Keywords: Learning and Predictive Control
Abstract: Game theory can provide a scalable framework to address decision-making of multiple interacting agents. While game theoretic formulations have been applied in distributed or multiagent model predictive control frameworks, an underlying assumption has been the knowledge of the model dynamics and the cost functions. In many practical settings, dynamics and cost functions are hard to model due to complex interactions of the subsystems or agents. The payoff-based information framework accounts for the case in which a given agent is neither aware of the number of other agents in the system, nor their chosen actions and the objective functions of any agent. Each agent nevertheless attempts to optimize her/his own objective function based on the payoff information, that is, the objective function values at a joint chosen action by all agents. In this model-free setting, we will present approaches to learn equilibria of multi-agent systems, showcase their applicability, and highlight open problems, specifically in the context of dynamical games and model predictive control.

Keywords: Stability and Recursive Feasibility, Robust Model Predictive Control, Learning and Predictive Control
Abstract: Predictive safety filters provide a way of projecting potentially unsafe inputs, proposed, e.g. by a human or learning-based controller, onto the set of inputs that guarantee recursive state and input constraint satisfaction by leveraging model predictive control techniques. In this paper, we extend this framework such that in addition, robust asymptotic stability of the closed-loop system can be guaranteed by enforcing a decrease of an implicit Lyapunov function which is constructed using a predicted system trajectory. Differently from previous results, we show robust asymptotic stability with respect to a predefined disturbance set on an extended state consisting of the system state and a warmstart input sequence. The proposed strategy is applied to an automotive lane keeping example in simulation.

Keywords: Learning and Predictive Control, Optimization and Model Predictive Control
Abstract: Designing predictive controllers towards optimal closed-loop performance while maintaining safety and stability is challenging. This work explores closed-loop learning for predictive control parameters under imperfect information while considering closed-loop stability. We employ constrained Bayesian optimization to learn a model predictive controller's (MPC) cost function parametrized as a feedforward neural network, optimizing closed-loop behavior as well as minimizing model-plant mismatch. Doing so offers a high degree of freedom and, thus, the opportunity for efficient and global optimization towards the desired and optimal closed-loop behavior. We extend this framework by stability constraints on the learned controller parameters, exploiting the optimal value function of the underlying MPC as a Lyapunov candidate. The effectiveness of the proposed approach is underlined in simulations, highlighting its performance and safety capabilities.

Keywords: Learning and Predictive Control
Abstract: The design of advanced model predictive control (MPC) strategies relies on the selection of several continuous, discrete, and/or categorical design choices and tuning parameters that can influence the control performance in non-trivial and non-convex ways. A largely unaddressed problem in the increasingly popular Bayesian optimization (BO) approaches for systematic and resource-efficient controller calibration is when the system and/or environment undergo dynamic changes and drifts. Inspired by recent work on mixed-variable BO and positional embedding in natural language processing, this paper presents a time-varying BO (TVBO) method with a discrete-temporal kernel that can effectively handle time-varying system dynamics that occur over a sequence of discrete system runs. The core idea of the proposed method is to encode an integer variable as a latent vector variable for representing a discrete run index, while preserving the relative information among discrete system runs. Simulation results on an offset-free MPC calibration problem show the superior performance of TVBO with discrete-temporal kernel in coping with run-to-run system drifts, as compared to TVBO with stationary and non-stationary temporal kernels where run indices are used directly as ``time." The proposed TVBO method can be useful for control of run-to-run drifting systems, for example, in pharmaceutical and semiconductor manufacturing processes.

Keywords: Learning and Predictive Control, Big Data and Predictive Control, Robust Model Predictive Control
Abstract: Predictive control requires a model of the system to compute the input. If the nominal model is not known, data-driven model predictive control approaches can be employed, which enables to obtain the input directly from past measured trajectories. We consider the problem of data-driven predictive control for Lur'e systems. Existing data-driven control approaches for Lur'e type systems assume that the output data of the nonlinearity is available, enabling the use of Willems’ Fundamental Lemma. We propose to utilize prior knowledge of the systems into the data collection process for Lur'e systems. The data is purposely collected in the region where the system behaves nearly linear, while the nonlinearity effects are considered as noise in the controller design. Using the tailored data, we can formulate the control problem as a semi-definite optimization problem exploiting robust control ideas. The resulting controller stabilizes the closed-loop system asymptotically and guarantees constraint satisfaction. A numerical example is conducted to illustrate the method.

