Model Predictive Control Control Law Research Articles

Model predictive path tracking control of intelligent vehicles based on dual-stage disturbance observer under multi-channel disturbances

Abstract Parameter fluctuations, unmodeled dynamics, speed variation, steering actuator faults, and other multi-channel uncertain disturbances are the key challenges faced by the path tracking control of intelligent vehicles, which will affect the accuracy and stability of the path tracking. Therefore, a model predictive control (MPC) method based on a dual-stage disturbance observer (DDOB) is proposed in this paper. First, a tracking error dynamics model considering multi-channel uncertain disturbances is constructed, based on which a model predictive controller is designed to obtain the nominal front wheel steering angle by the Karush–Kuhn–Tucker (KKT) condition. Furthermore, the DDOB is designed to enable real-time estimation of the system disturbances, and then the estimated disturbances are used as the compensation for the nominal front wheel steering angle, which establishes the MPC control law with parallel compensation of the DDOB. Finally, the error boundedness of the DDOB and the global stability of the model predictive controller are analyzed. The effectiveness and superiority of the proposed algorithm are verified through Carsim–Simulink simulation and hardware-in-the-loop experiments.

Reliably-Stabilizing Piecewise-Affine Neural Network Controllers

A common problem affecting neural network (NN) approximations of model predictive control (MPC) policies is the lack of analytical tools to assess the stability of the closed-loop system under the action of the NN-based controller. We present a general procedure to quantify the performance of such a controller, or to design minimum complexity NNs with rectified linear units (ReLUs) that preserve the desirable properties of a given MPC scheme. By quantifying the approximation error between NN-based and MPC-based state-to-input mappings, we first establish suitable conditions involving two key quantities, the worst-case error and the Lipschitz constant, guaranteeing the stability of the closed-loop system. We then develop an offline, mixed-integer optimization-based method to compute those quantities exactly. Together these techniques provide conditions sufficient to certify the stability and performance of a ReLU-based approximation of an MPC control law.

Dissipativity-constrained learning of MPC with guaranteeing closed-loop stability

This paper addresses the data-driven approximation of model predictive control (MPC) designed for nonlinear plant systems. MPC has high ability of handling complex system-specifications and of improving the control performance, while it requires high computational complexity. Aiming at reducing the complexity, this paper addresses the data-driven approximation of MPC. To this end, the control law in MPC is described by the Koopman operator, which is a linear operator defined on the infinite-dimensional lifted state space. Then, the problem of data-driven finite-dimensional approximation of the operator is addressed. The problem is formulated as an optimization problem subject to a specified dissipativity constraint, which guarantees closed-loop stability and is modeled by a set of matrix inequalities. This paper also presents a computationally efficient algorithm of solving the optimization problem. Finally, a numerical simulation of controller construction is performed. The approximated MPC control law shows the stability of the overall control system while demonstrating high control performance.

Optimization of the model predictive control meta-parameters through reinforcement learning

Model predictive control (MPC) is increasingly being considered for control of fast systems and embedded applications. However, MPC has some significant challenges for such systems, such as its high computational complexity. Further, the MPC parameters must be tuned, which is largely a trial-and-error process that affects the control performance, the robustness, and the computational complexity of the controller to a high degree. This paper presents a multivariate optimization method based on reinforcement learning (RL) that automatically tunes the control algorithm’s parameters from data to achieve optimal closed-loop performance. The main contribution of our method is the inclusion of state-dependent optimization of the meta-parameters of MPC, i.e. parameters that are non-differentiable wrt. the MPC solution. Our control algorithm is based on an event-triggered MPC, where we learn when the MPC should be re-computed, and a dual-mode MPC and linear state feedback control law applied in between MPC computations. We formulate a novel mixture-distribution RL policy determining the meta-parameters of our control algorithm and show that with joint optimization we achieve improvements that do not present themselves with univariate optimization of the same parameters. We demonstrate our framework on the inverted pendulum control task, reducing the total computation time of the control system by 36% while also improving the control performance by 18.4%.

