A.P. de Madrid

Reduction of the dimensionality of dynamic programming: a case study

This paper deals with the reduction of the computational complexity of dynamic programming, the well known curse of dimensionality. We show how it can be overcome by using different reduction techniques. Three of the most significant ones are introduced and compared with an example. The main conclusion is that the computational load can be reduced several orders of magnitude in an easy and intuitive way.

IIR approximations to the fractional differentiator/integrator using Chebyshev polynomials theory

This paper deals with the use of Chebyshev polynomials theory to achieve accurate discrete-time approximations to the fractional-order differentiator/integrator in terms of IIR filters. These filters are obtained using the Chebyshev-Padé and the Rational Chebyshev approximations, two highly accurate numerical methods that can be computed with ease using available software. They are compared against other highly accurate approximations proposed in the literature. It is also shown how the frequency response of the fractional-order integrator approximations can be easily improved at low frequencies.

Between fuzzy-PID and PID-conventional controllers: a good choice

The main problem in the synthesis of a control system is its parameter adjustment. Fuzzy logic controllers (FLC) have been proved to be very efficient in controlling complex and difficult-to-model processes. One of the main problems of these fuzzy controllers is that there is no systematic procedure for tuning. So, the necessity of methods for guiding the initial selection of the fuzzy controller parameters is clear. We propose an indirect method of tuning. It consists of describing the FLC like a classical controller from the external point of view. This allows the plant operator to feel comfortable with this regulator because he knows the direct influence between the variation of the FLC tuning parameters and the system response. It also facilitates the selection of some initial values that assure a reasonable behavior for the FLC, that could be improved by the qualitative tuning of these parameters.

Towards More Realistic Self Contained Models of Neurons: High-Order, Recurrence and Local Learning

The anatomy and physiology of biological neurons is revisited looking at a minimum set of computational requirements to be included in new and more complex models of self-contained local computation ANN. Some of these functionalities are then integrated and the corresponding model is evaluated. Properties included are: (1) locality and autonomy in all the computations including the learning algorithms. (2) a layered architecture with high-order recurrent neurons, (3) self and external programming via input spaces and (4) fault tolerance after physical lesion, or even elimination of one or more neurons.

Fractional-Order Generalized Predictive Control: Application for Low-Speed Control of Gasoline-Propelled Cars

There is an increasing interest in using fractional calculus applied to control theory generalizing classical control strategies as the PID controller and developing new ones with the intention of taking advantage of characteristics supplied by this mathematical tool for the controller definition. In this work, the fractional generalization of the successful and spread control strategy known as model predictive control is applied to drive autonomously a gasoline-propelled vehicle at low speeds. The vehicle is a Citroen C3 Pluriel that was modified to act over the throttle and brake pedals. Its highly nonlinear dynamics are an excellent test bed for applying beneficial characteristics of fractional predictive formulation to compensate unmodeled dynamics and external disturbances.

Parallel dynamic programming on clusters of workstations

The standard DP (dynamic programming) algorithms are limited by the substantial computational demands they put on contemporary serial computers. In this work, the theory behind the solution to serial monadic dynamic programming problems highlights the theory and application of parallel dynamic programming on a general-purpose architecture (cluster or network of workstations). A simple and well-known technique, message passing, is considered. Several parallel serial monadic DP algorithms are proposed, based on the parallelization in the state variables and the parallelization in the decision variables. Algorithms with no interpolation are also proposed. It is demonstrated how constraints introduce load unbalance which affect scalability and how this problem is inherent to DP.

Tuning predictive controllers with optimization: Application to GPC and FGPC

Abstract This work proposes a method, based on optimization, for tuning model–based predictive controllers. The optimized controller has to guarantee appropriated gain and phase margins, sensitivity functions and robustness specifications. The method will be illustrated on Generalized Predictive Control, GPC, and its fractional–order counterpart, FGPC. The method has been tested out and validated in a real time application, the control of a rail–vehicle.

A survey of Fractional-Order Generalized Predictive Control

This work describes the fractional generalization of GPC, known as Fractional-Order Generalized Predictive Control (FGPC). Based on a real-order fractional cost function, FGPC combines valuable characteristics of fractional calculus and predictive control. The mathematical fundamentals of FGPC as well as a possible tuning algorithm are reviewed. We also present application examples where FGPC has proved to be a versatile and valuable control strategy to control real plants.

Dynamic Programming Predictive Control

Abstract This paper deals with the development and characterization of Dynamic Programming Predictive Controllers (DPPC), advanced predictive controllers that make use of dynamic programming to solve highly nonlinear / nonquadratic constrained control problems. Some computational techniques to reduce the computational load are proposed, and an application example, pH control, is analyzed using this new methodology.

Tuning Fuzzy Logic Controllers by Classical Techniques

Fuzzy Control provides a good support to translate the knowledge of a skilled plant operator into rules, making intelligent control possible. But it is difficult to represent the experts knowledge with no degradation, so a tuning phase is required. This is not an easy task, and there is not a general procedure for it. On the other hand, most of the control systems are still based on the conventional PID regulator. Astrom has developed an empirical tool to predict the achievable performance of these controllers and to assess whether they are properly tuned. Based on Buckleys results, that have analytically proved the equivalence between one of the simplest fuzzy logic controller (FLC) and a PI, it is possible to apply Astroms tool to evaluate the performance of a FLC.