Keywords: Learning and Predictive Control, Stability and Recursive Feasibility, Output Feedback Predictive Control
Abstract: In this paper the design of a nonlinear Model Predictive Control algorithm based on Recurrent Equilibrium Network models is addressed. Firstly, a tailored observer for the Recurrent Equilibrium Network model is proposed, in order to provide to the Model Predictive Control optimization an initialization that takes into account the past history of the system. Then, the Model Predictive Control optimization is designed including a proper terminal cost to guarantee closed loop stability for any choice of the prediction horizon.

Keywords: Robotics
Abstract: We present our latest research in learning deep sensorimotor policies for agile, vision-based quadrotor flight. We show methodologies for the successful transfer of such policies from simulation to the real world. In addition, we discuss the open research questions that still need to be answered to improve the agility and robustness of autonomous drones toward human-pilot performance.

Keywords: Stochastic Model Predictive Control, Learning and Predictive Control, Process Control
Abstract: Current stochastic nonlinear model predictive control (SNMPC) hinges on the lack of high-fidelity models that describe the system behavior and the lack of tractable solution methods that handle chance constraints. Motivated by this, a model-and data-driven predictive control approach using Gaussian processes (GP-MDPC) is synthesized in this paper. It exploits GPs to learn the unknown dynamics and apply Taylor expansion for uncertainty propagation through probabilistic modeling. A backoff approximation method is explored to reformulate the chance constraints into tractable expressions. Finally, a finite-horizon stochastic optimal control problem (FH-SOCP) is formulated.

Keywords: Process Control, Economic Predictive Control, Biological Systems
Abstract: Viral particle systems are integral parts of modern biotechnology, finding use in vaccines, drug delivery platforms, and recombinant protein production. Continuous manufacturing of these systems can offer improved manufacturability and quality control. However, viral systems often have complex kinetics which can introduce undesirable process dynamics and lower product titers in continuous operation. This article explores the use of economic nonlinear dynamic optimization and model predictive control to achieve multiple process objectives such as maximizing productivity and/or purity. Economic nonlinear model predictive control is also demonstrated to robustly control the bioreactor under plant-model mismatch in different scenarios.

Keywords: Healthcare, Biological Systems, Big Data and Predictive Control
Abstract: This study introduces a model predictive control methodology to determine optimal measures for mitigating air pollution, assisting Local Authorities in policy development. Anchored in an auto-regressive model, it analyzes dynamic air quality patterns over a defined timeframe using daily observed pollutant concentration, meteorological variables, and estimated emission data. Employing model predictive control methodology, the approach aims to optimize daily emission reductions. Evaluated in Milan, a heavily polluted European city, the findings highlight the methodology’s potential as a robust tool for Local Authorities, enabling informed decisions in crafting efficient air quality management strategies, in the specific context of NO2.

Keywords: Output Feedback Predictive Control, Stability and Recursive Feasibility, Aerospace
Abstract: This paper considers the control of uncertain discrete-time linear systems subject to time-varying polytopic constraints. The proposed methodology recasts the problem into one with time-invariant constraints and an unmeasured disturbance input. Through the use of an extended observer the disturbance input is estimated and canceled. Then, a time dependent sequence of safe sets is employed to bound the estimation error. A robust reference governor based on such a sequence is designed to robustly ensure constraint enforcement. Simulation results for several dynamical systems are reported.

Keywords: Process Control, Distributed Model Predictive Control
Abstract: In this paper, we present a novel approach to distributed moving horizon estimation for nonlinear processes. The method involves approximating the arrival costs of local estimators through a recursive framework. First, we formulate distributed full-information estimation for linear unconstrained systems, which serves as the foundation for deriving the analytical expression of the arrival cost. Subsequently, a recursive arrival cost design for linear distributed moving horizon estimation is developed. Then, we extend the arrival cost design obtained for linear systems to account for the nonlinear context, and a partition-based constrained distributed moving horizon estimation algorithm for nonlinear systems is formulated. A chemical process is introduced to illustrate the effectiveness of the proposed method.