Offline Computation of the Explicit Robust Model Predictive Control Law Based on Deep Neural Networks

A significant challenge in robust model predictive control (MPC) is the online computational complexity. This paper proposes a learning-based approach to accelerate online calculations by combining recent advances in deep learning with robust MPC. The use of soft constraint variables addresses feasibility issues in the robust MPC design, while the employment of a symmetrical structure deep neural network (DNN) approximates the robust MPC control law. The symmetry of the network structure facilitates the training process. The use of soft constraints expands the feasible region and also increases the complexity of the training data, making the network difficult to train. To overcome this issue, a dataset construction method is employed. The performance of the proposed method is demonstrated through simulated examples, and the proposed algorithm can be applied to control systems in various fields such as aerospace, three-dimensional printing, optical imaging, and chemical production.

Stability and Robustness of Distributed Suboptimal Model Predictive Control

In distributed model predictive control (MPC), the control input at each sampling time is computed by solving a large-scale optimal control problem (OCP) over a finite horizon using distributed algorithms. Typically, such algorithms require several (virtually, infinite) communication rounds between the subsystems to converge, which is a major drawback both computationally and from an energetic perspective (for wireless systems). Motivated by these challenges, we propose a suboptimal distributed MPC scheme in which the total communication burden is distributed also in time, by maintaining a running solution estimate for the large-scale OCP and updating it at each sampling time. We demonstrate that, under some regularity conditions, the resulting time-distributed suboptimal MPC control law recovers the qualitative robust stability properties of optimal MPC, if the communication budget at each sampling time is large enough.

Handling model uncertainty in control of a pressure swing adsorption unit for syngas purification: A multi-model zone control scheme-based robust model predictive control strategy

The application of a robustly stabilizing model predictive control (MPC) strategy to a pressure swing adsorption (PSA) unit, hitherto unexplored in the literature, is addressed in this work. Here, a set of linear models to handle model uncertainties describes the PSA nonlinear dynamic behaviour. Each model represents a different operating condition of the PSA, generating a multi-model uncertainty description. In addition to incorporating the multi-model uncertainty, the proposed MPC control law deals with a controlled output zone tracking scheme to systematically accommodate typical cyclic steady states of a PSA process. From the industrial standpoint, economic targets on process variables (controlled outputs, manipulated inputs, or both) are also incorporated into the robust control method. A Real-Time Optimizer usually defines these targets, making up a two-layer control scheme. The effectiveness of the robust MPC is evaluated in a syngas purification process via a single bed, six-step PSA unit composed of a porous amino-functionalized titanium terephthalate MIL-125-type MOF adsorbent.

Path tracking control strategy for off-road 4WS4WD vehicle based on robust model predictive control

With the increasing requirements for vehicle adaptability and maneuverability in various road environments, four-wheel-steering four-wheel-drive (4WS4WD) vehicles have attracted wider attention. This paper presents a robust model predictive control-based strategy for the path tracking of 4WS4WD vehicles considering external disturbances. The strategy combines model predictive control (MPC) and control allocation under an upper–lower structure. The main objective of the present work is to improve the robustness and stability of path tracking by developing an MPC algorithm in the upper layer. The controller design considers general disturbances caused by allocation errors and sudden disturbances caused by an outer force in the offset model. Based on the offset model, a robust MPC control law is obtained by converting the robustness constraints into a linear matrix inequality. The control law is mathematically demonstrated to be stable in multidisturbed conditions via the Lyapunov stability theorem. Through comparison with a similar control algorithm of path tracking and applying it on different uneven ground conditions, the proposed robust algorithm is found to effectively overcome disturbances on the system.

