Adaptive fuzzy control with output feedback for H infinity tracking of SISO nonlinear systems

Observer-based adaptive fuzzy H(infinity) control is proposed to achieve H(infinity) tracking performance for a class of nonlinear systems, which are subject to model uncertainty and external disturbances and in which only a measurement of the output is available. The key ideas in the design of the proposed controller are (i) to transform the nonlinear control problem into a regulation problem through suitable output feedback, (ii) to design a state observer for the estimation of the non-measurable elements of the system's state vector, (iii) to design neuro-fuzzy approximators that receive as inputs the parameters of the reconstructed state vector and give as output an estimation of the system's unknown dynamics, (iv) to use an H(infinity) control term for the compensation of external disturbances and modelling errors, (v) to use Lyapunov stability analysis in order to find the learning law for the neuro-fuzzy approximators, and a supervisory control term for disturbance and modelling error rejection. The control scheme is tested in the cart-pole balancing problem and in a DC-motor model.     

Efficient nonlinear predictive control of a biochemical reactor using neural models

This paper describes the application of artificial neural networks to modelling and control of a continuous fermentor. A computationally efficient nonlinear model predictive control (MPC) algorithm with nonlinear prediction and linearisation (MPC-NPL) which needs solving on-line a quadratic programming problem is developed. It is demonstrated that the algorithm results in closed-loop control performance similar to that obtained in nonlinear MPC, which hinges on full on-line non-convex optimisation. The computational complexity of the MPC-NPL algorithm is shown, control accuracy and robustness are also demonstrated in the case of noisy measurements and disturbances affecting the process.     

Disturbance analysis of nonlinear differential equation models of genetic SUM regulatory networks

Noise disturbances and time delays are frequently met in cellular genetic regulatory systems. This paper is concerned with the disturbance analysis of a class of genetic regulatory networks described by nonlinear differential equation models. The mechanisms of genetic regulatory networks to amplify (attenuate) external disturbance are explored, and a simple measure of the amplification (attenuation) level is developed from a nonlinear robust control point of view. It should be noted that the conditions used to measure the disturbance level are delay-independent or delay-dependent, and are expressed within the framework of linear matrix inequalities, which can be characterized as convex optimization, and computed by the interior-point algorithm easily. Finally, by the proposed method, a numerical example is provided to illustrate how to measure the attenuation of proteins in the presence of external disturbances.     

An intelligent control method based on fuzzy logic for a robotic testing system for the human spine

In previous biomechanical studies of the human spine, we implemented a hybrid controller to investigate load-displacement characteristics. We found that measurement errors in both position and force caused the controller to be less accurate than predicted. As an alternative to hybrid control, a fuzzy logic controller (FLC) has been developed and implemented in a robotic testing system for the human spine. An FLC is a real-time expert system that can emulate part of a human operator's knowledge by using a set of action rules. The FLC provides simple but robust solutions that cover a wide range of system parameters and can cope with significant disturbances. It can be viewed as a heuristic and modular way of defining a nonlinear, table-based control system. In this study, an FLC is developed which uses the force difference and the change in force difference as the input parameters, and the displacement as the output parameter. A rule-table based on these parameters is designed for the controller Experiments on a physical model composed of springs demonstrate the improved performance of the proposed method.     

Nonlinear feedforward control of bioreactors with input multiplicities

A steady-state nonlinear feedforward controller (FFC) for measurable disturbances is designed for a continuous bioreactor, which is represented by Hammerstein type nonlinear model wherein the nonlinearity is a polynomial with input multiplicities. The manipulated variable is the feed substrate concentration (S_f) and the disturbance variable is the dilution rate (D). The productivity (Q=DP) is considered as the controlled variable. The desired value of Q=3.73 gives two values of feed substrate concentration. The nonlinearity in the gain is considered for relating output to the manipulated variable and separately for the relation between output to disturbance variable. The FFC is also designed for the overall linearized system. The performance of the FFC is evaluated on the nonlinear differential equation model. The FFC is also designed for the model based on a single nonlinear steady-state equation containing both D and S_f. This nonlinear FFC gives the best performance. The nonlinear FFC is also designed by using only linear gain for the disturbance and nonlinear gain for the manipulated variable. Similarly, nonlinear FFC is also designed by using linear gain for the manipulated variable and the nonlinear gain for the disturbance variable. The performances of these FFC schemes are compared.     

