Romain S.C. Lambert

Combined model approximation techniques and multiparametric programming for explicit nonlinear model predictive control

Abstract This work presents a methodology to derive explicit multiparametric controllers for nonlinear systems, combining model approximation techniques and multiparametric model predictive control (mp-MPC) algorithms. Particular emphasis is given to an approach that applies a nonlinear model reduction technique, based on balancing of empirical gramians, which generates a reduced order model suitable for nonlinear mp-MPC algorithms. This approach is compared with a recently proposed method that uses a meta-modelling based model approximation technique which can be directly combined with standard multiparametric programming algorithms. The methodology is illustrated for two nonlinear models, of a distillation column and a train of CSTRs, respectively.

A Monte-Carlo based model approximation technique for linear model predictive control of nonlinear systems

In this paper we present a model approximation technique based on N-step-ahead affine representations obtained via Monte-Carlo integrations. The approach enables simultaneous linearization and model order reduction of nonlinear systems in the original state space thus allowing the application of linear MPC algorithms to nonlinear systems. The methodology is detailed through its application to benchmark model examples.

Simultaneous Multi-Parametric Model Predictive Control and State Estimation with Application to Distillation Column and Intravenous Anaesthesia

Abstract The objective of this paper is to implement simultaneous multi-parametric model predictive control (mp-MPC) and moving horizon estimation (MHE). The approach is tested on two different processes: the control of a high dimensional chemical process, the distillation column and the regulation of the depth of anaesthesia (DOA). Due to the high dimensionality of the distillation column, model order reduction techniques were used together with the simultaneous mp-MPC and MHE. The methods show good performances and a good behavior in dealing with the effect of noise and the presence of constraints.

Simultaneous reduced order multi-parametric moving horizon estimation and model based control

In this paper we apply model order reductions techniques to efficiently implement simultaneous model predictive control and moving horizon estimation for high dimensional chemical processes. Two model approximation schemes that both combine order reduction and linearization are employed and compared. The approach is demonstrated on a benchmark distillation column example model.

A combined estimation and multi-parametric model predictive control approach for intravenous anaesthesia

This paper describes a strategy for the control of intravenous depth of anaesthesia (DOA). Based on a mathematical model of the system, global sensitivity analysis is first presented to determine the relative influence of the uncertain pharmacokinetic and pharmacodynamic parameters and variables. Then estimation techniques are applied for the key parameters that cannot be measured directly, combined with a multi-parametric/explicit model predictive control strategy. The two estimation strategies: a Kalman filter and multi-parametric moving horizon estimation are employed and tested on a set of twelve patients.

Global sensitivity analysis using sparse high dimensional model representations generated by the group method of data handling

In this paper, the parameter selection capabilities of the group method of data handling (GMDH) as an inductive self-organizing modelling method are used to construct sparse random sampling high dimensional model representations (RS-HDMR), from which the Sobol’s first and second order global sensitivity indices can be derived. The proposed method is capable of dealing with high-dimensional problems without the prior use of a screening technique and can perform with a relatively limited number of function evaluations, even in the case of under-determined modelling problems. Four classical benchmark test functions are used for the evaluation of the proposed technique.

A novel approximation technique for online and multi-parametric model predictive control

Abstract Multi-parametric model predictive control has been widely recognized in the control literature. The objective of explicit MPC is to solve the constrained optimal control problem and derive the control variables as explicit functions of the states. Explicit MPC is particularly relevant for systems in which classical real time MPC implementation is impractical; In effect, the computations to derive the optimal control moves are performed offline. A framework for the development of such multiparametric/explicit controllers has been presented in [1]. The framework emphasizes the need for model approximation as a key challenge for a wider use of multiparametric/explicit MPC. We propose an approach that uses an interpolation method employed in a receding horizon fashion as a transient system identification technique to derive linear explicit algebraic expressions of the dynamics of the system under the form of linear expressions in the state parameter and controls. A major advantage of the approach is the availability of an a priori global error bound for the model mismatch due to the approximation. Linear dependency on the state parameters and controls enables to recast nonlinear and non convex MPC problems, into mp-QP optimization problems. The approach is demonstrated on a nonlinear benchmark model example of a 30 stages distillation column.

Combined nonlinear model reduction and multiparametric nonlinear programming for nonlinear model predictive control

Abstract This work presents a methodology which combines nonlinear model reduction techniques with recent advances in multiparametric nonlinear programming (mp-NLP) to derive explicit multiparametric controllers for nonlinear MPC (NMPC). Nonlinear model order reduction (NMOR) techniques based on empirical gramians are used for the model reduction step. The approach is illustrated on a 32 states distillation column model example.