Model Predictive Control Scheme of a Four-Level Quasi-Nested Converter Fed AC-Drive, with dc-Link Voltage-Drift Compensation

In this paper, a Model Predictive Control (MPC) strategy is introduced for its application in a four-level quasi-nested topology, feeding an Interior Permanent Magnet Synchronous Machine (IPMSM) AC-drive. The proposed control strategy is capable to synthesize the required output space vectors to ensure perfect tracking of the AC-drive speed reference under different loading conditions, while also ensuring voltage balance between the dc-link capacitors. The proposed converter topology is based on a reduced number of components compared to other mature converter topologies, such as the neutral-point clamped converter (NPC) or the active neutral-point clamped converter (ANPC) topologies, when compared in terms of the number of output voltage levels, since this quasi-nested topology does not require passive clamping devices such as diodes or active switches. Moreover, no floating dc-link capacitors with asymmetrical voltage levels are employed, thus simplifying the dc-link capacitor voltage balance mechanism. This work presents the switching operation principles and MPC control law when supplying an IPMSM AC-drive load are addressed in detail. Simulation and validation results using a Hardware in the Loop (HIL) prototype under different operation conditions are presented in order to validate the proposed converter topology and control strategy.

Advanced hybrid artificial pancreas system improves on unannounced meal response - In silico comparison to currently available system

Background and objective: Glycemic control, especially meal-related disturbance rejection, has proven to be a major challenge for people with type 1 diabetes. In this manuscript, we introduce a novel, personalized, advanced hybrid insulin infusion system (a.k.a. artificial pancreas) based on the Model Predictive Control (MPC) methodology to adjust insulin infusion while automatically rejecting uninformed meals. Methods: The proposed advanced hybrid closed-loop system relies on the integration of three key elements: (i) an adaptive personalized MPC control law that modulates the control strength depending on recent past control actions, glucose measurements, and its derivative, (ii) an automatic Bolus Priming System (BPS) that commands additional insulin injections safely upon the detection of enabling metabolic conditions (e.g., an unacknowledged meal), and (iii) a new hyperglycemia mitigation system to avoid prevailing hyperglycemia. The benefits of the proposed system are demonstrated through simulations and tests using the most up-to-date Type 1 UVA/Padova simulator as preclinical stage prior to in vivo clinical tests. We used a legacy algorithm (USS Virginia), currently used in clinical care, as a benchmark controller. Results: Overall, the proposed control strategy enhanced by an automatic BPS improves glycemic control when compared with an available system. When a large meal is not announced (80g CHO), the proposed controller outperformed the legacy controller in time-in-target-range TIR (postprandial and overnight) and time-in-tight-range TTR (overall, postprandial, and overnight). Conclusion: The integration of a novel BPS into an advanced control system allowed to automatically reject unannounced meals. Exhaustive simulation studies indicated the safety and feasibility of the proposed controller to be deployed in human clinical trials.

Online learning with stability guarantees: A memory-based warm starting for real-time MPC

We propose and analyze a real-time model predictive control (MPC) scheme that utilizes stored data to improve its performance by learning the value function online with stability guarantees. For linear and nonlinear systems, a learning method is presented that makes use of basic analytic properties of the cost function and is proven to learn the MPC control law and the value function on the limit set of the closed-loop state trajectory. The main idea is to generate a smart warm start based on historical data that improves future data points and thus future warm starts. We show that these warm starts are asymptotically exact and converge to the solution of the MPC optimization problem. Thereby, the suboptimality of the applied control input resulting from the real-time requirements vanishes over time. Numerical examples show that existing real-time MPC schemes can be improved by storing optimization data and using the proposed learning scheme.

Deep Neural Network Approximation of Nonlinear Model Predictive Control

This paper focuses on developing effective computational methods to enable the real-time application of model predictive control (MPC) for nonlinear systems. To achieve this goal, we follow the idea of approximating the MPC control law with a Deep Neural Network (DNN). To train the deep neural network offline, we propose a new “optimize and train” method that combines the steps of data generation and neural network training into a single high-dimensional stochastic optimization problem. This approach directly optimizes the closed loop performance of the DNN controller over a finite horizon for a number of initial states. The large-scale optimization problem can be solved efficiently using parallel computing techniques. The benefits of this approach over the conventional “optimize then train” protocol is illustrated through numerical results.

