Genetic algorithms for optimal control of beer fermentation

This paper uses genetic algorithms to optimise the mathematical model of a beer fermentation process that operates in batch mode. The optimisation is based in adjusting the temperature profile of the mixture during a fixed period of time in order to reach the required ethanol levels but considering certain operational and quality restrictions.

Optimal control of nonlinear systems represented by differential algebraic equations

An iterative procedure is described for solving nonlinear optimal control problems subject to differential algebraic equations. The procedure iterates on an integrated modified simplified model based problem with parameter updating in such a manner that the correct solution of the original nonlinear problem is achieved.

Relationship between åström control and the kalman linear regulator — Caines revisited

The relationship between minimum variance and minimum expected quadratic loss feedback controllers for linear univariate discrete-time stochastic systems is reviewed by taking the approach used by Caines. It is shown how the two methods can be regarded as providing identical control actions as long as a noise-free measurement state-space model is employed.

Optimal kinematic control of an autonomous underwater vehicle

This note investigates the motion control of an autonomous underwater vehicle (AUV). The AUV is modeled as a nonholonomic system as any lateral motion of a conventional, slender AUV is quickly damped out. The problem is formulated as an optimal kinematic control problem on the Euclidean Group of Motions SE(3), where the cost function to be minimized is equal to the integral of a quadratic function of the velocity components. An application of the Maximum Principle to this optimal control problem yields the appropriate Hamiltonian and the corresponding vector fields give the necessary conditions for optimality. For a special case of the cost function, the necessary conditions for optimality can be characterized more easily and we proceed to investigate its solutions. Finally, it is shown that a particular set of optimal motions trace helical paths. Throughout this note we highlight a particular case where the quadratic cost function is weighted in such a way that it equates to the Lagrangian (kinetic energy) of the AUV. For this case, the regular extremal curves are constrained to equate to the AUV's components of momentum and the resulting vector fields are the d'Alembert-Lagrange equations in Hamiltonian form.

Novel developments in process optimisation using predictive control

In industrial practice, constrained steady state optimisation and predictive control are separate, albeit closely related functions within the control hierarchy. This paper presents a method which integrates predictive control with on-line optimisation with economic objectives. A receding horizon optimal control problem is formulated using linear state space models. This optimal control problem is very similar to the one presented in many predictive control formulations, but the main difference is that it includes in its formulation a general steady state objective depending on the magnitudes of manipulated and measured output variables. This steady state objective may include the standard quadratic regulatory objective, together with economic objectives which are often linear. Assuming that the system settles to a steady state operating point under receding horizon control, conditions are given for the satisfaction of the necessary optimality conditions of the steady-state optimisation problem. The method is based on adaptive linear state space models, which are obtained by using on-line identification techniques. The use of model adaptation is justified from a theoretical standpoint and its beneficial effects are shown in simulations. The method is tested with simulations of an industrial distillation column and a system of chemical reactors.

A new approach for the solution of the optimal set-point tracking problem for nonlinear systems

In this paper, a discrete time dynamic integrated system optimisation and parameter estimation algorithm is applied to the solution of the nonlinear tracking optimal control problem. A version of the algorithm with a linear-quadratic model-based problem is developed and implemented in software. The algorithm implemented is tested with simulation examples.

Optimal growth strategies when mortality and production rates are size-dependent

Pontryagin's maximum principle from optimal control theory is used to find the optimal allocation of energy between growth and reproduction when lifespan may be finite and the trade-off between growth and reproduction is linear. Analyses of the optimal allocation problem to date have generally yielded bang-bang solutions, i.e. determinate growth: life-histories in which growth is followed by reproduction, with no intermediate phase of simultaneous reproduction and growth. Here we show that an intermediate strategy (indeterminate growth) can be selected for if the rates of production and mortality either both increase or both decrease with increasing body size, this arises as a singular solution to the problem. Our conclusion is that indeterminate growth is optimal in more cases than was previously realized. The relevance of our results to natural situations is discussed.