Alexandra Grancharova

Computational aspects of approximate explicit nonlinear model predictive control

It has recently been shown that the feedback solution to linear and quadratic constrained Model Predictive Control (MPC) problems has an explicit representation as a piecewise linear (PWL) state feedback. For nonlinear MPC the prospects of explicit solutions are even higher than for linear MPC, since the benefits of computational efficiency and verifiability are even more important. Preliminary studies on approximate explicit PWL solutions of convex nonlinear MPC problems, based on multi-parametric Nonlinear Programming (mp-NLP) ideas show that sub-optimal PWL controllers of practical complexity can indeed be computed off-line. However, for non-convex problems there is a need to investigate practical computational methods that not necessarily lead to guaranteed properties, but when combined with verification and analysis methods will give a practical tool for development and implementation of explicit NMPC. The present paper focuses on the development of such methods. As a case study, the application of the developed approaches to compressor surge control is considered.

APPROXIMATE EXPLICIT MODEL PREDICTIVE CONTROL IMPLEMENTED VIA ORTHOGONAL SEARCH TREE PARTITIONING

Solutions to constrained linear model predictive control (MPC) problems can be pre-computed off-line in an explicit form as a piecewise linear (PWL) state feedback defined on a polyhedral partitioning of the state space. Even though real-time optimization is avoided, implementation of the PWL state feedback may still require a significant amount of computations. We suggest an algorithm that will determine an approximate explicit PWL state feedback solution by imposing an orthogonal search tree structure on the partition. This leads to efficient real-time computations and admits implementation at high sampling frequencies in embedded systems with inexpensive processors and low software complexity. The algorithm yields guarantees on the cost function error and constraint violations.

Explicit model predictive control of gas–liquid separation plant via orthogonal search tree partitioning

Exact or approximate solutions to constrained linear model predictive control problems can be pre-computed off-line in an explicit form as a piecewise linear state feedback defined on a polyhedral partition of the state space. This leads to efficient real-time computations and admits implementation at high sampling frequencies in real-time systems with high reliability and low software complexity. In this paper, an explicit model predictive controller for a gas-liquid separation plant is designed and experimentally tested.

Approximate explicit model predictive control incorporating heuristics

Explicit piecewise linear state feedback solutions to the constrained linear model predictive control problem have recently been characterized and computed numerically using multiparametric quadratic programming. The piecewise linear state feedback is defined on a polyhedral partitioning of the state space, which may be quite complex. Here we suggest an approximate multi-parametric quadratic programming approach, which has the advantages that the partition is structured as a binary search tree. This leads to real-time computation of the piecewise linear state feedback with a computational complexity that is logarithmic with respect to the number of regions in the partition. The algorithm is based on heuristic rules that are used to partition the state space and estimate the approximation error.

Survey of explicit approaches to constrained optimal control

This chapter presents a review of the explicit approaches to optimal control. It is organized as follows. Section 1 gives a summary of the main results of the optimal control theory. Section 2 presents briefly the methods for unconstrained optimal state feedback control of linear systems. Sections 3, 4 and 5 consider in details the explicit methods for constrained linear quadratic regulation (LQR) together with several examples. The main motivation behind the explicit solution is that it avoids the need for real-time optimization, and thus allows implementation at high sampling frequencies in real-time systems with high reliability and low software complexity. These sections include formulation of the constrained LQR problem, summary of the implicit approaches, basics of the model predictive control (MPC), description of the exact and the approximate approaches to explicit solution of MPC problems and the experimental evaluation of explicit MPC controller performance for laboratory gas-liquid separation plant.

EXPLICIT MIN-MAX MODEL PREDICTIVE CONTROL OF CONSTRAINED NONLINEAR SYSTEMS WITH MODEL UNCERTAINTY

Abstract This paper presents an approximate multi-parametric nonlinear programming approach to explicit solution of constrained nonlinear model predictive control (MPC) problems in the presence of model uncertainty. The case of time-invariant parameter uncertainty is considered. The explicit MPC controller is based on an orthogonal search tree structure of the state space partition and is designed by solving a min-max optimization problem. It is robust in the sense that all constraints are satisfied for all possible values of the uncertain parameters. The approach is applied to design an explicit min-max MPC controller for a continuous stirred tank reactor, where the heat transfer coefficient is an uncertain parameter.

Design of reduced dimension explicit model predictive controller for a gas-liquid separation plant

Exact or approximate solutions to constrained linear model predictive control (MPC) problems can be precomputed offline in an explicit form as a piecewise linear state feedback defined on a polyhedral partition of the state phase. However, the complexity of the polyhedral partition often increases rapidly with the dimension of the state vector, and the number of constraints. Recently, several approaches for reducing the dimension of the explicit solution to constraint MPC problems have been developed. This paper considers the design of a reduced dimension explicit model predictive controller for a gas-liquid separation plant.

Reduced Dimension Approach to Approximate Explicit Model Predictive Control

Abstract Exact or approximate solutions to constrained linear model predictive control (MPC) problems can be pre-computed off-line in an explicit form as a piecewise linear state feedback defined on a polyhedral partition of the state space. However, the complexity of the polyhedral partition often increases rapidly with the dimension of the state vector, and the number of constraints. This paper presents an approach for reducing the dimension of the approximate explicit solution to linear constraint MPC problems.

General strategy for decision support in integrated process synthesis, design and control

Publisher Summary This chapter discusses the general strategy for decision support in integrated-process synthesis, design, and control. The strategy is represented by four stages: (i) determination of the ordered set of the satisfactory alternatives of process flowsheets, (ii) determination of the ordered set of satisfactory alternatives of process design, (iii) determination of the ordered set of satisfactory alternatives of process control system, and (iv) determination of the best combination of process flowsheet, process design, and process control. There are three alternative flowsheets for the production of Triple Super Phosphate (TSP): (1) Den process for the production of granular TSP, (2) Ex-den direct granulation of TSP––the flowsheet of this alternative is similar to that of alternative one except that the stage of storage curing of TSP is excluded––and (3) Slurry-type process for the production of granular TSP.