A Framework for Time-Consistent, Risk-Sensitive Model Predictive Control: Theory and Algorithms

In this paper, we present a framework for risk-sensitive model predictive control (MPC) of linear systems affected by stochastic multiplicative uncertainty. Our key innovation is to consider a time-consistent, dynamic risk evaluation of the cumulative cost as the objective function to be minimized. This framework is axiomatically justified in terms of time-consistency of risk assessments, is amenable to dynamic optimization, and is unifying in the sense that it captures a full range of risk preferences from risk neutral (i.e., expectation) to worst case. Within this framework, we propose and analyze an online risk-sensitive MPC algorithm that is provably stabilizing. Furthermore, by exploiting the dual representation of time-consistent, dynamic risk measures, we cast the computation of the MPC control law as a convex optimization problem amenable to real-time implementation. Simulation results are presented and discussed.

Economic Feedback Model Predictive Control of Wave Energy Converters

In this paper, we propose an economic feedback model predictive control (MPC) scheme to improve energy conversion efficiency of wave energy converters (WECs) and guarantee their safe operation over a wide range of sea conditions. The proposed MPC control law consists of two terms: one state feedback gain designed offline to maximize operating range and one term calculated online to maximize the energy output. Compared with the existing MPC strategies developed for the WEC control problem, the proposed feedback economic MPC strategy has the following distinguishing advantages: First, the satisfaction of safety constraints and the recursive feasibility can be guaranteed to ensure WEC's safe operation in a large range of sea states. Second, the novel MPC can notably improve energy production efficiency. Third, the controller design procedure is more convenient and straightforward compared with the existing MPC strategies. The efficacy of the proposed MPC strategy is demonstrated by numerical simulations with a point absorber as a case study. By comparison with a representative existing MPC strategy, the proposed economic MPC can significantly improve energy output.

Optimization of the Energy Consumption of Depth Tracking Control Based on Model Predictive Control for Autonomous Underwater Vehicles.

For long-term missions in complex seas, the onboard energy resources of autonomous underwater vehicles (AUVs) are limited. Thus, energy consumption reduction is an important aspect of the study of AUVs. This paper addresses energy consumption reduction using model predictive control (MPC) based on the state space model of AUVs for trajectory tracking control. Unlike the previous approaches, which use a cost function that consists of quadratic deviations of the predicted controlled output from the reference trajectory and quadratic input changes, a term of quadratic energy (i.e., quadratic input) is introduced into the cost function in this paper. Then, the MPC control law with the new cost function is constructed, and an analysis on the effect of the quadratic energy term on the stability is given. Finally, simulation results for depth tracking control are given to demonstrate the feasibility and effectiveness of the improved MPC on energy consumption optimization for AUVs.

Sequential distributed predictive control of a 3D tower crane

An asymptotically stabilizing sequential distributed model predictive control (MPC) of a 3D tower crane is proposed. Stability is ensured by employing three locally stabilizing MPC control laws. In the case of Lipschitz continuous local MPC control laws, a terminal cost and a terminal set constraint are used as stabilizing ingredients while robust control invariant feasible set is used as an additional constraint to guarantee recursive feasibility. On the other hand, in the case of an arbitrary cost function, switching to a robust dual-mode local control law is used inside of the terminal set to guarantee asymptotic stability.

