Output Feedback Nonlinear Model Predictive Control Research Articles

A Synergistic Approach to Robust Output Feedback Control: Tube-based Multi-stage NMPC

Plant-model mismatch and estimation errors are critical issues in the practical implementation of Nonlinear Model Predictive Control (NMPC). To address these challenges, we formulate a robust output feedback NMPC scheme that is real-time implementable and provides robust constraint satisfaction in the presence of parametric and additive uncertainties, and estimation errors. The robustness is achieved by combining the tube-based and the multi-stage NMPC approaches. Two controllers are used in the proposed framework: a primary controller with tightened constraints that optimizes a given objective and an ancillary controller that tracks the trajectories provided by the primary controller. Unlike standard tube-based NMPC, the primary controller predicts different state trajectories for different realizations of the most important uncertainties using the multi-stage NMPC framework. The synergy between the two approaches leads to a better trade-off between optimality and complexity. The advantages of the proposed approach are demonstrated for an industrial-scale fed-batch polymerization reactor example.

Adaptive Multi-stage Output Feedback NMPC using the Extended Kalman Filter for time varying uncertainties applied to a CSTR

Nonlinear Model Predictive control (NMPC) is one of the advanced control strategies for multi-dimensional nonlinear systems with constraints. With uncertainties present in the model, robust NMPC strategies are proposed in order to counteract the effects of the uncertainties and have a safe operation of the plant.Multi-stage NMPC offers a non-conservative alternative as it models the feedback information explicitly in the problem formulation by means of a scenario tree. In order to be robust to both the model uncertainties and the estimation error, we formulate a multi-stage output feedback NMPC strategy by creating additional scenarios by sampling the innovations and use observer equations to predict the future evolution of the plant. Since the observers such as the Extended Kalman Filter (EKF) can be used to estimate the uncertain parameters along with the states, the output feedback NMPC strategy is improved to be adaptive with respect to time varying uncertain parameters and the performance of the controller is improved. We demonstrate the advantages of the proposed adaptive scheme using a nonlinear Continuous Stirred Tank Reactor (CSTR) example.

Robust output feedback NMPC with guaranteed constraint satisfaction

Nonlinear Model Predictive Control (NMPC) employs a plant model to compute a sequence of optimal control inputs for a finite horizon. As, in reality, there always exists a plant-model mismatch and not all states of the plant can be measured, the NMPC scheme must be robust to plant uncertainties and to estimation errors. Different robust NMPC strategies have been proposed to deal with these uncertainties. Among them, a multi-stage NMPC, which is based upon a scenario tree of future plant evolutions, is less conservative compared to worst-case open-loop approaches because the presence of feedback at future sampling instants is explicitly considered. In multi-stage output feedback NMPC, additional scenarios are created by sampling the innovations that are used to estimate the future states of the plant along the scenario tree. In this paper, we refine our previously published approach to include state estimation errors. Moreover we extend the scheme to guarantee robust constraint satisfaction by calculating reachable sets using Taylor models. The method is demonstrated for a nonlinear chemical process example.

Economic Multi-stage Output Feedback NMPC using the Unscented Kalman Filter

Nonlinear Model predictive control (NMPC) is a popular control strategy for highly nonlinear chemical processes. The ability to handle safety and environmental constraints along with the use of an economic objective makes NMPC highly appealing to industries. The performance of NMPC depends strongly on the accuracy of the model. In reality, there always are plant-model mismatch and state estimation errors. Hence the NMPC controller must be robust to uncertainties in the model as well as against estimation errors. Among the several approaches presented in the literature, the scenario-tree based multi-stage NMPC approach is a non-conservative and efficient formulation. In this approach, the evolutions of the plant for different realizations of the uncertainties are considered as different scenarios and the optimization problem is formulated as a multi-stage stochastic programming problem with recourse. In this work, we consider multi-stage output feedback NMPC using the Unscented Kalman Filter (UKF) where the nonlinearities are represented using deterministically chosen sigma points for state estimation. In the control problem, we explicitly consider the UKF estimation equations to predict the future evolution of the system. The proposed approach is illustrated by simulation results of fed-batch chemical reactor with an economic cost function.

