In this chapter, we explore model predictive control of fuel cell electric vehicles (FCEVs), a type of vehicle that utilizes the chemical energy of hydrogen to generate electricity for their power train. Since vehicles are typically utilized for mobility purposes only for a fraction of the time, the energy stored in the onboard hydrogen tanks of these vehicles also can be used to supply power when they are parked. Our focus is on examining how to control the operation of FCEVs, ensuring the fulfilment of constraints imposed by both electrical and transportation networks while minimizing operational costs.

Greenhouse climate control is concerned with maximizing performance in terms of crop yield and resource efficiency. One promising approach is model predictive control (MPC), which leverages a model of the system to optimize the control inputs, while enforcing physical constraints. However, prediction models for greenhouse systems are inherently inaccurate due to the complexity of the real system and the uncertainty in predicted weather profiles. For model-based control approaches such as MPC, this can degrade performance and lead to constraint violations. Existing approaches address uncertainty in the prediction model with robust or stochastic MPC methodology; however, these necessarily reduce crop yield due to conservatism and often bear higher computational loads. In contrast, learning-based control approaches, such as reinforcement learning (RL), can handle uncertainty naturally by leveraging data to improve performance. This work proposes an MPC-based RL control framework to optimize the climate control performance in the presence of prediction uncertainty. The approach employs a parametrized MPC scheme that learns directly from data, in an online fashion, the parametrization of the constraints, prediction model, and optimization cost that minimizes constraint violations and maximizes climate control performance. Simulations show that the approach can learn an MPC controller that significantly outperforms the current state-of-the-art in terms of constraint violations and efficient crop growth.

Implementing model predictive control (MPC) in practice faces many subtle but prevalent problems, including modeling errors, solver errors, and actuator faults. In essence, the real control input applied to the system always deviates from the ideal one based on a perfect controller, resulting in an imperfect controller. In this letter, we provide a general analysis to quantify the suboptimality of MPC for Lipschitz-continuous nonlinear systems due to imperfect control inputs in terms of dynamic regret. Based on a general assumption about how the imperfect controller may improve over time, sublinear regret upper bounds are established for cases where the closed-loop system under the ideal controller is Lipschitz-contractive (i.e., its Lipschitz constant is smaller than one). In addition, we also discuss how the regret scales when the closed-loop system under the oracle controller is not Lipschitz-contractive. The results provide insights into designing suitable MPC strategies, especially for learning-based MPC.

Temperature plays a critical role in performance and stability of anaerobic digestion processes, subject to frequent meteorological fluctuations. However, state-of-the-art modeling and process control approaches for anaerobic digestion often do not consider the temporal dynamics of the temperature, which can influence microbial communities, kinetics, and chemical equilibrium, and consequently, biogas production efficiency. Therefore, to account for anaerobic digesters operating under fluctuating meteorological conditions, the Anaerobic Digestion Model no. 1 (ADM1) is mechanistically extended in this paper to incorporate temporal changes into temperature-dependent parameters by defining inhibition functions for microbial activities using the cardinal temperature model, and accounting for the lag in microbial adaptation to temperature fluctuations using a time-lag adaptation function. Thereafter, given that temperature fluctuations are a significant disturbance, a control framework based on Model Predictive Control (MPC) is developed to regulate the feeding flow rate and to ensure stable production rates despite temperature disturbances without relying on direct temperature control. An adaptive MPC approach is formulated based on a linear input–output model, where the parameters of the linear model are updated online to capture the nonlinear dynamics of the process and frequent changes in the dynamics accurately. In addition, a fuzzy logic system is employed to assign a reference trajectory for the production rate based on the temperature and its rate of change. Integrating this fuzzy logic system with the MPC controller enhances the production rate on warm days and avoids the operational failure in production on cold days. Additionally, to enhance biogas production rates, the feasibility of utilizing a portion of the produced biogas for external heating purposes is also investigated. It is demonstrated that by utilizing the proposed MPC approach, the additional amount of feed for the digester to produce methane required for a self-consumption biogas-fueled heating system can be calculated according to the meteorological variations. This enhances the process performance and stability. Finally, a thermally optimized dome digester semi-buried in the ground, operating under climate conditions of The Netherlands is considered as a case study to validate the extended model in agreement with biological and physicochemical behaviors of real-world applications, and to demonstrate the effectiveness of the proposed control system in handling temperature changes and enhancing performance.

