The paper presents a gradient-based algorithm for optimal control of nonlinear multivariable systems with control and state vectors constraints. The algorithm has a backward-intime recurrent structure similar to the backpropagation-throughtime algorithm, which is mostly used as a learning algorithm for dynamic neural networks. Other main features of the algorithm include the use of higher order Adams time-discretization schemes, numerical calculation of Jacobians, and advanced conjugate gradient methods for favorable convergence properties. The algorithm performance is illustrated on an example of off-line vehicle dynamics control optimization based on a realistic high-order vehicle model. The optimized control variables are active rear differential torque transfer and active rear steering road wheel angle, while the optimization tasks are trajectory tracking and roll minimization for a double lane change maneuver.

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In this paper, a design procedure and experimental implementation of a PID controller is presented. The PID controller is tuned according to damping optimum in order to achieve precise position control of a pneumatic servo drive. It is extended by a friction compensation and stabilization algorithm in order to deal with friction effects. In a case of supply pressure variations, more robust control system is needed. It is implemented by extending the proposed PID controller with friction compensator with the gain scheduling algorithm, which is provided by means of fuzzy logic. The effectiveness of proposed control algorithms is experimentally verified on an industrial cylindrical rodless actuator controlled by a proportional valve.

Abstract-Forecasting performances of feed-forward and recurrent neural networks (NN) trained with different learning algorithms are analyzed and compared using the MackeyGlass nonlinear chaotic time series. This system is a known benchmark test whose elements are hard to predict. Multilayer Perceptron NN was chosen as a feed-forward neural network because it is still the most commonly used network in financial forecasting models. It is compared with the modified version of the so-called Dynamic Multi-layer Perceptron NN characterized with a dynamic neuron model, i.e., Auto Regressive Moving Average filter built into the hidden layer neurons. Thus, every hidden layer neuron has the ability to process previous values of its own activity together with new input signals. The obtained results indicate satisfactory forecasting characteristics of both networks. However, recurrent NN was more accurate in practically all tests using less number of hidden layer neurons than the feed-forward NN. This study once again confirmed a great effectiveness and potential of dynamic neural networks in modeling and predicting highly nonlinear processes. Their application in the design of financial forecasting models is therefore most recommended.

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