MPC Scheme Research Articles

Guaranteed Closed-Loop Learning in Model Predictive Control

In this article, we propose a novel learning-based model predictive control framework for nonlinear systems which is able to guarantee closed-loop learning of the controlled system. We consider a cost function that combines a general economic cost with a user-defined learning cost function that aims at incentivizing learning of the unknown system. In particular, due to the finite horizon of the MPC scheme and to the presence of disturbances, the open-loop trajectory usually differs from the closed-loop one. Such a mismatch causes existing learning-based MPC schemes to only show a learning phase in the open-loop prediction, without providing any formal guarantee on the actual closed-loop learning. In this article, we show how existing MPC schemes can be easily modified in order to guarantee closed-loop learning of the system by including a suitable discount factor in the chosen learning cost function, and implementing an additional constraint in the original MPC scheme. We show that various techniques for online learning the system dynamics, such as kinky inference methods, Gaussian processes, or parametric approaches, can be used within the proposed general framework.

Robust model predictive control for linear sampled-data systems with irregular sampling times

This paper presents a sampled-data tube-based robust MPC scheme for linear continuous-time systems with irregular sampling times. The sampled-data control law is updated only at discrete sampling instances, but the proposed controller guarantees constraint satisfaction of the continuous-time state for all times. The proposed MPC scheme allows for two sources of uncertainty, (i) uncertain sampling times and (ii) an additional disturbance to the continuous-time system. A constraint adaptation is presented to handle this setting in a rigid tube MPC framework. Constraint satisfaction and convergence of the continuous-time state are shown for the proposed MPC scheme.

The model predictive control strategy of the transcritical CO2 air conditioning system used in railway vehicles

• A transcritical CO 2 air conditioning system was developed for use in a railway vehicle. • The model predictive control strategy was used to optimize the system performance. • The proposed control method maximized the real-time COP without sacrificing comfort. • The simulation results showed that the proposed control strategy is effective. This paper presented a model predictive control strategy to optimize the operation of the transcritical CO 2 air conditioning system used in railway vehicles, which had to balance the needs of the passengers' comfort with energy-saving effects. In this work, the discharge pressure and evaporator air volume flow rates were optimized while maintaining comfort using a multi-variable control technique called model predictive control strategy. The objective function and the predictive model, which were proposed in this work combining data and physical laws, were the basis for the model predictive controller's ability to foresee future operation-conditions and calculate the optimal inputs. The validation results showed that the prediction error was less than 4.5%. The model predictive controller was adopted in GT-SUITE platform to realize the real-time maximization of the energy efficiency and maintain comfort requirement by adjusting discharge pressure, evaporator air volume flow rate and compressor speed. The simulation was conducted under fixed conditions and realistic conditions. As for the fixed conditions, the coefficient of performance achieved at 2.24, equaling to the maximum value of the map. Under the realistic conditions, the overall energy consumption of the control method using the MPC strategy was lower than that using the PID control strategy, and the average COP was increased by 7.4%. Further, there was a 1% error in coefficient of performance between the extreme value gained by the model predictive control method and the extreme value offered by the map method, which validated that the model predictive control strategy can be an effective control method for the optimal operation of the transcritical CO 2 air conditioning system.

Evaluation of optimisation techniques on the performance of an on-line MPC controller in an occupancy grid for autonomous mobile robots

Computational capabilities on embedded platforms, especially for autonomous mobile robotics, enable them to be used for more challenging tasks, e.g., to apply advanced control methods like an on-line MPC controller on the robot itself. In the last decades, many improvements in direct methods to solve the optimal control problem were proposed, which speed up the optimisation process. We apply the multiple shooting approach to solve the Optimal Control Problem in a parallel manner. We apply the on-line MPC scheme with the multiple shooting approach in simulations, assess them in a hardware-in-the-loop scenario and conduct experiments on a Raspberry Pi 4-based differential-drive-platform to assess the realtime capability to control the robot while the optimisation is carried out locally.