Control of piecewise affine (PWA) systems under complex constraints faces challenges in guaranteeing both safety and online computational efficiency. Learning-based methods can rapidly generate control signals with good performance, but rarely provide safety guarantees. A safety filter is a modular method to improve safety for any controller. When applied to PWA systems, a traditional safety filter usually need to solve a mixed-integer convex program, which reduces the computational benefit of learning-based controllers. We propose a novel optimization-free safety filter designed to handle state constraints that involve a combination of polyhedra and ellipsoids. The proposed safety filter only utilizes algebraic and min-max operations to determine safe control inputs. This offers a notable advantage compared with traditional safety filters by allowing for significantly more efficient computation of control signals. The proposed safety filter can be integrated into various function approximators, such as neural networks, enabling safe learning throughout the learning process. Simulation results on a bicycle model with PWA approximation validate the proposed method regarding constraint satisfaction, CPU time, and the preservation of sub-optimality.

Uncertainty in the behavior of other traffic participants is a crucial factor in collision avoidance for automated driving; here, stochastic metrics could avoid overly conservative decisions. This article introduces a stochastic model predictive control (SMPC) planner for emergency collision avoidance in highway scenarios to proactively minimize collision risk while ensuring safety through chance constraints. To guarantee that the emergency trajectory can be attained, we incorporate nonlinear tire dynamics in the prediction model of the ego vehicle. Further, we exploit max-min-plus-scaling (MMPS) approximations of the nonlinearities to avoid conservatism, enforce proactive collision avoidance, and improve computational efficiency in terms of performance and speed. Consequently, our contributions include integrating a dynamic ego vehicle model into the SMPC planner, introducing the MMPS approximation for real-time implementation in emergency scenarios, and integrating SMPC with hybridized chance constraints and risk minimization. We evaluate our SMPC formulation in terms of proactivity and efficiency in various hazardous scenarios. Moreover, we demonstrate the effectiveness of our proposed approach by comparing it with a state-of-the-art SMPC planner and we validate that the generated trajectories can be attained using a high-fidelity vehicle model in IPG CarMaker.

In this paper, the disjunctive and conjunctive lattice piecewise affine (PWA) approximations of explicit linear model predictive control (MPC) are proposed. Training data consisting of states and corresponding affine control laws are generated in a control invariant set, and redundant sample points are removed to simplify the construction of lattice PWA approximations. Resampling is proposed to guarantee the equivalence of lattice PWA approximations and optimal MPC control law at the sample points. Under certain conditions, the disjunctive lattice PWA approximation constitutes a lower bound, while the conjunctive version formulates an upper bound of the original optimal control law. The equivalence of the two lattice PWA approximations then guarantees error-free approximations in the domain of interest, which is tested through a statistical guarantee. The performance of the proposed approximation strategy is tested through two simulation examples, and the results show that error-free lattice PWA approximations can be obtained with low offline complexity and small storage requirements. Besides, the online complexity is less compared with the state-of-the-art method.

In the backdrop of an increasingly pressing need for effective urban and highway transportation systems, this work explores the synergy between model-based and learning-based strategies to enhance traffic flow management by use of an innovative approach to the problem of ramp metering control that embeds Reinforcement Learning (RL) techniques within the Model Predictive Control (MPC) framework. The control problem is formulated as an RL task by crafting a suitable stage cost function that is representative of the traffic conditions, variability in the control action, and violations of the constraint on the maximum number of vehicles in queue. An MPC-based RL approach, which leverages the MPC optimal problem as a function approximation for the RL algorithm, is proposed to learn to efficiently control an on-ramp and satisfy its constraints despite uncertainties in the system model and variable demands. Simulations are performed on a benchmark small-scale highway network to compare the proposed methodology against other state-of-the-art control approaches. Results show that, starting from an MPC controller that has an imprecise model and is poorly tuned, the proposed methodology is able to effectively learn to improve the control policy such that congestion in the network is reduced and constraints are satisfied, yielding an improved performance that is superior to the other controllers.

Game-theoretic models are frequently used to analyse the effects of information availability and quality on supply chain decision-making. Although information asymmetry plays a vital role in shaping sustainable supply chains, a comprehensive review of these models within this context remains lacking. This study conducts a systematic literature review and performs an in-depth content-based analysis of 73 peer-reviewed journal articles, categorising them based on their assumptions regarding supply chain structure, information structure, and interaction among supply chain members. We find that researchers are extending traditional supply chain models to address emerging challenges and opportunities driven by sustainable practices under asymmetric information. However, the research remains in a preliminary phase, with most models relying on simplified settings – typically dyadic, single-product, and single-period frameworks – and focusing primarily on demand and cost information asymmetries. Multilateral information structures and non-contractual coordination mechanisms remain largely unexplored. Theoretical advancements have considerably outpaced empirical validation, revealing a critical gap in the integration of real-world practices. Our findings highlight the importance of information sharing and coordination mechanisms in achieving sustainability outcomes and improving supply chain performance. These insights enrich the theoretical discourse on information asymmetry in sustainable supply chains.