Keywords: Tracking and Path Following Predictive Control, Real-Time Implementation of Model Predictive Control, Aerospace
Abstract: The use of Linear Time Varying (LTV) Model Predictive Control (MPC) to stabilize a set of trajectories of a nonlinear system is considered. This technique has been successfully applied in simulations and experiments, but only few contributions investigate stability aspects and the essential involved quantities: the terminal penalty and terminal constraint. Deriving the former is not always thoroughly addressed or it is based on the -rather restrictive- assumption that the whole set of linearized dynamics is quadratically stabilizable. In this article, we propose Linear Matrix Inequality (LMI) conditions to co-design a gain-scheduled auxiliary feedback and Lyapunov function, used to derive offline terminal set conditions and a terminal penalty constraint for an LTV MPC scheme guaranteeing stability and recursive constraint satisfaction. Recent results by the authors are extended to the case of a varying stage cost, such that the controller can be tuned to meet time-varying trade-offs between tracking accuracy and input activity. The approach is demonstrated in embedded hardware running on a CrazyFlie drone.

Keywords: Learning and Predictive Control, Real-Time Implementation of Model Predictive Control, Tracking and Path Following Predictive Control
Abstract: Supervised learning, combined with model predictive control (MPC), has garnered recent attention, especially in approximate explicit MPC. Here, deep neural networks learn the MPC policy from optimal state-action pairs offline. However, while approximate explicit MPC aims to replicate the MPC policy, it often sacrifices performance guarantees inherent in online optimization. This paper proposes an alternative approach: offline supervised learning to derive the optimal value function instead of the policy. This function serves as the cost-to-go in a myopic MPC with a short prediction horizon, significantly reducing online computation without compromising controller performance. Additionally, we augment the offline supervised learning with a descent property constraint, that steers the learning process such that the successor states have lower cost-to-go than current states. Unlike existing approaches, our method learns the cost-to-go function from offline state-action-value tuples, as opposed to closed-loop performance data.

Keywords: Learning and Predictive Control, Real-Time Implementation of Model Predictive Control, Hybrid Model Predictive Control
Abstract: Application of nonlinear model predictive control (NMPC) to problems with hybrid dynamical systems, disjoint constraint sets, or discrete controls often results in mixed-integer formulations with both continuous and discrete decision variables. However, solving mixed-integer nonlinear programming (MINLP) problems in real-time is challenging, which can be a limiting factor in many applications. To address the computational complexity of solving mixed-integer nonlinear model predictive control (MINMPC) problems in real-time, this paper proposes a myopic MINMPC formulation based on value function approximation. The key idea here is to divide the prediction horizon into two parts by leveraging Bellman's principle of optimality, where the cost-to-go is approximated with the KKT residual minimization method of inverse optimization offline using expert demonstrations of the original MINMPC controller. This learned cost-to-go is then appended to a myopic MINMPC controller, where the considerably shorter prediction horizon significantly reduces the online computation cost. The Lotka-Volterra fishing problem is used to illustrate this new approach.

Keywords: Learning and Predictive Control, Big Data and Predictive Control
Abstract: In this research, we investigate a system identification method based on deep neural networks for nonlinear Model Predictive Control (MPC), focusing on efficiently managing massive multi-output systems. This method involves the direct synthesis of state estimators and output predictors represented by neural networks from experimental data. The integration of these components with the Levenberg-Marquardt optimization method, coupled with the use of automatic differentiation, enables efficient realization of nonlinear MPC. In this research, we propose a specific architecture for the state estimator and output predictor, designed to suit multi-output systems. This approach is applied to a miniature four-wheeled vehicle equipped with a 1D camera, which generates 160-pixel image outputs. The experimental application to this test vehicle demonstrates the method's capability in effectively managing complex, multi-output systems.

Keywords: Process Control, Real-Time Implementation of Model Predictive Control
Abstract: To realize a carbon-neutral society, it is necessary to reduce the amount of CO2 emitted artificially as much as possible, while the CO2 amount that is still inevitably emitted needs to be offset to zero by capturing the same amount of CO2. This paper presents an application of nonlinear model predictive control (NMPC) to a CO2 capture plant in order to improve the controllability of the CO2 capture ratio of the plant. This paper especially, focuses on the transient performance of controllability during rapid load changes of fuel gas feed flow. The C/GMRES method is employed, and a nonlinear dynamic model that can be solved faster than the original model is developed to realize fast load tracking. Numerical simulation results show that NMPC is updated fast enough to run in real time and more accurate than baseline controller, which is based on feed-froward control.