Robust Tube-Based Model Predictive Control for Wave Energy Converters

This paper proposes an efficient robust tube-based model predictive control (RTMPC) strategy for energy-maximization control of wave energy converters (WECs) subject to constraints due to safety considerations. Compared with the existing MPC strategies developed for the WEC control problem, the RTMPC method provides an effective approach to explicitly handle plant-model mismatches with guaranteed constraint satisfaction, contributing to improved energy capture efficiency. The fundamental idea is to integrate disturbance invariant sets into the MPC scheme for energy-maximization control to form a tube-based predictive controller, which enhances the robustness of MPC for a WEC without increasing online computational complexity. The resulting RTMPC controller can bound the WEC plant trajectories in a tube centered around a nominal WEC model trajectory, and uncertainties from un-modeled WEC dynamics and unmeasured disturbances can be mitigated by an error feedback portion. Numerical simulations demonstrate the effectiveness of the proposed control strategy.

Model Predictive Control for Linear Uncertain Systems Using Integral Quadratic Constraints

In this work, we propose a tube-based MPC scheme for state- and input-constrained linear systems subject to dynamic uncertainties characterized by dynamic integral quadratic constraints (IQCs). In particular, we extend the framework of $\rho$-hard IQCs for exponential stability analysis to external inputs. This result yields that the error between the true uncertain system and the nominal prediction model is bounded by an exponentially stable scalar system. In the proposed tube-based MPC scheme, the state of this error bounding system is predicted along with the nominal model and used as a scaling parameter for the tube size. We prove that this method achieves robust constraint satisfaction and input-to-state stability despite dynamic uncertainties and additive bounded disturbances. A numerical example demonstrates the reduced conservatism of this IQC approach compared to state-of-the-art robust MPC approaches for dynamic uncertainties.

Hybrid Cost Function Distributed MPC for Vehicle Platoons With Stability and String Stability Properties

Distributed MPC schemes for control of vehicle platoons typically employ a p-norms based cost function to achieve stability and string stability. Quadratic cost functions yield smoother trajectories, but they are not aligned with string stability conditions. Hence, in this paper, we develop distributed MPC controllers for vehicle platoons based on a hybrid cost function, which combines infinity norms and quadratic forms. Sufficient conditions for global platoon stability and leader-follower string stability are derived for the developed hybrid cost function and applied to lateral dynamics control. Simulation results show that the hybrid cost function yields lateral position errors that are 10 times smaller (for the maximum error) compared with an infinity norms based cost function.

Experimental Results of an MPC Strategy for Total Intravenous Anesthesia

In this paper we present experimental results obtained by applying a Model Predictive Control strategy for the control of Depth of Hypnosis in general anesthesia. In particular, the Bispectral Index Scale is employed as the controlled variable and the administration of the hypnotic drug propofol is determined by applying a Generalized Predictive Control algorithm, which considers a process model that is linearized by means of an external predictor. The results of four patients who underwent elective plastic surgeries are analyzed and discussed, showing the feasibility of the approach in a practical context.

Distributed Energy Scheduling for Integrated Energy System Clusters With Peer-to-Peer Energy Transaction

Surplus electricity energy from renewable sources can be efficiently utilized by converting it into other forms of energy in the integrated energy system (IES). Local electricity energy sharing can be realized through effective dispatching and independent transaction between producers and consumers. This features the merits on energy consumption and operational cost reduction. In this paper, a novel energy scheduling regime is proposed for the electricity-hydrogen-heat IES clusters under a peer-to-peer (P2P) electricity and heat energy transaction structure. To instantly control the robustness of the scheduling decisions, a weighted MPC strategy is newly proposed for online decision-makings. Furthermore, an adaptive alternating direction method of multipliers (ADMM) with varying penalties algorithm that can effectively preserve prosumer privacy is proposed, which enables the operators to coordinate various parties in the multi-energy microgrids. Extensive case studies based on a typical testing system are carried out, of which the simulation results demonstrate the effectiveness of the proposed scheduling regime and suggest potential for practical application.

