Lyapunov-based Model Predictive Control Research Articles

A Lyapunov-Based Model Predictive Control Design With Reduced Sensors for a PUC7 Rectifier

This article proposes a Lyapunov-based model predictive control (MPC) design for a dual output multilevel rectifier. The investigated topology, a seven-level packed U-cell (PUC7) converter, is selected based on its high reliability, compactness, and low cost. The proposed controller has the following advantages over the conventional MPC controllers: First, no gain tuning is required; second, easy implementation; and third, reduced number of sensors (the load currents are estimated using the mathematical model of the PUC7 rectifier). Simulation and experimental results are provided to show the high dynamic performance and effectiveness of the Lyapunov-based MPC controller in tracking the output voltage references under grid change and parameters mismatch conditions.

A cyber‐secure control‐detector architecture for nonlinear processes

AbstractThis work presents a detector‐integrated two‐tier control architecture capable of identifying the presence of various types of cyber‐attacks, and ensuring closed‐loop system stability upon detection of the cyber‐attacks. Working with a general class of nonlinear systems, an upper‐tier Lyapunov‐based Model Predictive Controller (LMPC), using networked sensor measurements to improve closed‐loop performance, is coupled with lower‐tier cyber‐secure explicit feedback controllers to drive a nonlinear multivariable process to its steady state. Although the networked sensor measurements may be vulnerable to cyber‐attacks, the two‐tier control architecture ensures that the process will stay immune to destabilizing malicious cyber‐attacks. Data‐based attack detectors are developed using sensor measurements via machine‐learning methods, namely artificial neural networks (ANN), under nominal and noisy operating conditions, and applied online to a simulated reactor‐reactor‐separator process. Simulation results demonstrate the effectiveness of these detection algorithms in detecting and distinguishing between multiple classes of intelligent cyber‐attacks. Upon successful detection of cyber‐attacks, the two‐tier control architecture allows convenient reconfiguration of the control system to stabilize the process to its operating steady state.

Lyapunov-Based Model Predictive Control of a PUC7 Grid-Connected Multilevel Inverter

In this paper, a new Lyapunov-based model predictive controller is proposed for a 7-level packed U-cell (PUC7) grid-connected inverter. A cost function of the proposed model predictive controller is designed from the system stability point of view, inspired by the Lyapunov control theory. The proposed controller eliminates the need for gains that are associated with cost function coefficients, as seen in classical model predictive control based controllers. Therefore, the control design problem is significantly simplified. In addition, the average switching frequency is also reduced, as shown in both simulation and experimental results, leading to a reduction in switching losses. Simulation and experimental tests, on a PUC7 lab prototype, demonstrate the excellent performance of the proposed control system, in terms of high disturbance rejection, robustness to parameter mismatches, and fast dynamic response. Such features qualify the proposed control strategy as a good candidate for grid-tied applications.

Koopman Lyapunov‐based model predictive control of nonlinear chemical process systems

AbstractIn this work, we propose the integration of Koopman operator methodology with Lyapunov‐based model predictive control (LMPC) for stabilization of nonlinear systems. The Koopman operator enables global linear representations of nonlinear dynamical systems. The basic idea is to transform the nonlinear dynamics into a higher dimensional space using a set of observable functions whose evolution is governed by the linear but infinite dimensional Koopman operator. In practice, it is numerically approximated and therefore the tightness of these linear representations cannot be guaranteed which may lead to unstable closed‐loop designs. To address this issue, we integrate the Koopman linear predictors in an LMPC framework which guarantees controller feasibility and closed‐loop stability. Moreover, the proposed design results in a standard convex optimization problem which is computationally attractive compared to a nonconvex problem encountered when the original nonlinear model is used. We illustrate the application of this methodology on a chemical process example.

Machine learning‐based predictive control of nonlinear processes. Part I: Theory

AbstractThis article focuses on the design of model predictive control (MPC) systems for nonlinear processes that utilize an ensemble of recurrent neural network (RNN) models to predict nonlinear dynamics. Specifically, RNN models are initially developed based on a data set generated from extensive open‐loop simulations within a desired process operation region to capture process dynamics with a sufficiently small modeling error between the RNN model and the actual nonlinear process model. Subsequently, Lyapunov‐based MPC (LMPC) that utilizes RNN models as the prediction model is developed to achieve closed‐loop state boundedness and convergence to the origin. Additionally, machine learning ensemble regression modeling tools are employed in the formulation of LMPC to improve prediction accuracy of RNN models and overall closed‐loop performance while parallel computing is utilized to reduce computation time. Computational implementation of the method and application to a chemical reactor example is discussed in the second article of this series.