Keywords: Distributed Model Predictive Control, Learning and Predictive Control, Process Control
Abstract: The distributed model predictive control (dMPC) provides a computationally efficient framework for designing controllers for a large dimensional plant. The performance of such dMPC scheme critically depends upon the quality of the control relevant models used for predictions. In continuously operated processes, model plant mismatch (MPM) arises due to the time- varying nature of process parameters and shift in the operating conditions due to economic considerations and this results in performance degradation. Recently an adaptive version of dMPC (dAMPC) has been developed that achieves better control performance using online model parameter update. A conventional adaptive MPC scheme, however, requires external dither signal to be injected to generate sufficient excitation needed for parameter estimation. In this work, dAMPC is cast in the dual control framework (dADMPC) which ensured sufficient input excitation as and when needed for better online parameter estimation. The proposed controller is based on black-box models parameterized using generalized orthogonal basis filters (GOBF). The Fourier coefficients of the GOBF models are dynamically updated online using recursive parameter estimators to account for MPM. The efficacy of the proposed scheme is demonstrated by simulating servo and regulatory problems associated with the benchmark octuple tank process. The simulation study reveals that performance of the proposed dADMPC scheme is comparable to a centralized ADMPC while achieving a considerable reduction in the online computation time.

Keywords: Process Control, IoT/IoE, Optimization and Model Predictive Control
Abstract: The VESNA smart greenhouse system aims for sustainable, ecological, and organic food production. This study explores an offset-free model predictive controller (MPC) for temperature tracking. The MPC proves effective in maintaining temperature within constraints. Extensive experiments assess different MPC setups, focusing on environmental factors, including energy use and carbon footprint. Additionally, a novel software toolbox simplifies analysis and remote control, enhancing user-friendliness. Together, the designed offset-free reference tracking MPC controllers and the toolbox offer a comprehensive solution for smart greenhouse control.

Keywords: Fluid Dynamics, Real-Time Implementation of Model Predictive Control, Economic Predictive Control
Abstract: Hydraulic cylinders are pivotal components in various industrial, construction, and off-highway applications, where efficient actuation is crucial for reducing energy consumption, minimizing heat generation, and extending components' lifespan. The integration of Independent Metering Control, a valve topology allowing five valves to independently control the flow, represents a significant advancement in enhancing hydraulic systems' performance. However, the lack of a reliable and flexible control solution remains a challenge. In this paper, we present the implementation of nonlinear Model Predictive Control, using a favorable model formulation and a state-of-the-art solver acados. We show how it can deliver close-to-optimal performance with real-time capabilities, addressing the current gap in achieving efficient control for hydraulic cylinders with Independent Metering Control.

Keywords: Optimization and Model Predictive Control, Automotive, Hybrid Model Predictive Control

Keywords: Optimization and Model Predictive Control, Economic Predictive Control, Process Control
Abstract: This paper considers the optimal boundary control of chemical systems described by advection-diffusion-reaction (ADR) equations. We use a discontinuous Galerkin finite element method (DG-FEM) for the spatial discretization of the governing partial differential equations, and the optimal control problem is directly discretized using multiple shooting. The temporal discretization and the corresponding sensitivity calculations are achieved by an explicit singly diagonally-implicit Runge Kutta (ESDIRK) method. ADR systems arise in process systems engineering and their operation can potentially be improved by nonlinear model predictive control (NMPC). We demonstrate a numerical approach for the solution to their optimal control problems (OCPs) in a chromatography case study. Preparative liquid chromatography is an important downstream process in biopharmaceutical manufacturing. We show that multi-step elution trajectories for batch processes can be optimized for economic objectives, providing superior performance compared to classical gradient elution trajectories.

Keywords: Autonomous Transportation, Robotics, Tracking and Path Following Predictive Control
Abstract: This article proposes an approach for collision avoidance, path following, and anti-grounding of autonomous surface vessels under consideration of environmental forces based on Nonlinear Model Predictive Control (NMPC). Artificial Potential Fields (APFs) set the foundation for the cost function of the optimal control problem in terms of collision avoidance and anti-grounding. Depending on the risk of a collision given by the resulting force of the APFs, the controller optimizes regarding an adapted heading and travel speed by additionally following a desired path. For this purpose, nonlinear vessel dynamics are used for the NMPC. To extend the situational awareness concerning environmental disturbances impacted by wind, waves, and sea currents, a nonlinear disturbance observer is coupled to the entire NMPC scheme, allowing for the correction of an incorrect vessel motion due to external forces. In addition, the most essential rules according to the Convention on the International Regulations for Preventing Collisions at Sea (COLREGs) are considered. The results of the simulations show that the proposed framework can control an autonomous surface vessel under various challenging scenarios, including environmental disturbances, to avoid collisions and follow desired paths.

