of workload transitions in addition to IT and cooling power consumption. To approximate the solution, we first linearize the problem; the result is a mixed integer programming problem. A modified heuristic is then proposed to approximate the solution of the linear problem. Finally, a Model Predictive Control (MPC) approach is integrated with the proposed heuristics for automatic workload reconfiguration when future demand is not known exactly, but predictions are available. Numerical results show that the proposed schemes are attractive in different settings.
The driving style of an Autonomous Vehicle (AV) refers to how it behaves and interacts with other AVs. In a multi-vehicle autonomous driving system, an AV capable of identifying the driving styles of its nearby AVs can reliably evaluate the risk of collisions and make more reasonable driving decisions. However, there has not been a consistent definition of driving styles for an AV in the literature, although it is considered that the driving style is encoded in the AV's trajectories and can be identified using Maximum Entropy Inverse Reinforcement Learning (ME-IRL) methods as a cost function. Nevertheless, an important indicator of the driving style, i.e., how an AV reacts to its nearby AVs, is not fully incorporated in the feature design of previous ME-IRL methods. In this paper, we describe the driving style as a cost function of a series of weighted features. We design additional novel features to capture the AV's reaction-aware characteristics. Then, we identify the driving styles from the demonstration trajectories generated by the Stochastic Model Predictive Control (SMPC) using a modified ME-IRL method with our newly proposed features. The proposed method is validated using MATLAB simulation and an off-the-shelf experiment.
This paper has developed a closed-loop control algorithm to operate the G2V/V2G action, tested under varying battery voltage conditions and load and source power differences. Under V2G action, to maintain total harmonic distortion under minimum level and grid frequency under the standard limit, a Model predictive controller (MPC) has been used to control the gate driver circuit of the inverter. The state space model of the plant has been created using the system identification toolbox, and the MPC Controller block has been designed using the Model Predictive Control Toolbox of MATLAB. The proposed methodology is tested using MATLAB/Simulink and OPAL-RT (OP4510) in a real-time environment. This methodology reduces %THD to less than 0.5%, improves waveform quality of grid voltage, inverter output voltage, grid current, and inverter output current to nearly 99%, and maintains the grid frequency in standard limit while in G2V/V2G action.
In light of the increasing adoption of edge computing in areas such as intelligent furniture, robotics, and smart homes, this paper introduces HyperSNN, an innovative method for control tasks that uses spiking neural networks (SNNs) in combination with hyperdimensional computing. HyperSNN substitutes expensive 32-bit floating point multiplications with 8-bit integer additions, resulting in reduced energy consumption while enhancing robustness and potentially improving accuracy. Our model was tested on AI Gym benchmarks, including Cartpole, Acrobot, MountainCar, and Lunar Lander. HyperSNN achieves control accuracies that are on par with conventional machine learning methods but with only 1.36% to 9.96% of the energy expenditure. Furthermore, our experiments showed increased robustness when using HyperSNN. We believe that HyperSNN is especially suitable for interactive, mobile, and wearable devices, promoting energy-efficient and robust system design. Furthermore, it paves the way for the practical implementation of complex algorithms like model predictive control (MPC) in real-world industrial scenarios.
Model Predictive Control (MPC) has proven to be a powerful tool for the control of systems with constraints. Nonetheless, in many applications, a major challenge arises, that is finding the optimal solution within a single sampling instant to apply a receding-horizon policy. In such cases, many suboptimal solutions have been proposed, among which the possibility of "blocking" some moves a-priori. In this paper, we propose a dynamic approach to move blocking, to exploit the solution already available at the previous iteration, and we show not only that such an approach preserves asymptotic stability, but also that the decrease of performance with respect to the ideal solution can be theoretically bounded.
Aiming to mimic the brachiation locomotion of primates, we establish a brachiation robot model capable of swinging between different bars. The robot's design is based on a four-link underactuated structure. We propose an offline trajectory generator with optimization for minimizing energy consumption, which is implemented by direct collocation method to generate joint-space trajectories. We also propose a linear Model Predictive Control (MPC) algorithm as the feedback controller. The proposed MPC concurrently tracks both trajectories in joint space and Cartesian space. In simulation experiments, we analyzed the influence of lower-to-upper arm length ratio and swing time on the motion performance. The simulation results also demonstrate the robot has satisfied ability in trajectory tracking, obstacle avoidance and robustness.
Ramp metering, which regulates the flow entering the freeway, is one of the most effective freeway traffic control methods. This paper introduces an output-feedback adaptive approach to ramp metering that combines model predictive control (MPC) with set-membership parameter and state estimation. The set-membership estimator is based on a mixed-monotone embedding of underlying traffic dynamics. The embedding is also used as the modeling basis for MPC optimization. For a freeway stretch with unknown parameters and partial measurement on the freeway mainline, we provide sufficient conditions on the control horizon, cost functions, terminal sets of MPC, and inflow demand at the ramps such that the queue lengths in the closed-loop system remain bounded. The sufficient condition on the demand matches the necessary condition, thereby proving maximal throughput under the proposed controller. The result is strengthened to input-to-state stability when model parameters and demand are known. The stability analysis is conducted for the case of constant demand and unbounded on-ramps. The closed-loop trajectory data generated by the proposed controller is shown to facilitate finite time estimation of free-flow model parameters, i.e., free-flow speed and turning ratios. Simulation results illustrate stability of the closed-loop system under the proposed controller with time-varying demand and few mainline measurements, for which the system becomes unstable under a well-known approach from the literature. This indicates that the proposed controller renders higher throughput than the well-known approach, possibly using more computing resources.