An Intrinsically Stable MPC Approach for Anti-Jackknifing Control of Tractor-Trailer Vehicles

Tractor-trailer vehicles are affected by jackknifing, a phenomenon that consists in the divergence of the trailer hitch angle and ultimately causes the vehicle to fold up. For the case of backward motions, in which jackknifing can occur at any speed, we present a control method that drives the vehicle along generic reference Cartesian trajectories while avoiding the divergence of the hitch angle. This is obtained thanks to a feedback control law that combines two actions: a tracking term, computed using input–output linearization, and a corrective term, generated via IS-MPC, an intrinsically stable MPC scheme which is effective for stable inversion of non-minimum phase systems. The successful performance of the proposed anti-jackknifing control is verified through simulations and experiments on a purposely built one-trailer prototype. To show the generality of the approach, we also apply and test the proposed method on a two-trailer vehicle.

Predictive Algorithm for Control of Common Mode Voltage and Switching Frequency in Direct Matrix Converter Fed System

Multiobjective model predictive control (Mo-MPC), owing to its simplicity and adaptability to comply with diverse constraints, has gained popularity in the control of direct matrix converters (DMCs). However, the MPC strategy makes the converter operate at an uncontrolled and variable switching frequency, which may inhibit high power density applications due to increased power losses. This article proposes a method for controlling the switching frequency of the converter and simultaneously regulating the common mode voltage in the DMC fed system while maintaining sinusoidal load and source currents at near unity input power factor. Furthermore, in order to streamline the control while simultaneously dealing with these objectives, a suitable normalization technique is implemented for scaling the errors in each objective. This method is validated through simulation and experimental results.

Development of adaptive dual predictive control schemes based on Wiener–Hammerstein models

Adaptive MPC schemes often employ local linear approximation of the system dynamics, which may not be adequate to capture the dynamic behavior of systems exhibiting strongly nonlinear dynamics. In particular, it is challenging to control a system exhibiting input multiplicity behavior at its optimum operating point as the steady-state gain matrix can smoothly become singular at the optimum operating point. In this work, with the aim of controlling systems with fading memory that exhibit such strongly nonlinear dynamics, a novel adaptive dual nonlinear MPC (ADNMPC) formulation is developed based on discrete-time block-oriented models. The block-oriented models are parameterized using the generalized orthonormal basis filters (GOBF). The nonlinear black-box model is further used to formulate a stochastic optimal control problem. A deterministic approximation to the stochastic optimal control problem is then systematically derived. Subsequently, an ADNMPC scheme is developed using the deterministic approximation as a basis. The efficacy of the proposed approach is demonstrated by simulating the problem of controlling a continuously operated fermenter system at its optimum operating point. Analysis of the simulation study shows that in contrast to the conventional nonlinear MPC (NMPC), the proposed ADNMPC scheme injects perturbation to the process whenever a model update is needed while meeting the control objectives. Moreover, with reference to a non-adaptive NMPC controller, the proposed ADNMPC schemes achieve better servo control performance while controlling the fermenter at the singular optimum operating point.

Design of multi-constraint robust formation controller based on error model

UAVs formation is a complex nonlinear system. Although quadrotor has many advantages, its dynamics model is nonlinear, coupled, and under driven. For model-based controller design, physical constraints, model uncertainties and external disturbances significantly deteriorate control performance. Therefore, a multi-constraints MPC strategy based on error model is proposed for the quadrotor formation. Firstly, a 3D model for quadrotor is established by using the Lagrange-Euler formulation, in which the model is divided into RS and TS. The corresponding multi-constraint MPC is designed for the two subsystems respectively. The tracking errors caused by external disturbances can be eliminated because of the integrator embedded in the augmented model. Comparing with RMPC, by making reasonable modifications to the cost function, the asymptotic stability of the open loop and the closed-loop subsystem can be ensured by MMPC. Moreover, the stability analysis of the above-mentioned algorithm is carried out. The simulation results show that the controller of the formation can not only achieve good path tracking, but also robustness to the multiple constraints and disturbances.