Maintenance is a necessary to keep assets, in this case, a pavement system, in good condition. Spending too much on maintenance is not efficient, while not spending enough may cause the condition to drop below a desired level. Therefore, in this paper, a conceptual approach, based on systems and control theory, is developed to improve the efficiency of maintenance of a pavement system, compared to the currently used maintenance approach where often only fixed bounds of the condition determine whether or not a maintenance action is required.  A state-space description of the condition of the pavement system is chosen for predicting the future evolution of the health condition. This allows the use of a moving-horizon optimisation approach, to determine optimal anticipative maintenance actions. Furthermore, in this approach, the maintenance cost and the condition of the pavement system are optimised. This model-based approach can be applied in practice as well-documented data, from which degradation models can be constructed, are often available. In this paper, we also show how degradation models from the literature can be converted for use in the proposed condition-based maintenance approach. Note that because of the general character of the proposed maintenance optimisation approach, the degradation model and the chosen optimisation method that are used as illustration in this paper can easily be replaced by another one, depending on the needs of the user. A case study is performed, where a representative situation is considered using the developed approach and the maintenance approach currently used in practice. This case study shows how the approach works and what the cost reduction can be assuming that the models are accurate. The paper ends with a discussion and recommendations.

The partitioning problem is a key problem for distributed control techniques. The problem consists in the definition of the subnetworks of a dynamical system that can be considered as individual control agents in the distributed control approach. Despite its relevance and the different approaches proposed in the literature, no generalized technique to perform the partitioning of a network of dynamical systems is present yet. In this article, we introduce a general approach to partitioning for distributed control. This approach is composed by an algorithmic part selecting elementary subnetworks, and by an integer program, which aggregates the elementary components according to a global index. We empirically evaluated our approach on a distributed predictive control problem in the context of power systems, obtaining promising performances in terms of reduction of computation speed and resource cost, while retaining a good level of performance.

Infinite-horizon optimal control of constrained piecewise affine (PWA) systems has been approximately addressed by hybrid model predictive control (MPC), which, however, has computational limitations, both in offline design and online implementation. In this article, we consider an alternative approach based on approximate dynamic programming (ADP), an important class of methods in reinforcement learning. We accommodate nonconvex union-of-polyhedra state constraints and linear input constraints into ADP by designing PWA penalty functions. PWA function approximation is used, which allows for a mixed-integer encoding to implement ADP. The main advantage of the proposed ADP method is its online computational efficiency. Particularly, we propose two control policies, which lead to solving a smaller-scale mixed-integer linear program than conventional hybrid MPC, or a single convex quadratic program, depending on whether the policy is implicitly determined online or explicitly computed offline. We characterize the stability and safety properties of the closed-loop systems, as well as the suboptimality of the proposed policies, by quantifying the approximation errors of value functions and policies. We also develop an offline mixed-integer-linear-programming-based method to certify the reliability of the proposed method. Simulation results on an inverted pendulum with elastic walls and on an adaptive cruise control problem validate the control performance in terms of constraint satisfaction and CPU time.

Model mismatch often presents significant challenges in model-based controller design. This paper investigates model predictive control (MPC) for uncertain linear systems with input constraints, where the uncertainty is characterized by a parametric mismatch between the true system and its estimated model. The main contributions of this work are twofold. First, a theoretical performance bound is derived using relaxed dynamic programming. This bound provides a novel insight into how the prediction horizon and modeling errors affect the suboptimality of the MPC controller to the oracle infinite-horizon optimal controller, which has complete knowledge of the true system. Second, sufficient conditions are established under which the nominal MPC controller, which relies solely on the estimated system model, can stabilize the true system despite model mismatch. Numerical simulations are presented to validate these theoretical results, demonstrating the practical applicability of the derived conditions and bounds. These findings offer practical guidelines for achieving desired modeling accuracy and selecting an appropriate prediction horizon in designing certainty-equivalence MPC controllers for uncertain linear systems.

Approximate dynamic programming (ADP) faces challenges in dealing with constraints in control problems. Model predictive control (MPC) is, in comparison, well-known for its accommodation of constraints and stability guarantees, although its computation is sometimes prohibitive. This paper introduces an approach combining the two methodologies to overcome their individual limitations. The predictive control law for constrained linear quadratic regulation (CLQR) problems has been proven to be piecewise affine (PWA) while the value function is piecewise quadratic. We exploit these formal results from MPC to design an ADP method for CLQR problems with a known model. A novel convex and piecewise quadratic neural network with a local–global architecture is proposed to provide an accurate approximation of the value function, which is used as the cost-to-go function in the online dynamic programming problem. An efficient decomposition algorithm is developed to generate the control policy and speed up the online computation. Rigorous stability analysis of the closed-loop system is conducted for the proposed control scheme under the condition that a good approximation of the value function is achieved. Comparative simulations are carried out to demonstrate the potential of the proposed method in terms of online computation and optimality.