Robust stability of nonlinear model predictive control based on extended Kalman filter

This work deals with state estimation and process control for nonlinear systems, especially when nonlinear model predictive control (NMPC) is integrated with extended Kalman filter (EKF) as the state estimator. In particular, we focus on the robust stability of NMPC and EKF in the presence of plant–model mismatch. The convergence property of the estimation error from the EKF in the presence of non-vanishing perturbations is established based on our previous work [1]. In addition, a so-called one way interaction is shown that the EKF error is not influenced by control action from the NMPC. Hence, the EKF analysis is still valid in the output-feedback NMPC framework, even though there is no separation principle for general nonlinear systems. With this result, we study the robust stability of the output-feedback NMPC under the impact of the estimation error. It turns out the output-feedback NMPC with EKF is Input-to-State practical Stable (ISpS). Finally, two offset-free strategies of output-feedback NMPC are presented and illustrated through a simulation example.

Explicit output-feedback nonlinear predictive control based on black-box models

Nonlinear model predictive control (NMPC) algorithms are based on various nonlinear models. A number of on-line optimization approaches for output-feedback NMPC based on various black-box models can be found in the literature. However, NMPC involving on-line optimization is computationally very demanding. On the other hand, an explicit solution to the NMPC problem would allow efficient on-line computations as well as verifiability of the implementation. This paper applies an approximate multi-parametric nonlinear programming approach to explicitly solve output-feedback NMPC problems for constrained nonlinear systems described by black-box models. In particular, neural network models are used and the optimal regulation problem is considered. A dual-mode control strategy is employed in order to achieve an offset-free closed-loop response in the presence of bounded disturbances and/or model errors. The approach is applied to design an explicit NMPC for regulation of a pH maintaining system. The verification of the NMPC controller performance is based on simulation experiments.

Dual-mode Explicit Output-feedback Predictive Control Based on Neural Network Models

This paper applies an approximate multi-parametric Nonlinear Programming approach to explicitly solve output-feedback Nonlinear Model Predictive Control (NMPC) problems for constrained nonlinear systems described by black-box models. In particular, neural network models are used and the optimal regulation problem is considered. A dual-mode control strategy is employed in order to achieve an offset-free closed-loop response in the presence of bounded disturbances and/or model errors. The approach is applied to design an explicit NMPC for regulation of a pH maintaining system.

A note on stability, robustness and performance of output feedback nonlinear model predictive control

In recent years, nonlinear model predictive control (NMPC) schemes have been derived that guarantee stability of the closed loop under the assumption of full state information. However, only limited advances have been made with respect to output feedback in the framework of nonlinear predictive control. This paper combines stabilizing instantaneous state feedback NMPC schemes with high-gain observers to achieve output feedback stabilization. For a uniformly observable MIMO system class it is shown that the resulting closed loop is asymptotically stable. Furthermore, the output feedback NMPC scheme recovers the performance of the state feedback in the sense that the region of attraction and the trajectories of the state feedback scheme can be recovered to any degree of accuracy for large enough observer gains, thus leading to semi-regional results. Additionally, it is shown that the output feedback controller is robust with respect to static sector bounded nonlinear input uncertainties.

Output Feedback Stabilization with Nonlinear Predictive Control: Asymptotic properties

State space based nonlinear model predictive control (NMPC) needs the state for the prediction of the system behaviour. Unfortunately, for most applications, not all states are directly measurable. To recover the unmeasured states, typically a stable state observer is used. However, this implies that the stability of the closed-loop should be examined carefully, since no general nonlinear separation principle exists. Recently semi-global practical stability results for output feedback NMPC using a high-gain observer for state estimation have been established. One drawback of this result is that (in general) the observer gain must be increased, if the desired set the state should converge to is made smaller. We show that under slightly stronger assumptions, not only practical stability, but also convergence of the system states and observer error to the origin for a sufficiently large but bounded observer gain can be achieved.

State and Output Feedback Nonlinear Model Predictive Control: An Overview

The purpose of this paper is twofold. In the first part, we give a review on the current state of nonlinear model predictive control (NMPC). After a brief presentation of the basic principle of predictive control we outline some of the theoretical, computational, and implemen-tational aspects of this control strategy. Most of the theoretical developments in the area of NMPC are based on the assumption that the full state is available for measurement, an assumption that does not hold in the typical practical case. Thus, in the second part of this paper we focus on the output feedback problem in NMPC. After a brief overview on existing output feedback NMPC approaches we derive conditions that guarantee stability of the closed-loop if an NMPC state feedback controller is used together with a full state observer for the recovery of the system state.