An LMI approach to design H(infinity) controllers for discrete-time nonlinear systems based on unified models

A unified neural network model termed standard neural network model (SNNM) is advanced. Based on the robust L(2) gain (i.e. robust H(infinity) performance) analysis of the SNNM with external disturbances, a state-feedback control law is designed for the SNNM to stabilize the closed-loop system and eliminate the effect of external disturbances. The control design constraints are shown to be a set of linear matrix inequalities (LMIs) which can be easily solved by various convex optimization algorithms (e.g. interior-point algorithms) to determine the control law. Most discrete-time recurrent neural network (RNNs) and discrete-time nonlinear systems modelled by neural networks or Takagi and Sugeno (T-S) fuzzy models can be transformed into the SNNMs to be robust H(infinity) performance analyzed or robust H(infinity) controller synthesized in a unified SNNM's framework. Finally, some examples are presented to illustrate the wide application of the SNNMs to the nonlinear systems, and the proposed approach is compared with related methods reported in the literature.     

Maximizing productivity of a continuous fermenter using nonlinear adaptive optimizing control

The control of a continuously operated fermenter at its maximum productivity level gives rise to a difficult control problem as the location of the optimum operating point changes due to the disturbances. In addition, the fermenter exhibits a change in the sign of the steady state gain near the optimum operating point. This study is aimed at developing an on-line optimizing control scheme that can track the changing location of the steady state optimum so as to maximize the fermenter productivity. A nonlinear Laguerre model, whose parameters are estimated on-line, is used for tracking the optimum operating point. The control at the optimum point is achieved using an adaptive nonlinear MPC strategy that uses the nonlinear Laguerre model for prediction. The efficiency of the proposed algorithm is demonstrated by simulating the control of a continuous fermenter that exhibits shift in the location of the optimum operating point in response to the changes in the maximum specific growth rate. The proposed on-line optimizing control strategy is shown to result in a considerable improvement in the closed loop performance even in the presence of measurement noise.     

Robust model matching control of immune systems under environmental disturbances: dynamic game approach

A robust model matching control of immune response is proposed for therapeutic enhancement to match a prescribed immune response under uncertain initial states and environmental disturbances, including continuous intrusion of exogenous pathogens. The worst-case effect of all possible environmental disturbances and uncertain initial states on the matching for a desired immune response is minimized for the enhanced immune system, i.e. a robust control is designed to track a prescribed immune model response from the minimax matching perspective. This minimax matching problem could herein be transformed to an equivalent dynamic game problem. The exogenous pathogens and environmental disturbances are considered as a player to maximize (worsen) the matching error when the therapeutic control agents are considered as another player to minimize the matching error. Since the innate immune system is highly nonlinear, it is not easy to solve the robust model matching control problem by the nonlinear dynamic game method directly. A fuzzy model is proposed to interpolate several linearized immune systems at different operating points to approximate the innate immune system via smooth fuzzy membership functions. With the help of fuzzy approximation method, the minimax matching control problem of immune systems could be easily solved by the proposed fuzzy dynamic game method via the linear matrix inequality (LMI) technique with the help of Robust Control Toolbox in Matlab. Finally, in silico examples are given to illustrate the design procedure and to confirm the efficiency and efficacy of the proposed method.     

Cholinergic receptor alterations in the cerebral cortex of spinal cord injured rat

Many areas of the cerebral cortex process sensory information or coordinate motor output necessary for control of movement. Disturbances in cortical cholinergic system can affect locomotor coordination. Spinal cord injury causes severe motor impairment and disturbances in cholinergic signalling can aggravate the situation. Considering the impact of cortical cholinergic firing in locomotion, we focussed the study in understanding the cholinergic alterations in cerebral cortex during spinal cord injury. The gene expression of key enzymes in cholinergic pathway - acetylcholine esterase and choline acetyl transferase showed significant upregulation in the cerebral cortex of spinal cord injured group compared to control with the fold increase in expression of acetylcholine esterase prominently higher than cholineacetyl transferase. The decreased muscarinic receptor density and reduced immunostaining of muscarinic receptor subtypes along with down regulated gene expression of muscarinic M1 and M3 receptor subtypes accounts for dysfunction of metabotropic acetylcholine receptors in spinal cord injury group. Ionotropic acetylcholine receptor alterations were evident from the decreased gene expression of alpha 7 nicotinic receptors and reduced immunostaining of alpha 7 nicotinic receptors in confocal imaging. Our data pin points the disturbances in cortical cholinergic function due to spinal cord injury; which can augment the locomotor deficits. This can be taken into account while devising a proper therapeutic approach to manage spinal cord injury.     

