Ali Mesbah

Stochastic nonlinear model predictive control with probabilistic constraints

Stochastic uncertainties are ubiquitous in complex dynamical systems and can lead to undesired variability of system outputs and, therefore, a notable degradation of closed-loop performance. This paper investigates model predictive control of nonlinear dynamical systems subject to probabilistic parametric uncertainties. A nonlinear model predictive control framework is presented for control of the probability distribution of system states while ensuring the satisfaction of constraints with some desired probability levels. To obtain a computationally tractable formulation for real control applications, polynomial chaos expansions are utilized to propagate the probabilistic parametric uncertainties through the system model. The paper considers individual probabilistic constraints, which are converted explicitly into convex second-order cone constraints for a general class of probability distributions. An algorithm is presented for receding horizon implementation of the finite-horizon stochastic optimal control problem. The capability of the stochastic model predictive control approach in terms of shaping the probability distribution of system states and fulfilling state constraints in a stochastic setting is demonstrated for optimal control of polymorphic transformation in batch crystallization.

Stochastic Model Predictive Control: An Overview and Perspectives for Future Research

Model predictive control (MPC) has demonstrated exceptional success for the high-performance control of complex systems. The conceptual simplicity of MPC as well as its ability to effectively cope with the complex dynamics of systems with multiple inputs and outputs, input and state/output constraints, and conflicting control objectives have made it an attractive multivariable constrained control approach. This article gives an overview of the main developments in the area of stochastic model predictive control (SMPC) in the past decade and provides the reader with an impression of the different SMPC algorithms and the key theoretical challenges in stochastic predictive control without undue mathematical complexity. The general formulation of a stochastic OCP is first presented, followed by an overview of SMPC approaches for linear and nonlinear systems. Suggestions of some avenues for future research in this rapidly evolving field concludes the article.

Active Fault Diagnosis for Nonlinear Systems with Probabilistic Uncertainties

Abstract Stringent requirements on safety and availability of high-performance systems necessitate reliable fault detection and isolation in the event of system failures. This paper investigates active fault diagnosis of nonlinear systems with probabilistic, time-invariant uncertainties of the parameters and initial conditions. A probabilistic model-based approach is presented for the design of auxiliary input signals enhancing fault diagnosability by separation of multiple nonlinear models pertaining to nominal and faulty system operations in the presence of the probabilistic uncertainties. To obtain a computationally tractable formulation, polynomial chaos expansions are used to propagate the probabilistic uncertainties through the system models. The input design problem is formulated in terms of a metric that characterizes the similarity of arbitrarily shaped distributions of the model outputs. An optimal input sequence is generated while considering hard input and state constraints. The simulation results for active diagnosis of multiple faults in a three-tank system indicate the capability of the presented approach to improve fault detectability and isolability under probabilistic uncertainties of the parameters and initial conditions.

Fast stochastic model predictive control of high-dimensional systems

Probabilistic uncertainties and constraints are ubiquitous in complex dynamical systems and can lead to severe closed-loop performance degradation. This paper presents a fast algorithm for stochastic model predictive control (SMPC) of high-dimensional stable linear systems with time-invariant probabilistic uncertainties in initial conditions and system parameters. Tools and concepts from polynomial chaos theory and quadratic dynamic matrix control inform the development of an input-output formulation for SMPC with output constraints. Generalized polynomial chaos theory is used to enable efficient uncertainty propagation through the high-dimensional system model. Galerkin projection is used to construct the polynomial chaos expansion for a general class of linear differential algebraic equations (DAEs), so that the SMPC algorithm is applicable to both regular and singular/descriptor systems. The fast SMPC approach is applied for control of an end-to-end continuous pharmaceutical manufacturing process with approximately 8000 states. The on-line computational cost of the proposed probabilistic input-output SMPC algorithm is independent of the state dimension and, therefore, alleviates the prohibitive computational costs of control of uncertain systems with large state dimension.

Stability for receding-horizon stochastic model predictive control

A stochastic model predictive control (SMPC) approach is presented for discrete-time linear systems with arbitrary time-invariant probabilistic uncertainties and additive Gaussian process noise. Closed-loop stability of the SMPC approach is established by appropriate selection of the cost function. Polynomial chaos is used for uncertainty propagation through system dynamics. The performance of the SMPC approach is demonstrated using the Van de Vusse reactions.