Scenario reduction algorithms can be an effective means to provide a tractable description of the uncertainty in optimal control problems. However, they might significantly compromise the performance of the controlled system. In this paper, we propose a method to compensate for the effect of scenario reduction on stochastic optimal control problems for chance-constrained linear systems with additive uncertainty. We consider a setting in which the uncertainty has a discrete distribution, where the number of possible realizations is large. We then propose a reduction algorithm with a problem-dependent loss function, and we define sufficient conditions on the stochastic optimal control problem to ensure out-of-sample guarantees (i.e., against the original distribution of the uncertainty) for the controlled system in terms of performance and chance constraint satisfaction. Finally, we demonstrate the effectiveness of the approach on a numerical example.

Nonlinear Programs (NLPs) are prevalent in optimization-based control of nonlinear systems. Solving general NLPs is computationally expensive, necessitating the development of fast hardware or tractable suboptimal approximations. This paper investigates the sensitivity of the solutions of NLPs with polytopic constraints when the nonlinear continuous objective function is approximated by a PieceWise-Affine (PWA) counterpart. By leveraging perturbation analysis using a convex modulus, we derive guaranteed bounds on the distance between the optimal solution of the original polytopically-constrained NLP and that of its approximated formulation. Our approach aids in determining criteria for achieving desired solution bounds. Two case studies on the Eggholder function and nonlinear model predictive control of an inverted pendulum demonstrate the theoretical results.

Purple Phototrophic Bacteria (PPB) are increasingly being applied in resource recovery from wastewater. Open raceway-pond reactors offer a more cost-effective option, but subject to biological and environmental perturbations. This study proposes a hierarchical control system based on Adaptive Generalized Model Predictive Control (AGMPC) for PPB raceway reactors. The AGMPC uses simple linear models updated adaptively to project the complex process dynamics and capture changes. The hierarchical approach uses the AGMPC controller to optimize PPB growth as the core of the system. The developed supervisory layer adjusts set-points for the core controller based on two operational scenarios: maximizing PPB concentration for quality, or increasing yield for quantity through effluent recycling. Lastly, due to competing PPB and non-PPB bacteria during start-up phase, an override strategy for this transition is investigated through simulation studies. The Purple Bacteria Model (PBM) simulates this process, and simulation results demonstrate the control system's effectiveness and robustness.

This paper proposes an approach to find the eigenvalues and eigenvectors of a class of autonomous max-min-plus-scaling (MMPS) systems. First we show that time invariant, monotone and non-expansive MMPS systems with only time variables has a unique structural eigenvalue and eigenvector under some conditions. Then, we propose a mixed integer linear programming (MILP) algorithm to calculate the eigenvalue and the corresponding eigenvector for such systems. Finally, we present a modified linear programming (LP) algorithm to find all the eigenvalues of a general time invariant MMPS system.

In this article we consider the problem of tether entanglement for tethered mobile robots. One of the main risks of using a tethered connection between a mobile robot and an anchor point is that the tether may get entangled with the obstacles present in the environment or with itself. To avoid these situations, a non-entanglement constraint can be considered in the motion planning problem for tethered robots. This constraint is typically expressed as a set of specific tether configurations that must be avoided. However, the literature lacks a generally accepted definition of entanglement, with existing definitions being limited and partial in the sense that they only focus on specific instances of entanglement. In practice, this means that the existing definitions do not effectively cover all instances of tether entanglement. Our goal in this article is to bridge this gap and to provide new definitions of entanglement, which, together with the existing ones, can be effectively used to qualify the entanglement state of a tethered robot in diverse situations. The new definitions find application in motion planning for tethered robots, where they can be used to obtain more safe and robust entanglement-free trajectories.

Humans and autonomous vehicles will jointly use the roads in smart cities. Therefore, it is a requirement for autonomous vehicles to properly handle the information and uncertainties that are introduced by humans (e.g., drivers, pedestrians, traffic managers) into the traffic, to accordingly make proper decisions. Such information is commonly available as linguistic, fuzzy (non-quantified) terms. Thus, we need mathematical modeling approaches that, at the same time, handle mixed (i.e., quantified and non-quantified) data. For this, we introduce novel type-2 sets and membership functions to translate such mixed traffic data into mathematical concepts that handle different levels and types of uncertainties and that can undergo mathematical operations. Next, we propose rule-based data processing and modeling approaches to exploit the advantages of these sets. This is inspired by the rule-based reasoning of humans, which has proven to be very effective and efficient in various applications, especially in traffic. The resulting models, hence, handle more than one level and type of uncertainty, which results in precise estimations of traffic dynamics that are comparable in accuracy with similar analyses if only one level of uncertainty (either probabilistic or fuzzy) would exist in the dataset. This will significantly improve the analysis, prediction, management, and safety of traffic in future smart cities.