An adaptive and predictive control strategy for an activated sludge process

This paper focuses on the development of a simple adaptive and predictive control algorithm, used to regulate the effluent quality of an activated sludge treatment process. This control algorithm is based on the development of a linear incremental second order model which takes distinctively into account the main disturbances on the process. The model is employed to predict the effluent pollution over a finite horizon. Then, the control inputs are computed from the predictions and the desired output set point. The simulations conducted with a non linear process model showed that such a control strategy could improve the process performances by minimizing the effluent pollution and the energetic cost of the system.     

Model predictive control of glucose concentration in type I diabetic patients: An in silico trial

In this paper, the feedback control of glucose concentration in type I diabetic patients using subcutaneous insulin delivery and subcutaneous continuous glucose monitoring is considered. A recently developed in silico model of glucose metabolism is employed to generate virtual patients on which control algorithms can be validated against interindividual variability. An in silico trial consisting of 100 patients is used to assess the performances of a linear output feedback and a nonlinear state-feedback model predictive controller, designed on the basis of the in silico model. More than satisfactory results are obtained in the great majority of virtual patients. The experiments highlight the crucial role of the anticipative feedforward action driven by the meal announcement information. Preliminary results indicate that further improvements may be achieved by means of a nonlinear model predictive control scheme.     

Dynamic sensitivity and nonlinear interactions influence the system-level evolutionary patterns of phototransduction proteins

Determining the influence of complex, molecular-system dynamics on the evolution of proteins is hindered by the significant challenge of quantifying the control exerted by the proteins on system output. We have employed a combination of systems biology and molecular evolution analyses in a first attempt to unravel this relationship. We employed a comprehensive mathematical model of mammalian phototransduction to predict the degree of influence that each protein in the system exerts on the high-level dynamic behaviour. We found that the genes encoding the most dynamically sensitive proteins exhibit relatively relaxed evolutionary constraint. We also investigated the evolutionary and epistatic influences of the many nonlinear interactions between proteins in the system and found several pairs to have coevolved, including those whose interactions are purely dynamical with respect to system output. This evidence points to a key role played by nonlinear system dynamics in influencing patterns of molecular evolution.     

Dynamic output feedback stabilization for nonlinear systems based on standard neural network models

A neural-model-based control design for some nonlinear systems is addressed. The design approach is to approximate the nonlinear systems with neural networks of which the activation functions satisfy the sector conditions. A novel neural network model termed standard neural network model (SNNM) is advanced for describing this class of approximating neural networks. Full-order dynamic output feedback control laws are then designed for the SNNMs with inputs and outputs to stabilize the closed-loop systems. The control design equations are shown to be a set of linear matrix inequalities (LMIs) which can be easily solved by various convex optimization algorithms to determine the control signals. It is shown that most neural-network-based nonlinear systems can be transformed into input-output SNNMs to be stabilization synthesized in a unified way. Finally, some application examples are presented to illustrate the control design procedures.     

An environ analysis for nonlinear compartment models

Environ analysis, an input-output analysis for models of ecological systems, has been previously formulated for linear systems. This note has a twofold purpose: first, we indicate that a variation of parameters technique can be applied, at least in principle, to computeboth input and output environs; and second, we show that this technique may be used for computation of environs in nonautonomous, nonlinear compartment models. This nonlinear theory, obtained as a direct extension of dynamical system developments, allows the traditional environ partitioning of compartmental storages and flows. An example of a nonlinear nutrient-producer-consumer system whose output environs can be computed asymptotically is presented to illustrate these concepts. This research was supported by the U.S. Environmental Protection Agency under cooperative agreement R806727030.     