Machine‐learning‐based predictive control of nonlinear processes. Part II: Computational implementation

AbstractMachine learning is receiving more attention in classical engineering fields, and in particular, recurrent neural networks (RNNs) coupled with ensemble regression tools have demonstrated the capability of modeling nonlinear dynamic processes. In Part I of this two‐article series, the Lyapunov‐based model predictive control (LMPC) method using a single RNN model and an ensemble of RNN models, respectively, was rigorously developed for a general class of nonlinear systems. In the present article, computational implementation issues of this new control method ranging from training of the RNN models, ensemble regression of the RNN models, and parallel computation for accelerating the real‐time model calculations are addressed. Furthermore, a chemical reactor example is used to demonstrate the implementation and effectiveness of these machine‐learning tools in LMPC as well as compare them with standard state‐space model identification tools.

Lyapunov-based Model Predictive Control of an Input Delayed Functional Electrical Simulation

Abstract In this paper a Lyapunov-based model predictive control (LMPC) method to control knee extension during an input-delayed neuromuscular electrical stimulation is developed. This method incorporates a contractive constraint under a delay compensation control law that achieves system stability despite an unknown constant input delay and imperfectly estimated model parameters The simulations were performed to compare the LMPC method with the delay compensation control law. Robustness of the LMPC method and the boundedness of the LMPC inputs are depicted.

Backstepping control integrated with Lyapunov-based model predictive control

In this study, backstepping control integrated with Lyapunov-based model predictive control (BS-MPC) is proposed for nonlinear systems in a strict-feedback form. The virtual input of the first step is designed by solving the finite-horizon optimal control problem (FHOCP), and the real input is designed by the backstepping method. BS-MPC guarantees (semiglobal) ultimate boundedness of the closed-loop system when the control is implemented in a zero-order hold manner. When the robustness of BS-MPC is analyzed for uniformly bounded disturbances, the ultimate boundedness of the solution of perturbed system is guaranteed. BS-MPC can provide a better desired value of the virtual input of the first step by solving the FHOCP, resulting in a faster stabilization of the system compared with the backstepping control. In addition, BS-MPC requires less computational load compared with MPC because the dimension of the states considered in the on-line optimization problem of BS-MPC is lower than that of MPC.

Ellipsoidal Lyapunov-based hybrid model predictive control for mixed logical dynamical systems with a recursive feasibility guarantee

This paper proposes an ellipsoidal hybrid model predictive control approach to solve the robust stability problem of uncertain hybrid dynamical systems modelled by the mixed logical dynamical framework. In this approach, the traditional terminal equality constraint is replaced by an ellipsoid that results in a maximal positive invariant set for the closed-loop system. Then, a Lyapunov decreasing condition along with the robustness criterion is introduced to the optimization problem to achieve the robust stability of the closed-loop system. As the main advantages, the ellipsoidal terminal set proposed in this paper attains a larger domain of attraction along with the recursive feasibility guarantee. Moreover, the stability and robustness constraints are achieved by a lower prediction horizon, which leads to a smaller dimension optimization problem. In addition, to reduce the computational complexity of the corresponding optimization problem, a suboptimal version of the proposed algorithm is introduced. Finally, numerical and car suspension system examples show the capabilities of the proposed method.

Detecting and Handling Cyber-Attacks in Model Predictive Control of Chemical Processes

Since industrial control systems are usually integrated with numerous physical devices, the security of control systems plays an important role in safe operation of industrial chemical processes. However, due to the use of a large number of control actuators and measurement sensors and the increasing use of wireless communication, control systems are becoming increasingly vulnerable to cyber-attacks, which may spread rapidly and may cause severe industrial incidents. To mitigate the impact of cyber-attacks in chemical processes, this work integrates a neural network (NN)-based detection method and a Lyapunov-based model predictive controller for a class of nonlinear systems. A chemical process example is used to illustrate the application of the proposed NN-based detection and LMPC methods to handle cyber-attacks.

Trajectory Tracking Control of an Autonomous Underwater Vehicle Using Lyapunov-Based Model Predictive Control

This paper studies the trajectory tracking control problem of an autonomous underwater vehicle (AUV). We develop a novel Lyapunov-based model predictive control (LMPC) framework for the AUV to utilize computational resource (online optimization) to improve the trajectory tracking performance. Within the LMPC framework, the practical constraints, such as actuator saturation, can be explicitly considered. Also, the thrust allocation subproblem can be addressed simultaneously with the LMPC controller design. Taking advantage of a nonlinear backstepping tracking control law, we construct the contraction constraint in the formulated LMPC problem so that the closed-loop stability is theoretically guaranteed. Sufficient conditions that ensure the recursive feasibility, and hence the closed-loop stability, are provided analytically. A guaranteed region of attraction is explicitly characterized. In the meantime, the robustness of the tracking control can be improved by the receding horizon implementation that is adopted in the LMPC control algorithm. Simulation results on the Saab SeaEye Falcon model AUV demonstrate the significantly enhance trajectory tracking control performance via the proposed LMPC method.