Keywords: Real-Time Implementation of Model Predictive Control, Autonomous Transportation, Robotics
Abstract: The use of AGVs and AMRs is expanding to improve the efficiency of logistics warehouse operations. For flexible navigation of multiple AMRs, path planning methods utilizing nonlinear model predictive control have been studied, but the reduction of computational cost has been a challenge. In this study, we investigated the application of lifted bilinear model-based linear MPC to AMR systems, leveraging the Koopman approach, which can be computed faster than conventional methods. In particular, we extended the optimization problem to accommodate nonlinear constraints that have not been considered in previous studies. Numerical simulations verified that the proposed method could satisfy the nonlinear constraint condition of collision avoidance between AMRs and reduce the computation time compared to NMPC.

Keywords: Robotics, Motion Control, Optimization and Model Predictive Control
Abstract: The construction of a space partition in a cluttered environment allows for the creation of graph-based paths, establishing safe navigation corridors for agents. Then, it exploits them according to the available control degrees of freedom and dynamical constraints. Evaluating corridor safety relies on the distance between the path points and the nearest obstacles, influencing the real-time performance and robustness of navigation. This paper revisits the convex lifting method for space partition, emphasizing the generation and enlargement of safe corridors. The iterative enlargement algorithm pursues an increase in average corridor width while ensuring a monotonic increase in the minimum corridor width.

Keywords: Robust Model Predictive Control, Motion Control, Real-Time Implementation of Model Predictive Control
Abstract: In this paper, we present a novel Reduced Robustified NMPC (R²NMPC) algorithm that has the same complexity as an equivalent nominal NMPC while enhancing it with robustified constraints based on the dynamics of ellipsoidal uncertainty sets. This promises both a closed-loop- and constraint satisfaction performance equivalent to common Robustified NMPC approaches, while drastically reducing the computational complexity. The main idea lies in approximating the ellipsoidal uncertainty sets propagation over the prediction horizon with the system dynamics' sensitivities inferred from the last optimal control problem (OCP) solution, and similarly for the gradients to robustify the constraints. Thus, we do not require the decision variables related to the uncertainty propagation within the OCP, rendering it computationally tractable. Next, we illustrate the real-time control capabilities of our algorithm in handling a complex, high-dimensional, and highly nonlinear system, namely the trajectory following of an autonomous passenger vehicle modeled with a dynamic nonlinear single-track model. Our experimental findings, alongside a comparative assessment against other Robust NMPC approaches, affirm the robustness of our method in effectively tracking an optimal racetrack trajectory while satisfying the nonlinear constraints. This performance is achieved while fully utilizing the vehicle's interface limits, even at high speeds of up to 37.5unit{meterpersecond}, and successfully managing state estimation disturbances. Remarkably, our approach maintains a mean solving frequency of 144unit{hertz}.

Keywords: Robust Model Predictive Control, Optimization and Model Predictive Control
Abstract: Discrete-time robust optimal control problems generally take a min-max structure over continuous variable spaces, which can be difficult to solve in practice. In this paper, we extend the class of such problems that can be solved through a previously proposed local reduction method to consider those with existence constraints on the uncountable variables. We also consider the possibility of non-unique trajectories that satisfy equality and inequality constraints. Crucially, we show that the problems of interest can be cast into a standard semi-infinite program and demonstrate how to generate optimal uncertainty scenario sets in order to obtain numerical solutions. We also include examples on model predictive control for obstacle avoidance with logical conditions, control with input saturation affected by uncertainty, and optimal parameter estimation to highlight the need for the proposed extension. Our method solves each of the examples considered, producing violation-free and locally optimal solutions.

Keywords: Robust Model Predictive Control, Learning and Predictive Control, Robotics
Abstract: Model Predictive Control (MPC) optimizes an objective function within a prediction window subject to various constraints. In the presence of bounded disturbances, robust versions of MPC are used. Recently, a promising robust MPC approach, called state-dependent dynamic tube MPC (SDD-TMPC) was introduced that outperforms state-of-the-art methods. However, solving the optimization problem of SDD-TMPC online is computationally expensive. An efficient approximate method based on spiking neural networks, which are suitable for on-board computations, is proposed to accelerate the online computation of SDD-TMPC. We model the discrepancies between the actual and approximate control inputs as bounded state-dependent disturbances, to control wheeled robots.