This paper investigates robust tube-based Model Predictive Control (MPC) of a tiltwing Vertical Take-Off and Landing (VTOL) aircraft subject to wind disturbances and model uncertainty. Our approach is based on a Difference of Convex (DC) function decomposition of the dynamics to develop a computationally tractable optimisation with robust tubes for the system trajectories. We consider a case study of a VTOL aircraft subject to wind gusts and whose aerodynamics is defined from data.
Extreme event are sudden large-amplitude changes in the state or observables of chaotic nonlinear systems, which characterize many scientific phenomena. Because of their violent nature, extreme events typically have adverse consequences, which call for methods to prevent the events from happening. In this work, we introduce the control-aware echo state network (Ca-ESN) to seamlessly combine ESNs and control strategies, such as proportional-integral-derivative and model predictive control, to suppress extreme events. The methodology is showcased on a chaotic-turbulent flow, in which we reduce the occurrence of extreme events with respect to traditional methods by two orders of magnitude. This works opens up new possibilities for the efficient control of nonlinear systems with neural networks.
The hybridization process has recently touched also the world of agricultural vehicles. Within this context, we develop an Energy Management Strategy (EMS) aiming at optimizing fuel consumption, while maintaining the battery state of charge. A typical feature of agricultural machines is that their internal combustion engine is speed controlled, tracking the reference requested by the driver. In view of avoiding any modification on this original control loop, an add-on EMS strategy is proposed. In particular, we employ a multi-objective Model Predictive Control (MPC), taking into account the fuel consumption minimization and the speed tracking requirement, including the engine speed controller in the predictive model. The proposed MPC is tested in an experimentally-validated simulation environment, representative of an orchard vineyard tractor.
(Economic) nonlinear model predictive control ((e)NMPC) requires dynamic models that are sufficiently accurate and computationally tractable. Data-driven surrogate models for mechanistic models can reduce the computational burden of (e)NMPC; however, such models are typically trained by system identification for maximum prediction accuracy on simulation samples and perform suboptimally in (e)NMPC. We present a method for end-to-end reinforcement learning of Koopman surrogate models for optimal performance as part of (e)NMPC. We apply our method to two applications derived from an established nonlinear continuous stirred-tank reactor model. The controller performance is compared to that of (e)NMPCs utilizing models trained using system identification, and model-free neural network controllers trained using reinforcement learning. We show that the end-to-end trained models outperform those trained using system identification in (e)NMPC, and that, in contrast to the neural network controllers, the (e)NMPC controllers can react to changes in the control setting without retraining.
This work addresses the ecological-adaptive cruise control problem for connected electric vehicles by a computationally efficient robust control strategy. The problem is formulated in the space-domain with a realistic description of the nonlinear electric powertrain model and motion dynamics to yield a convex optimal control problem (OCP). The OCP is approached by a novel robust model predictive control (RMPC) method handling various disturbances due to modelling mismatch and inaccurate leading vehicle information. The RMPC problem is solved by semi-definite programming relaxation and single linear matrix inequality (sLMI) techniques for further enhanced computational efficiency. The performance of the proposed real-time robust ecological-adaptive cruise control (REACC) method is evaluated using an experimentally collected driving cycle. Its robustness is verified by comparison with a nominal MPC which is shown to result in speed-limit constraint violations. The energy economy of the proposed method outperforms a state-of-the-art time-domain RMPC scheme, as a more precisely fitted convex powertrain model can be integrated into the space-domain scheme. The additional comparison with a traditional constant distance following strategy (CDFS) further verifies the effectiveness of the proposed REACC. Finally, it is verified that the REACC can be potentially implemented in real-time owing to the sLMI and resulting convex algorithm.
A model predictive control (MPC) method for enhancing post-fault transient stability of a grid-forming (GFM) inverter based resources (IBRs) is developed in this paper. This proposed controller is activated as soon as the converter enters into the post-fault current-saturation mode. It aims at mitigating the instability arising from insufficient deceleration due to current saturation and thus improving the transient stability of a GFM-IBR. The MPC approach optimises the post-fault trajectory of GFM IBRs by introducing appropriate corrective phase angle jumps and active power references where the post-fault dynamics of GFM IBRs are addressed. These two signals provide controllability over GFM IBR's post-fault trajectory. This paper addresses the mitigation of oscillations between current-saturation mode and normal mode by forced saturation if conditions for remaining in the normal mode do not hold. The performance of the proposal is tested via dynamic simulations under various grid conditions and compared with other existing strategies. The results demonstrate significant improvement in transient stability.
Although hyperthyroidism is a common disease, the pharmaceutical therapy is based on a trial-and-error approach. We extend a mathematical model of the pituitary-thyroid feedback loop such that the intake of one antithyroid agent, namely methimazole (MMI), can be considered and use a model predictive control (MPC) scheme to determine suitable dosages.