Forecast-Triggered Model Predictive Control of Constrained Nonlinear Processes with Control Actuator Faults

This paper addresses the problem of fault-tolerant stabilization of nonlinear processes subject to input constraints, control actuator faults and limited sensor–controller communication. A fault-tolerant Lyapunov-based model predictive control (MPC) formulation that enforces the fault-tolerant stabilization objective with reduced sensor–controller communication needs is developed. In the proposed formulation, the control action is obtained through the online solution of a finite-horizon optimal control problem based on an uncertain model of the plant. The optimization problem is solved in a receding horizon fashion subject to appropriate Lyapunov-based stability constraints which are designed to ensure that the desired stability and performance properties of the closed-loop system are met in the presence of faults. The state-space region where fault-tolerant stabilization is guaranteed is explicitly characterized in terms of the fault magnitude, the size of the plant-model mismatch and the choice of controller design parameters. To achieve the control objective with minimal sensor–controller communication, a forecast-triggered communication strategy is developed to determine when sensor–controller communication can be suspended and when it should be restored. In this strategy, transmission of the sensor measurement at a given sampling time over the sensor–controller communication channel to update the model state in the predictive controller is triggered only when the Lyapunov function or its time-derivative are forecasted to breach certain thresholds over the next sampling interval. The communication-triggering thresholds are derived from a Lyapunov stability analysis and are explicitly parameterized in terms of the fault size and a suitable fault accommodation parameter. Based on this characterization, fault accommodation strategies that guarantee closed-loop stability while simultaneously optimizing control and communication system resources are devised. Finally, a simulation case study involving a chemical process example is presented to illustrate the implementation and evaluate the efficacy of the developed fault-tolerant MPC formulation.

Data Driven Economic Model Predictive Control

This manuscript addresses the problem of data driven model based economic model predictive control (MPC) design. To this end, first, a data-driven Lyapunov-based MPC is designed, and shown to be capable of stabilizing a system at an unstable equilibrium point. The data driven Lyapunov-based MPC utilizes a linear time invariant (LTI) model cognizant of the fact that the training data, owing to the unstable nature of the equilibrium point, has to be obtained from closed-loop operation or experiments. Simulation results are first presented demonstrating closed-loop stability under the proposed data-driven Lyapunov-based MPC. The underlying data-driven model is then utilized as the basis to design an economic MPC. The economic improvements yielded by the proposed method are illustrated through simulations on a nonlinear chemical process system example.

Lyapunov-based model predictive control for tracking of nonholonomic mobile robots under input constraints

This paper studies the tracking problem of nonholonomic wheeled robots subject to control input constraints. In order to take optimality considerations into account while designing saturated tracking controllers, a Lyapunov-based predictive tracking controller is developed, in which the contractive constraint is characterized by a backup global saturated tracking controller. Theoretical results on ensuring global feasibility and closed-loop stability of the controller are provided. In addition, the proposed methodology admits suboptimal solutions. Finally, numerical simulations are performed to verify the effectiveness of the proposed control strategy.

Integrating Process Safety Considerations in Lyapunov-Based Model Predictive Control

In this work, two novel Lyapunov-based model predictive control (LMPC) designs that can ensure process operational safety (termed safety-LMPC) are presented. The two LMPC designs can drive the closed-loop state to a safety region (a level set within the stability region where process operational safety is ensured) at a prescribed rate, and also can drive the closed-loop state to a safe level set within the stability region of another steady-state. To demonstrate the effectiveness of the proposed schemes, a comparison between the safety-LMPC, which effectively integrates feedback control and safety considerations, and the classical LMPC method is presented with a chemical process example.

