José Luis Pitarch

Closed-Form Estimates of the Domain of Attraction for Nonlinear Systems via Fuzzy-Polynomial Models

In this paper, the domain of attraction of the origin of a nonlinear system is estimated in closed form via level sets with polynomial boundaries, iteratively computed. In particular, the domain of attraction is expanded from a previous estimate, such as a classical Lyapunov level set. With the use of fuzzy-polynomial models, the domain of attraction analysis can be carried out via sum of squares optimization and an iterative algorithm. The result is a function that bounds the domain of attraction, free from the usual restriction of being positive and decrescent in all the interior of its level sets.

Fuzzy Polynomial observers

Abstract This paper discusses some initial lines on how to design observers for nonlinear systems based on the polynomial Takagi-Sugeno (Taylor series) representation as fuzzy systems. If state and error (initially) lie in some operation regions, then, some bounds on the error can be proved.

Distributed Saturated Control for a Class of Semilinear PDE Systems: An SOS Approach

This paper presents a systematic approach to deal with the saturated control of a class of distributed parameter systems that can be modeled by the first-order hyperbolic partial differential equations (PDE). The approach extends (also improves over) the existing fuzzy Takagi–Sugeno (TS) state feedback designs for such systems by applying the concepts of the polynomial sum-of-squares (SOS) techniques. First, a fuzzy-polynomial model via Taylor series is used to model the semilinear hyperbolic PDE system. Second, the closed-loop exponential stability of the fuzzy-PDE system is studied through the Lyapunov theory. This allows us to derive a design methodology in which a more complex fuzzy state-feedback control is designed in terms of a set of SOS constraints, able to be numerically computed via semidefinite programming. Finally, the proposed approach is tested in simulation with the standard example of a nonisothermal plug-flow reactor.

Modifier Adaptation methodology based on transient and static measurements for RTO to cope with structural uncertainty

Abstract Optimal process operation is carried out by a Real-Time Optimization (RTO) layer which is not always able to achieve its targets due to the presence of plant-model mismatch. To overcome this issue, the economic optimization problem solved in the RTO is changed following the Modifier Adaptation methodology (MA), which uses plant measurements to find a point that satisfies the necessary optimality conditions (NCO) of an uncertain process. MA proceeds by iteratively adjusting the optimization problem with first and zeroth order corrections, calculated from steady-state information at each RTO execution. This implies a long convergence time. This paper presents a new method based on a recursive identification algorithm to estimate process gradients from transient measurements to speed up the convergence of MA. The proposed approach is implemented in a simulated depropanizer column that incorporates a simplified model in the RTO, reducing by 8 the convergence time compared with traditional MA.

Optimisation of transient and ultimate inescapable sets with polynomial boundaries for nonlinear systems

This paper addresses the problem of bounding the trajectories of nonlinear systems (transient and ultimate bounds) from initial conditions in given sets, when subject to possibly nonvanishing disturbances constrained by some finite-interval integral bounds, with a suitable controller. The so-called robustly-inescapable sets are determined from such initial conditions and disturbance bounds. In order to get numerical results, the approach considers embedding the nonlinear dynamics in a convex combination of polynomials, and solving sum-of-squares (SOS) problems on them, optimising some inescapable-set size parameters. Determination of approximate (locally) optimal solutions usually requires an iterative evaluation of SOS problems, because of products of decision variables.

Estimating domains of attraction of fuzzy polynomial systems

Most fuzzy control papers check LMI or SOS stability conditions in order to prove local stability results of nonlinear systems (Takagi-Sugeno fuzzy models or polynomial fuzzy models via Sector Nonlinearity approach). In case of having into account the shape of the membership functions in a particular region of interest, less conservative stability and stabilization conditions can be easily set up. In this paper local polynomial stability results are explored in order to obtain the largest basin of attraction for a particular system.

Robust multi-objective scheduling in an evaporation network

Considering uncertainty in continuous production processes is key to compute short-time optimal schedules which can be trusted in practice. This paper proposes a two-step stochastic approach to the robust scheduling of several evaporation plants. This approach considers the possibility of reacting in the future once the uncertainty materializes. Each evaporator has different features (capacity, equipment, etc.) and the individual performance is affected by external factors and fouling effects. Moreover, a multi-objective analysis has been carried out to provide a decision support for the operator who must take the concrete decisions about load allocation and cleaning tasks along a time horizon. The problem has been solved by discretizing the time horizon and adapting the general-precedence method to deal with an unknown number of tasks. The nonlinear behavior of each plant is approximated by surrogate linear models obtained experimentally, providing thus solutions in acceptable time.

Robust integrated production-maintenance scheduling for an evaporation network

Abstract This work aims to reduce the global resource consumption in an industrial evaporation network by better tasks management and coordination. The network works in continuous, processing some products in several evaporation plants, so optimal load allocation and product-plant assignment problems appear. The plants have different features (capacity, equipment, etc.) and their performance is affected by fouling inside the heat exchangers and external factors. Hereby, the optimizer has to decide when maintenance operations have to be triggered. Therefore, a mixed production/maintenance scheduling problem arises. The plant behavior is approximated by surrogate linear models obtained experimentally, allowing thus the use of mixed-integer linear optimization routines to obtain solutions in acceptable time. Furthermore, uncertainty in the weather forecast and in the production plan is also considered via a two-stage stochastic programming approach. Finally, a trade-off analysis between other objectives of interest is given to support the decision maker.

Optimal Operation of an Evaporation Process

Real-time optimization (RTO) aims to drive a process to its best efficient steady-state operation point. However, these optimizations often disregard long-term effects such as fouling, catalyst deactivation, etc., which leads to degraded operation or even equipment damage. This work deals with these issues in a multiple-effect evaporation process, with the goal of reducing the specific steam consumption. The proposed approach considers: a grey-box model of the process, data reconciliation to update the model, and RTO to search for the best operating point. The fouling effects arising in the heat exchangers are modeled as a function of the operation time and control decisions, and such model is integrated in the RTO. Moreover, fouling forces periodic stops for cleaning, with their corresponding associated costs. So, an economic optimization is proposed to predict the right day to perform maintenance tasks. Modern nonlinear-programming environments which include automatic differentiation have been used for implementation.

An Efficient Way to Tackle Uncertainty in the Scheduling of a Continuous Evaporation System

Abstract In this work a two-stage optimisation method is applied to provide robust schedules in real time for an industrial evaporation system. The scheduler must decide associations between products and plants, individual loads, and the right time to perform cleaning operations. The proposed approach discretises the prediction horizon in days and formulates a mixed-integer linear optimisation problem, where the target is to minimise costs. The schedule must be robust against uncertain external conditions, which may influence the equipment performance. The two-stage approach considers the possibility of reacting in the future once the uncertainty materialises. Thus, computed schedules may provide more savings than a single schedule fulfilling all considered scenarios.