Keywords: Motion Control, Stochastic Model Predictive Control, Optimization and Model Predictive Control
Abstract: At some sporting events, including baseball, the ball flew into the spectator area, resulting in serious injuries. Having witnessed such situations, we felt that the safety of the spectator environment needed to be improved. Therefore, the aim is to prevent such accidents by using drones that catch flying balls. Monte Carlo Model Predictive Control (MCMPC) is a sample-based model predictive control and does not require a gradient in the cost function, allowing discontinuous events such as collisions with obstacles to be incorporated into the predictive model. This study aims to utilize MCMPC to reduce the risk of drone collision after successful flying ball capture.

Keywords: Robotics, Tracking and Path Following Predictive Control, Aerospace
Abstract: In this study, we propose the Monte Carlo Model Predictive Control for a planetary exploration rover, enabling efficient locomotion over rough terrain while balancing the the remaining energy of its solar cells. Using an economic model predictive control framework that considers constraints on remaining energy and ground inclination angle, we realize path planning that avoids craters while managing the power generation amount. At the boundary between sun and shade, the amount of power generated by the solar cells changes discontinuously, and gradient-based optimization calculations may not be able to find a solution. To address this concern, we introduced Monte Carlo optimization as the MPC solver, probabilistically searching for an optimal trajectory while avoiding getting stuck due to the unexpected obstacle on the path designed offline by RRT* for global path planning. We performed a realistic simulation on an environment built using SLDEM2013, which is topographical map data on the lunar surface. The simulation results confirmed that avoiding dangerous areas is possible, taking shortcuts in shaded areas as necessary and moving to the target point while managing the energy balance adaptive to the time-varying shadow area.

Keywords: Real-Time Implementation of Model Predictive Control, Optimization and Model Predictive Control, Dedicated Optimization Solvers for Model Predictive Control
Abstract: Determining solving-time certificates of nonlinear model predictive control (NMPC) implementations is a pressing requirement when deploying NMPC in production environments. Such a certificate guarantees that the NMPC controller returns a solution before the next sampling time. However, NMPC formulations produce nonlinear programs (NLPs) for which it is very difficult to derive their solving-time certificates. Our previous work, cite{wu2023direct}, challenged this limitation with a proposed input-constrained MPC algorithm having exact iteration complexity but was restricted to linear MPC formulations. This work extends the algorithm to solve input-constrained NMPC problems, by using the Koopman operator and a condensing MPC technique. We illustrate the algorithm performance on a high-dimensional, nonlinear partial differential equation (PDE) control case study, in which we theoretically and numerically certify the solving time to be less than the sampling time.

Keywords: Output Feedback Predictive Control, Robust Model Predictive Control, Learning and Predictive Control
Abstract: We propose a moving horizon estimation scheme for estimating the states and time-varying parameters of nonlinear systems. We consider the case where observability of the parameters depends on the excitation of the system and may be absent during operation, with the parameter dynamics fulfilling a weak incremental bounded-energy bounded-state property to ensure boundedness of the estimation error (with respect to the disturbance energy). The proposed estimation scheme involves a standard quadratic cost function with an adaptive regularization term depending on the current parameter observability. We develop robustness guarantees for the overall estimation error that are valid for all times, and that improve the more often the parameters are detected to be observable during operation. The theoretical results are illustrated by a simulation example.

Keywords: Stability and Recursive Feasibility
Abstract: We consider a continuous-time nonlinear model predictive control formulation that is progressively tightening in path costs and constraints. We prove asymptotic stability of the origin for the corresponding closed-loop system and extend this result to formulations employing an auxiliary dynamic system. The theoretical results are illustrated on a numerical example.

Keywords: Fluid Dynamics
Abstract: All flow systems are subject to transport delays, which are determined by the flow rates in the system. When the flow rates themselves are control inputs, the system becomes subject to input-dependent state delays, which poses significant theoretical problems. In this paper we propose a model predictive control scheme for a generic multi-variable heat transport system, where flows to the individual consumers can be manipulated by a centralized controller. The control design takes the transport delay into account by means of an explicit discretization of the transport equation, which is a partial differential equation. Different discretization methods are considered, giving rise to a high-order bilinear system model in discrete time. The control problem is formulated as a linear quadratic receding horizon problem with terminal cost. Simulation studies show that the control problem can be solved using standard software and that the Lax-Friedrichs discretization method appears to be the most suitable of the investigated methods.