Michael Nikolaou

A hybrid approach to global optimization using a clustering algorithm in a genetic search framework

Abstract The concern of this work is global optimization using genetic algorithms (GAs). In this work we propose a synergy between the cluster analysis technique, popular in classical stochastic global optimization, and the GA to accomplish global optimization. This synergy minimizes redundant searches around local optima and enhances the capability of the GA to explore new areas in the search space. The proposed methodology demonstrates superior performance when compared with the simple GA on benchmark cases. We also report our solution of the optimal pumps configuration synthesis problem.

Effect of on-line optimization techniques on model predictive control and identification (MPCI)

Model predictive control and identification (MPCI) is an adaptive MPC scheme that employs the persistent excitation condition to generate non-convex constraints on process inputs, in addition to conventional constraints of on-line optimization of MPC. This results in a non-convex problem, which has to be solved at each time instant k. In this work we rigorously show that a locally optimal solution of the above problem can be obtained by the successive semidefinite programming algorithm. We then develop a deterministic branch-and-bound approach, to obtain the global minimum of the MPCI optimization problem. Simulation results are presented to demonstrate the applicability of the proposed MPCI algorithms to small-scale systems.

NONLINEARITY QUANTIFICATION AND ITS APPLICATION TO NONLINEAR SYSTEM IDENTIFICATION

Abstract In a series of previous works (Nikolaou, 1993) we introduced an inner product and a corresponding 2-norm for discrete-time nonlinear dynamic systems. Unlike induced norms of nonlinear systems, which are difficult to compute (albeit extremely useful), the 2-norm mentioned above is straightforward to compute, through Monte Carlo calculations with either experimental or simulated data. Loosely speaking, the 2-norm captures the average effect of a class of inputs on the output of a dynamic system. In this presentation we will give a brief introduction to this 2-norm, based on our previous results, and will discuss our latest work and applications on this subject. In particular, we will address the following points: (a) How is the nonlinearity of a dynamic system quantified by the 2-norm? (b) How adequate is a linear model for the representation of a nonlinear system? (c) What nonlinear model can be used for the representation of a nonlinear system for which a linear model is inadequate? An important ...

Solution of the self-consistent field model for polymer adsorption by genetic algorithms

A Genetic Algorithm (GA) is used to solve the equations of the self-consistent field model for polymer adsorption on a surface. The solution is cast as an optimization problem and a GA is used as a function optimizer to solve this problem. Comparison is made with a traditional gradient-based approach. It was found that convergence properties will improve if the GA is cascaded with a gradient search method. This cascaded search method guarantees convergence from any random initial population of guesses and does not need insight into the physics of the problem.

Constrained model predictive control with simultaneous identification using wavelets

Abstract Model Predictive Control (MPC) often requires that a new process model be developed from data collected while the process remains under feedback control. How can a good model be obtained for a process under constrained MPC, without excessive perturbation of the process? We propose a novel approach, model predictive control and identification (MPCI), that relies on augmenting the standard on-line MPC optimization with a series of persistent excitation (PE) constraints that current and future process inputs must satisfy over a finite horizon. For linear processes, the resulting on-line optimization problem is solved by solving a series of semi-definite programming (SP) problems, for which efficient numerical methods with guaranteed convergence exist. The addition of the PE constraint to standard MPC paves the way for a number of different MPCI variants. A variant of MPCI involving time-frequency process identification with wavelets is proposed in the paper.

Robust Control of Batch Processes

The computation of the optimal operating profile for batch processes through the maximum principle depends on the model involved. The real process, however may deviate from the assumed model due to external disturbances or parameter variations. In this paper we examine the effect of the above on the value of the objective function, when the nominal optimal policy is applied, as well as the effect on the optimum of the objective function. We present relations between quantities of the perturbed and the nominal problems and demonstrate their use through a number of examples.

RECURRENT NEURAL NETWORKS IN DECOUPLING CONTROL OF MULTIVARIABLE NONLINEAR SYSTEMS

In this work we focus on the synergy between modeling with RNNs, and nonlinear controller design for decoupling control. The thesis of the paper is that recurrent neural networks (RNNs) can be conveniently used in an integrated black-box modeling and controller design methodology for decoupling control of multivariable nonlinear systems. A simulation example on a multivariable continuous-stirred-tank-reactor (CSTR) is provided to elucidate related issues. The effects of modeling uncertainty and state reconstruction on decoupling performance are specifically discussed.

Analysis and Synthesis Methods for Robust Model Predictive Control

In this article we present a summary of our latest work on analysis and synthesis methods for robust constrained model predictive controllers. Processes modeled by multivariable linear time-invariant models as well as second-order Volterra series models are considered. Modeling uncertainty is characterized as upper and lower bounds on model parameters. Sufficient conditions for robust closed-loop stability with zero offset are presented for the kinds of processes mentioned above. In addition, robust performance bounds are discussed. Based on the robust stability and performance results, a tuning methodology for robust constrained model predictive control is developed. That methodology is elucidated through examples of linear and nonlinear model predictive control of a number of chemical processes.

Stability Aspects of Exact Linearization Methods: A Hybrid Approach

In this paper, we examine from an input-output viewpoint, the feedback exact-linearization of nonlinear systems of the form x = f(x) + g(x)u, y = h(x). We show that exact-linearization through any kind of feedback cannot eliminate, but only relocate nonlinearity within the exact-linearizing feedback loop. In this work we establish that for a stable nonlinear system, stability of the systems inverse is sufficient for stability of the exact-linearizing feedback loop, regardless of whether state or output, static or dynamic feedback is used. We also demonstrate that stability of the systems inverse is sufficient but not necessary for stability of the exact-linearizing state-feedback loop. Finally, using an inner-outer type factorization of the original system, we provide necessary and sufficient conditions for stability of such a loop in a presence of unstable zero dynamics.

SENSITIVITY ANALYSIS OF OPTIMAL CONTROL POLICIES FOR BATCH PROCESSES

The computation of optimal control policies for batch processes, critically depends on the process model employed. The real process may deviate from the assumed model due to external signal or model parameter variations. In this paper we examine the effects of these variations on (a) the value of the objective function, when the nominal optimal policy is applied (b) the optimum value of the objective function. We present quantitative relations between the perturbed and the nominal problems and demonstrate their use through a number of examples.