Control of Permanent Magnet Synchronous Motor Using MPC–MTPA Control for Deployment in Electric Tractor

This study aims to evaluate the interior permanent magnet synchronous motor (IPMSM) drive performance for various load conditions under steady state and dynamic conditions. Therefore, this paper proposes finite set model-predictive control (FS-MPC) for IPMSM with maximum torque per ampere (MTPA) for electric tractor application. The MTPA control technique is used to obtain maximum torque while maintaining a minimum current constraint. In addition to MTPA control, the MPC scheme is used as the suitable alternative control strategy in the electric tractor application, which eliminates the occurrence of torque ripples during the dynamic speed tracking under variable load conditions. The MPC is used to improve the dynamic response of the motor drive and reduce torque ripples under variable load conditions. MPC–MTPA is developed in the MATLAB/SIMULINK and validated in the real-time environment using the hardware-in-the-loop (HIL) simulator (OPAL-RT OP5700). The results prove that MPC improves the dynamic performance and MTPA reduces the stator copper loss and increases the drive efficiency.

Q-learning of the storage function in Economic Nonlinear Model Predictive Control

The closed-loop stability of an optimal policy provided by an Economic Nonlinear Model Predictive Control (ENMPC) scheme requires the existence of a storage function satisfying dissipativity conditions. Unfortunately, finding such a storage function is difficult in general. In contrast, tracking NMPC scheme uses a stage cost that is lower-bounded by a class-K∞ function and the closed-loop stability is fairly straightforward to establish. Under the dissipativity conditions, ENMPC has an equivalent tracking MPC that delivers the same optimal policy. In this paper, we use this idea and parameterize the stage cost and terminal cost of a tracking MPC with an additional parameterized storage function. We show that, if the parameterization of the tracking MPC scheme is rich enough to capture the exact optimal action-value function of the ENMPC scheme, then the parameterized storage function for the optimal parameters satisfies the dissipativity conditions for both discounted and undiscounted ENMPC schemes. In fact, we show that these conditions are met for dissipative problems. We propose to use Q-learning as a practical way of adjusting the parameters of the tracking MPC. Different numerical examples are provided to illustrate the efficiency of the proposed method, including LQR, non-dissipative, non-polynomial and a nonlinear chemical case studies. For instance, in the provided non-polynomial case study, the learning method can improve the storage function estimation by about 60% and 99.5% after 10 and 50 learning steps, respectively, compared with the Sum-of-Square method.

Implementable MPC-based surge avoidance nonlinear control strategies for non-ideally modeled natural gas compression systems

The surge avoidance control plays a pivotal role in a centrifugal compression process to maintain safety and high efficiency. In the literature, MPC-like schemes have shown promise for use in such tasks given that they can systematically deal with several process constraints. However, to obtain a good performance in the compression process with a significant deviation of gas ideality, the model used in MPC formulations has to be able to predict the process behavior correctly. This paper proposes surge avoidance feasible optimization-based MPC schemes for non-ideally modeled natural gas compression systems. Its pivotal contributions are: (i) extension of the isothermal and ideal gas thermodynamic behaviors commonly adopted in models of surge prevention MPC schemes to a non-isothermal flow and non-ideally behaved gas-like more realistic compression system; (ii) formulation of a proposed nonlinear model-based MPC control law with surge protection being managed by slacked nonlinear constraints; (iii) synthesis of an adaptive infinite horizon MPC-based surge avoidance scheme that relies upon the successive linearization of the proposed rigorous model for the compression system. From simulations carried out with a plant-model mismatch oriented by distinct equations of state, results obtained from the proposed rigorous model-based surge avoidance NMPC strategy are favorably compared to those obtained with the simplified model widely used in the literature. Finally, the proposed adaptive MPC-based surge prevention scheme showed convergence towards the corresponding NMPC with a drastically reduced computational cost.