Achieving operational process safety via model predictive control

Model predictive control (MPC) has been widely adopted in the chemical and petrochemical industry due to its ability to account for actuator constraints and multi-variable interactions for complex processes. However, closed-loop stability is not guaranteed within the framework of MPC without additional constraints or assumptions. An MPC formulation that can guarantee closed-loop stability in the presence of uncertainty is Lyapunov-based model predictive control (LMPC) which incorporates stability constraints based on a stabilizing Lyapunov-based controller. Though LMPC drives the closed-loop state trajectory to a steady-state, it lacks the ability to adjust the rate at which the closed-loop state approaches the steady-state in an explicit manner. However, there may be circumstances in which it would be desirable, for safety reasons, to be able to adjust this rate to avoid triggering of safety alarms or process shut-down. In addition, there may be scenarios in which the current region of operation is no longer safe to operate within, and another region of operation (i.e., a region around another steady-state) is appropriate. Motivated by these considerations, this work develops two novel LMPC schemes that can drive the closed-loop state to a safety region (a level set within the stability region where process functional safety is ensured) at a prescribed rate or can drive the closed-loop state to a safe level set within the stability region of another steady-state. Recursive feasibility and closed-loop stability are established for a sufficiently small LMPC sampling period. A comparison between the proposed method, which effectively integrates feedback control and safety considerations, and the classical LMPC method is demonstrated with a chemical process example. The chemical process example demonstrates that the safety-LMPC drives the closed-loop state into a safe level set of the stability region two sampling times faster than under the classical LMPC in the presence of process uncertainty.

Robust Control Invariant Sets and Lyapunov-Based MPC for IPM Synchronous Motor Drives

This paper proposes a novel simplified model predictive control (MPC) scheme for interior permanent-magnet synchronous machines (PMSM) drive systems. The control problem is formulated in the $\alpha\beta$ stator flux space. The current–flux relation is eliminated from the MPC formulation and can be implemented as nonlinear map or an affine approximation without affecting the MPC complexity. The model is combined with the Lyapunov-based MPC concept. This scheme is shown to be asymptotically stable using the convex control set (CCS) input constraint with space vector modulation or pulse width modulation and asymptotically set stable using the finite control set (FCS) input constraint (with direct actuation). The stability properties are guaranteed for any cost function that is globally defined and any prediction horizon $N\geq 1$ . These results are validated using a software-in-the-loop (SiL) platform and an experimental test bench.

On finite-time and infinite-time cost improvement of economic model predictive control for nonlinear systems

A novel two-layer economic model predictive control (EMPC) structure that addresses provable finite-time and infinite-time closed-loop economic performance of nonlinear systems in closed-loop with EMPC is presented. In the upper layer, a Lyapunov-based EMPC (LEMPC) scheme is formulated with performance constraints by taking advantage of an auxiliary Lyapunov-based model predictive control (LMPC) problem solution formulated with a quadratic cost function. The lower layer LEMPC uses a shorter prediction horizon and smaller sampling period than the upper layer LEMPC and involves explicit performance-based constraints computed by the upper layer LEMPC. Thus, the two-layer architecture allows for dividing dynamic optimization and control tasks into two layers for a computationally manageable control scheme at the feedback control (lower) layer. A chemical process example is used to demonstrate the performance and stability properties of the two-layer LEMPC structure.

Distributed lyapunov‐based model predictive control with neighbor‐to‐neighbor communication

This work considers distributed predictive control of large‐scale nonlinear systems with neighbor‐to‐neighbor communication. It fulfills the gap between the existing centralized Lyapunov‐based model predictive control (LMPC) and the cooperative distributed LMPC and provides a balanced solution in terms of implementation complexity and achievable performance. This work focuses on a class of nonlinear systems with subsystems interacting with each other via their states. For each subsystem, an LMPC is designed based on the subsystem model and the LMPC only communicates with its neighbors. At a sampling time, a subsystem LMPC optimizes its future control input trajectory assuming that the states of its upstream neighbors remain the same as (or close to) their predicted state trajectories obtained at the previous sampling time. Both noniterative and iterative implementation algorithms are considered. The performance of the proposed designs is illustrated via a chemical process example. © 2014 American Institute of Chemical Engineers AIChE J 60: 4124–4133, 2014

Multiple Model-Based Fault Detection and Diagnosis for Nonlinear Model Predictive Fault-Tolerant Control

This paper presents a novel fault-tolerant control system for a class of nonlinear systems with input constraints. A fault detection and diagnosis (FDD) is designed based on multiple model method. The bank of extended Kalman filters is used to detect the predefined actuator fault and estimate the unknown parameters of actuator position. On the other hand, until the fault detection instance, because of the mismatch between the process and the model, the system states may exit the stability region. Therefore, delay on FDD decision may lead to performance degradation or even instability for some systems. The timely proposed FDD approach could preserve system stability. When the fault is detected, the proposed FDD information is used to correct the model of faulty system recursively and reconfigure the controller. On the other hand, because of many important factors of MPC such as consideration of input and state constraints in optimization problem, it can be used as a powerful controller in the event of fault occurrence. So, the reconfigurable controller is designed based on the Lyapunov-based model predictive control approach that provides an explicit characterization of the stability region. Finally, a practical chemical process example, is presented to illustrate the effectiveness of this idea. It is shown that this scheme can provide the system stability when a fault occurs.