Kinetic Study of Acetone-Butanol-Ethanol Fermentation in Continuous Culture

Acetone-butanol-ethanol (ABE) fermentation by clostridia has shown promise for industrial-scale production of biobutanol. However, the continuous ABE fermentation suffers from low product yield, titer, and productivity. Systems analysis of the continuous ABE fermentation will offer insights into its metabolic pathway as well as into optimal fermentation design and operation. For the ABE fermentation in continuous Clostridium acetobutylicum culture, this paper presents a kinetic model that includes the effects of key metabolic intermediates and enzymes as well as culture pH, product inhibition, and glucose inhibition. The kinetic model is used for elucidating the behavior of the ABE fermentation under the conditions that are most relevant to continuous cultures. To this end, dynamic sensitivity analysis is performed to systematically investigate the effects of culture conditions, reaction kinetics, and enzymes on the dynamics of the ABE production pathway. The analysis provides guidance for future metabolic engineering and fermentation optimization studies.

Least costly closed-loop performance diagnosis and plant re-identification

The inherent time-varying nature of dynamics in chemical processes often limits the lifetime performance of model-based control systems, as the plant and disturbance dynamics change over time. A critical step in the maintenance of model-based controllers is distinguishing control-relevant plant changes from variations in disturbance characteristics. In this paper, prediction error identification is used to evaluate a hypothesis test that detects if the performance drop arises from control-relevant plant changes. The decision rule is assessed by verifying whether an identified model of the true plant lies outside the set of all plant models that lead to adequate closed-loop performance. A unified experiment design framework is presented in the least costly context (i.e., least intrusion of nominal plant operation) to address the problem of input signal design for performance diagnosis and plant re-identification when the performance drop is due to plant changes. The application of the presented performance diagnosis approach to a (nonlinear) chemical reactor demonstrates the effectiveness of the approach in detecting the cause of an observed closed-loop performance drop based on the designed least costly diagnosis experiment.

Optimal Experimental Design for Probabilistic Model Discrimination Using Polynomial Chaos

Abstract Building dynamic models is important in many applications including model-based design, optimization, and control. When multiple hypothesized models have predictions that are consistent with the measurements, experimental design is used to discriminate between the models. This task is particularly challenging for nonlinear systems subject to uncertainties. An optimal experimental design method for model discrimination for polynomial uncertain systems is presented that can be used to discriminate models based on dissimilarity of the probability densities of the model outputs. Generalized polynomial chaos theory in conjunction with Galerkin projection is used to derive an extended set of ordinary differential equations. Simulation of the extended system enables prediction of the propagation of probabilistic uncertainties associated with the model parameters and initial conditions, and to obtain the output probability densities. The simulation of the hypothetical models is embedded in a nonlinear optimization problem to determine an optimal input sequence that maximizes model dissimilarity. The experimental design method is demonstrated using a numerical example.

Receding-horizon Stochastic Model Predictive Control with Hard Input Constraints and Joint State Chance Constraints

ABSTRACT This article investigates model predictive control (MPC) of linear systems subject to arbitrary (possibly unbounded) stochastic disturbances. An MPC approach is presented to account for hard input constraints and joint state chance constraints in the presence of unbounded additive disturbances. The Cantelli–Chebyshev inequality is used in combination with risk allocation to obtain computationally tractable but accurate surrogates for the joint state chance constraints when only the mean and variance of the arbitrary disturbance distributions are known. An algorithm is presented for determining the optimal feedback gain and optimal risk allocation by iteratively solving a series of convex programs. The proposed stochastic MPC approach is demonstrated on a continuous acetone–butanol–ethanol fermentation process, which is used in the production of biofuels.This article investigates model predictive control (MPC) of linear systems subject to arbitrary (possibly unbounded) stochastic disturbances. An MPC approach is presented to account for hard input ...

Model predictive control of thermal effects of an atmospheric pressure plasma jet for biomedical applications

This paper investigates the application of model predictive control (MPC) for regulating the thermal effects of an atmospheric pressure plasma jet (APPJ). The control objective is to deliver a predetermined thermal dosage to a target surface without inducing any thermal damage. To this end, a nonlinear thermal model is developed for the APPJ under study, and a MPC strategy is designed through repeated linearization of the nonlinear model along the operating trajectory. The performance of the MPC strategy is demonstrated in simulations.