First Order Approximation of Model Predictive Control Solutions for High Frequency Feedback

The lack of computational power on mobile robots is a well-known challenge when it comes to implementing a real-time MPC scheme to perform complex motions. Currently the best solvers are barely able to reach 100 Hz for computing the control of a whole-body legged model, while modern robots are expecting new torque references in less than 1 ms. This problem is usually tackled by using a handcrafted low-level tracking control whose inputs are the low-frequency trajectory computed by the MPC. We show that a linear state feedback controller naturally arises from the optimal control formulation and can be used directly in the low-level control loop along with other sensitivities of relevant time-varying parameters of the problem. When the optimal control problem is solved by DDP, this linear controller can be computed for cheap as a by-product of the backward pass, and corresponds in part to the classical Riccati gains. A side effect of our proposition is to show that Riccati gains are valuable assets that must be used to achieve an efficient control and that they are not stiffer than the optimal control scheme itself. We propose a complete implementation of this idea on a full-scale humanoid robot and demonstrate its importance with real experiments on the robot Talos.

An Event-triggered Output Feedback Robust MPC Scheme for Time-varying System with Packet Loss and Bounded Disturbance

An Event-triggered Output Feedback Robust MPC Scheme for Time-varying System with Packet Loss and Bounded Disturbance

A model predictive control scheme for regenerative braking in vehicles with hybridized architectures via aftermarket kits

Regenerative braking is an established technique that can improve the driving range of vehicles with full-electric or hybrid/hybridized powertrain, thus promoting their large-scale adoption. In this paper, the design of an MPC strategy for maximizing regenerative braking in a real vehicle that has been hybridized by means of a kit is presented. The kit is entirely built by the partners of the European Horizon2020 LIFE-SAVE (Solar Aided Vehicle Electrification – LIFE16 ENV/IT/000442) funded project, and features two in-wheel-motors placed on the rear axle, PV panels installed on the roof and the bonnet and a battery pack placed in the trunk. The proposed MPC strategy will serve as a baseline for the implementation of an additional algorithm to the actual version of the hybridized powertrain control such that the new kit will endow the vehicle also with regenerative braking. Since the kit cannot access the vehicle’s ECU in order to avoid code infringements, the MPC relies only on information that can be retrieved via the vehicle’s CAN. In addition to the maximization of the energy recovery during braking, the proposed strategy considers aspects such as the in-wheel-motors non-ideal efficiency and rated specifications, the constraints given by the brake operating region and possible comfort requirements that have a positive impact on the driver’s experience. Furthermore, it also includes a penalty term to force the controller to trade-off with possible high-efficiency operations. The simulation outcomes show the effectiveness of the proposed MPC strategy, enabling the recovery up to approximately 18% of the vehicle’s kinetic energy, and suggest that it can be fruitfully used as a baseline for an additional regenerative braking algorithm to be implemented onto the real vehicle.

A stabilizing cooperative-distributed gradient-based economic model predictive control strategy for constrained linear systems

This paper proposes a stabilizing distributed gradient-based economic MPC strategy for cooperative control of constrained linear systems. This strategy is based on quadratic programming to limit the computational cost, and one key feature is the evaluation of an economically optimal steady-state directly in the control law, leading the closed-loop system towards it. The control law includes three ingredients to enlarge its domain of attraction and potentially avoid feasibility problems, namely: artificial steady-state, slack variables, and terminal equality constraints solely on non-stable states. A four-tank system is used to address the properties of the formulation, especially its stability in the nominal case, the capacity to track the desired target for a nonlinear performance economic function, and tackle unmeasured and persistent unmeasured disturbances.