The role of the thrombocyte-activating factor in the development of circulatory disorders in the postischemic shock reaction

Experiments carried out on anesthetized dogs have shown that reperfusion of long-ischemized leg tissues is accompanied by a significant decrease of the cardiac output and myocardial contractility. Restriction of the venous return to the heart is important in the cardiac output decrease due to an increase of venous compliance and blood pooling on the peripheral circulation. The preliminary blockade of platelet-activating factor (PAF) receptors decreases degree of the cardio- and hemodynamic disturbances after reperfusion of ischemized tissues and prevents development of pulmonary hypertension. Similarity of the postreperfusion central and peripheral hemodynamic disturbances and animal responses to injection of the exogenous PAF as well as the presence of the protective effect of PAF-receptor antagonist BNo. 52021 permit concluding, that PAF takes part in the development of postischemic shock reaction and its receptor blockade can be used to prevent postreperfusion hemodynamic disorders.     

Disturbed nonlinear multispecies models in ecology.

We analyze a disturbed form of the general Lotka-Volterra model of an ecosystem with m interacting species. The disturbances act on the intrinsic growth rates of the species and are assumed to be bounded but otherwise unknown. We employ a Lyapunov technique and the concept of "reachable set" from control theory to estimate the set of all possible population densities that are attainable as a result of the disturbances. To calculate estimates for this reachable set, a number of numerical methods that entail the solution to one or more global optimization problems are developed. Specific examples involving two, three, and four species are solved. We also derive an explicit analytical expression that represents an estimate for the reachable set in the m-dimensional case. The estimate is conservative but can be evaluated without carrying out any optimization procedure. We show that methods developed in this paper can be applied to certain other types of nonlinear ecosystem models.     

Hierarchical control of biotechnological complex systems

Application of hierarchical control for solution of some nonlinear optimization problems in fermentation systems, with the use of microprocessors, is described. Results presented show some advantages of the method of hierarchical control in comparison to some traditional one-level optimization methods. The advantage of the hierarchical control method is in less demand on memory and computing power of the control computer as the standard methods.In solving this problem two control schemes are used. In the first control scheme the method of objective coordination is used. In the second one the prediction method of coordination is used, with the aim to minimize selected disturbances in state and control variables.     

Ecological limitations to the resilience of coral reefs

The decline of coral reefs has been broadly attributed to human stressors being too strong and pervasive, whereas biological processes that may render coral reefs fragile have been sparsely considered. Here we review several ecological factors that can limit the ability of coral reefs to withstand disturbance. These include: (1) Many species lack the adaptive capacity to cope with the unprecedented disturbances they currently face; (2) human disturbances impact vulnerable life history stages, reducing reproductive output and the supply of recruits essential for recovery; (3) reefs can be vulnerable to the loss of few species, as niche specialization or temporal and spatial segregation makes each species unique (i.e., narrow ecological redundancy); in addition, many foundation species have similar sensitivity to disturbances, suggesting that entire functions can be lost to single disturbances; and (4) feedback loops and extinction vortices may stabilize degraded states or accelerate collapses even if stressors are removed. This review suggests that the degradation of coral reefs is due to not only the severity of human stressors but also the “fragility” of coral reefs. As such, appropriate governance is essential to manage stressors while being inclusive of ecological process and human uses across transnational scales. This is a considerable but necessary upgrade in current management if the integrity, and delivery of goods and services, of coral reefs is to be preserved.     

一类具有非线性控制和基层具有饱和吸收率的恒化器藻类模型

本文通过对藻类的增长率和基层的吸收率提出有生物意义的表达式,研究了一类具有非线性控制藻类恒花器模型．用定性理论证明了非线性控制可以使变产量的恒化器模型有一个全局渐进稳定的正平衡点．     

Maximization of learning speed in the motor cortex due to neuronal redundancy

Many redundancies play functional roles in motor control and motor learning. For example, kinematic and muscle redundancies contribute to stabilizing posture and impedance control, respectively. Another redundancy is the number of neurons themselves; there are overwhelmingly more neurons than muscles, and many combinations of neural activation can generate identical muscle activity. The functional roles of this neuronal redundancy remains unknown. Analysis of a redundant neural network model makes it possible to investigate these functional roles while varying the number of model neurons and holding constant the number of output units. Our analysis reveals that learning speed reaches its maximum value if and only if the model includes sufficient neuronal redundancy. This analytical result does not depend on whether the distribution of the preferred direction is uniform or a skewed bimodal, both of which have been reported in neurophysiological studies. Neuronal redundancy maximizes learning speed, even if the neural network model includes recurrent connections, a nonlinear activation function, or nonlinear muscle units. Furthermore, our results do not rely on the shape of the generalization function. The results of this study suggest that one of the functional roles of neuronal redundancy is to maximize learning speed.