Abstract
This work addresses the problem of computing the time evolution of the probability density function (pdf) of the state in a nonlinear neuromuscular blockade (NMB) model, assuming that the source of uncertainty is the knowledge about one parameter. The NMB state is enlarged with the parameter, that verifies an equation given by its derivative being zero and has an initial condition described by a known pdf. By treating the resulting enlarged state-space model as a stochastic differential equation, the pdf of the state verifies a special case of the Fokker-Planck equation in which the second derivative terms vanish. This partial differential equation is solved with a numerical method based on Trotter’s formula for semigroup decomposition. The method is illustrated with results for a reduced complexity NMB model. A comparison of the predicted state pdf with clinical data for real patients is provided. © Springer International Publishing Switzerland 2014.

Abstract
This paper addresses the problem of joint estimation of the state and parameters for a deterministic continuous time system, with discrete time observations, in which the parameter vector is constant but its value is not known, being a random variable with a known distribution. Along time, the uncertainty in the parameter induces uncertainty in the plant state. The joint probability density function (pdf) satisfies the Liouville partial differential equation that is a limit case of the Fokker-Planck equation for vanishing diffusion. The continuous-discrete filter proposed operates as follows: Between two consecutive output sampling time instants, the pdf is propagated by solving the Liouville equation for an augmented state and is then corrected by using the last observation and Bayes law. An application to state estimation of the neuromuscular blockade of patients subject to general anesthesia, where parameter uncertainty is due to inter-patient variability, is described.

Abstract
During surgical interventions, a muscle relaxant drug is frequently administered with the objective of inducing muscle paralysis. Clinical environment and patient safety issues lead to a huge variety of situations that must be taken into account requiring intensive simulation studies. Hence, population models are crucial for research and development in this field.This work develops a stochastic population model for the neuromuscular blockade (NMB) (muscle paralysis) level induced by atracurium based on a deterministic individual model already proposed in the literature. To achieve this goal, a joint Lognormal distribution is considered for the patient-dependent parameters. This study is based on clinical data collected during general anaesthesia. The procedure developed enables to construct a reliable reference bank of parametrized models that not only reproduces the overall features of the NMB, but also the inter-individual variability characteristic of physiological signals. It turns out that this bank constitutes a fundamental tool to support research on identification and control algorithms and is suitable to be integrated in clinical decision support systems.

Abstract
The power systems operation in the smart grid context increases significantly the complexity of their management. New approaches for ancillary services procurement are essential to ensure the operation of electric power systems with appropriate levels of stability, safety, quality, equity and competitiveness. These approaches should include market mechanisms which allow the participation of small and medium distributed energy resources players in a competitive market environment. In this paper, an energy and ancillary services joint market model used by an aggregator is proposed, considering bids of several types of distributed energy resources. In order to improve economic efficiency in the market, ancillary services cascading market mechanism is also considered in the model. The proposed model is included in MASCEM - a multi-agent system electricity market simulator. A case study considering a distribution network with high penetration of distributed energy resources is presented.

Abstract
The smart grid concept is a key issue in the future power systems, namely at the distribution level, with deep concerns in the operation and planning of these systems. Several advantages and benefits for both technical and economic operation of the power system and of the electricity markets are recognized. The increasing integration of demand response and distributed generation resources, all of them mostly with small scale distributed characteristics, leads to the need of aggregating entities such as Virtual Power Players. The operation business models become more complex in the context of smart grid operation. Computational intelligence methods can be used to give a suitable solution for the resources scheduling problem considering the time constraints. This paper proposes a methodology for a joint dispatch of demand response and distributed generation to provide energy and reserve by a virtual power player that operates a distribution network. The optimal schedule minimizes the operation costs and it is obtained using a particle swarm optimization approach, which is compared with a deterministic approach used as reference methodology. The proposed method is applied to a 33-bus distribution network with 32 medium voltage consumers and 66 distributed generation units.

Abstract
The provision of reserves in power systems is of great importance in what concerns keeping an adequate and acceptable level of security and reliability. This need for reserves and the way they are defined and dispatched gain increasing importance in the present and future context of smart grids and electricity markets due to their inherent competitive environment. This paper concerns a methodology proposed by the authors, which aims to jointly and optimally dispatch both generation and demand response resources to provide the amounts of reserve required for the system operation. Virtual Power Players are especially important for the aggregation of small size demand response and generation resources. The proposed methodology has been implemented in MASCEM, a multi agent system also developed at the authors’ research center for the simulation of electricity markets.