A new feedback predictive control approach for processes with time delay in the manipulated variable

The scope of this work is time delay (θ) in the manipulated variable (MV) and not in the controlled variable (CV), addressed by approaches such as the Smith Predictor. The classical algorithm for dead time in MV is model predictive control (MPC). The MPC control law is for the future predicted value of CV to be at the set point an integer value of sampling time steps (J) beyond θ time in the future. Hence, the effectiveness of MPC depends strongly on the accuracy of the future prediction of CV, which decreases as J increases. In addition, the larger the time lag for MV, the longer it takes to reach the set point and the greater J will be also. Therefore, to overcome these limitations, this work presents a new FBC predictive control approach that has a control law that uses a future prediction of CV a distance θ into the future. Thus, it prediction horizon is minimal and it is not affected by the MV time lag. This approach is compared with MPC in two studies. The first one uses a mathematical transfer function model and the second study uses a mathematically simulated CSTR.

Disturbance-Rejection-Based Model Predictive Control: Flexible-Mode Design With a Modulator for Three-Phase Inverters

This paper aims to investigate a disturbance-rejection-based model predictive control (MPC) with two flexible modes (i.e., unconstrained mode and constrained mode) for three-phase inverters with an $LC$ filter. A disturbance observer (DOB) is designed to both simplify the prediction model and achieve the robustness against uncertain parameters. First, the unconstrained mode is designed with a simple horizon-one MPC control law to precisely regulate the output voltage in the steady state. Next, the constrained mode is designed with long-horizon MPC to quickly drive the system to the unconstrained mode by further optimizing the modulation stage. Also, the proposed MPC ensures the robustness and optimality in all operating modes. Especially, the overall closed-loop stability with DOB dynamics is proven by using Lyapunov function. Unlike other MPC methods, the long-horizon MPC in the constrained mode is specialized by finite switching sequences of the sector-based space vector modulation. Comparative studies with the conventional linear quadratic regulator are conducted on a prototype test bed with a TI TMS320F28335 DSP. Then, the proposed MPC method verifies fast dynamic response and advanced voltage regulation (i.e., small steady-state errors and low total harmonic distortion) under various load conditions and uncertain parameters.

Cooperative distributed model predictive control for wind farms

SUMMARYThis paper focuses on cooperative distributed model predictive control (MPC) of wind farms, where the farms respond to active power control commands issued by the transmission system operator. A distributed MPC scheme is proposed, which aims at satisfying the requirements imposed by the grid code while minimizing the farm‐wide mechanical structure fatigue. The distributed MPC control law is defined by a global finite‐horizon optimal control problem, which is solved at every time step by distributed optimization. The computational approach is completely distributed, that is, every turbine evaluates its own globally optimal input by considering local measurements and communicating to neighboring turbines only. Two MPC versions are compared, in the first of which the farm‐wide power output constraint is implemented as a hard constraint, whereas in the second, it is implemented as a soft constraint. As for distributed optimization methods, the alternating direction method of multipliers as well as a dual decomposition scheme based on fast gradient updates are compared. The performance of the proposed distributed MPC controller, as well as the performance of the distributed optimization methods used for its operation, are compared in the simulation on four exemplary scenarios. The results of the simulations imply that the use of cooperative distributed MPC in wind farms is viable both from a performance and from a computational viewpoint. Copyright © 2014 John Wiley & Sons, Ltd.

Soft Constrained Model Predictive Control With Robust Stability Guarantees

Soft constrained model predictive control (MPC) is frequently applied in practice in order to ensure feasibility of the optimization during online operation. Standard techniques offer global feasibility by relaxing state or output constraints, but cannot ensure closed-loop stability. This paper presents a new soft constrained MPC approach for tracking that provides stability guarantees even for unstable systems. Two types of soft constraints and slack variables are proposed to enlarge the terminal constraint and relax the state constraints. The approach ensures feasibility of the MPC problem in a large region of the state space, depending on the imposed hard constraints, and stability is guaranteed by design. The optimal performance of the MPC control law is preserved whenever all state constraints can be enforced. Asymptotic stability of all feasible reference steady-states under the proposed control law is shown, as well as input-to-state stability for the system under additive disturbances. The soft constrained method can be combined with a robust MPC approach, in order to exploit the benefits of both techniques. The properties of the proposed methods are illustrated by numerical examples.