Modelling and control of nonlinear systems using Gaussian processes with partial model information

Gaussian processes are gaining increasing popularity among the control community, in particular for the modelling of discrete time state space systems. However, it has not been clear how to incorporate model information, in the form of known state relationships, when using a Gaussian process as a predictive model. An obvious example of known prior information is position and velocity related states. Incorporation of such information would be beneficial both computationally and for faster dynamics learning. This paper introduces a method of achieving this, yielding faster dynamics learning and a reduction in computational effort from O(Dn2) to O((D - F)n2) in the prediction stage for a system with D states, F known state relationships and n observations. The effectiveness of the method is demonstrated through its inclusion in the PILCO learning algorithm with application to the swing-up and balance of a torque-limited pendulum and the balancing of a robotic unicycle in simulation. © 2012 IEEE.

Stabilization and disturbance attenuation of nonlinear systems using dissipativity theory

In this paper, we survey some recent results on stabilization and disturbance attenuation for nonlinear systems using a dissipativity approach. After reviewing the basic dissipativity concept, we stress the connections between Lyapunov designs and the problem of achieving passivity by feedback. Focusing on physical models, we then illustrate how the design of stabilizing feedback can take advantage of the natural energy balance equation of the system. Here stabilization is viewed as the task of shaping the energy of the system to enforce a minimum at the desired equilibrium. Finally, we show the implications of dissipativity theory as an appropriate framework to study the nonlinear H∞ control problem. © 2002 EUCA.

Improving the performance of low-gain designs for bounded control of linear systems

An online scheduling of the parameter ensuring in addition to closed loop stability was presented. Attention was given to saturated linear low-gain control laws. Null controllability of the considered linear systems was assumed. The family of low gain control laws achieved semiglobal stabilization.

Slow peaking and low-gain designs for global stabilization of nonlinear systems

This paper presents an analysis of the slow-peaking phenomenon, a pitfall of low-gain designs that imposes basic limitations to large regions of attraction in nonlinear control systems. The phenomenon is best understood on a chain of integrators perturbed by a vector field up(x, u) that satisfies p(x, 0) = 0. Because small controls (or low-gain designs) are sufficient to stabilize the unperturbed chain of integrators, it may seem that smaller controls, which attenuate the perturbation up(x, u) in a large compact set, can be employed to achieve larger regions of attraction. This intuition is false, however, and peaking may cause a loss of global controllability unless severe growth restrictions are imposed on p(x, u). These growth restrictions are expressed as a higher order condition with respect to a particular weighted dilation related to the peaking exponents of the nominal system. When this higher order condition is satisfied, an explicit control law is derived that achieves global asymptotic stability of x = 0. This stabilization result is extended to more general cascade nonlinear systems in which the perturbation p(x, v) v, v = (ξ, u) T, contains the state ξ and the control u of a stabilizable subsystem ξ = a(ξ, u). As an illustration, a control law is derived that achieves global stabilization of the frictionless ball-and-beam model.

Global stabilization of feedforward systems with exponentially unstable Jacobian linearization

The global stabilization of a class of feedforward systems having an exponentially unstable Jacobian linearization is achieved by a high-gain feedback saturated at a low level. The control law forces the derivatives of the state variables to small values along the closed-loop trajectories. This "slow control" design is illustrated with a benchmark example and its limitations are emphasized. © 1999 Elsevier Science B.V. All rights reserved.

Tailored seeding geometries for the multi-fidelity design of compression systems

Design optimisation of compressor systems is a computationally expensive problem due to the large number of variables, complicated design space and expense of the analysis tools. One approach to reduce the expense of the process and make it achievable in industrial timescales is to employ multi-fidelity techniques, which utilise more rapid tools in conjunction with the highest fidelity analyses. The complexity of the compressor design landscape is such that the starting point for these optimisations can influence the achievable results; these starting points are often existing (optimised) compressor designs, which form a limited set in terms of both quantity and diversity of the design. To facilitate the multi-fidelity optimisation procedure, a compressor synthesis code was developed which allowed the performance attributes (e.g. stage loadings, inlet conditions) to be stipulated, enabling the generation of a variety of compressors covering a range of both design topology and quality to act as seeding geometries for the optimisation procedures. Analysis of the performance of the multi-fidelity optimisation system when restricting its exploration space to topologically different areas of the design space indicated little advantage over allowing the system to search the design space itself. However, comparing results from optimisations started from seed designs with different aerodynamic qualites indicated an improved performance could be achieved by starting an optimisation from a higher quality point, and thus that the choice of starting point did affect the final outcome of the optimisations. Both investigations indicated that the performance gains through the optimisation were largely defined by the early exploration of the design space where the multi-fidelity speedup could be exploited, thus extending this region is likely to have the greatest effect on performance of the optimisation system. © 2013 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

Tailored seeding geometries for the multi-fidelity design of compression systems

Design optimisation of compressor systems is a computationally expensive problem due to the large number of variables, complicated design space and expense of the analysis tools. One approach to reduce the expense of the process and make it achievable in industrial timescales is to employ multi-fidelity techniques, which utilise more rapid tools in conjunction with the highest fidelity analyses. The complexity of the compressor design landscape is such that the starting point for these optimisations can influence the achievable results; these starting points are often existing (optimised) compressor designs, which form a limited set in terms of both quantity and diversity of the design. To facilitate the multi-fidelity optimisation procedure, a compressor synthesis code was developed which allowed the performance attributes (e.g. stage loadings, inlet conditions) to be stipulated, enabling the generation of a variety of compressors covering a range of both design topology and quality to act as seeding geometries for the optimisation procedures. Analysis of the performance of the multi-fidelity optimisation system when restricting its exploration space to topologically different areas of the design space indicated little advantage over allowing the system to search the design space itself. However, comparing results from optimisations started from seed designs with different aerodynamic qualites indicated an improved performance could be achieved by starting an optimisation from a higher quality point, and thus that the choice of starting point did affect the final outcome of the optimisations. Both investigations indicated that the performance gains through the optimisation were largely defined by the early exploration of the design space where the multi-fidelity speedup could be exploited, thus extending this region is likely to have the greatest effect on performance of the optimisation system. © 2012 AIAA.

The response of antioxidant systems in Nostoc sphaeroides against UV-B radiation and the protective effects of exogenous antioxidants

UV radiation is one of many harmful factors found in space that are detrimental to organisms on earth in space exploration. In the present work, we examined the role of antioxidant system in Nostoc sphaeroides Kutz (Cyanobacterium) and the effects of exogenously applied antioxidant molecules on its photosynthetic rate under UV-B radiation. It was found that UV-B radiation promoted the activity of antioxidant system to protect photosystem 11 (PSII) and exogenously applied antioxidant: sodium nitroprusside (SNP) and N-acetylcysteine (NAC) had an obvious protection on PSII activity under UV-B radiation. The activity of superoxide dismutase (SOD, EC 1.15.1.1), catalase (CAT, EC 1.11.1.6), peroxidase (POD, EC 1.11.1.7) and content of NIDA (malondialdehyde) and ASC (ascorbate) were improved by 0.5 mM and 1 mM SNP, but 0.1 mM SNP decreased the activity of antioxidant system. Addition of exogenous NAC decreased the activity of SOD, POD, CAT and the content MDA and ASC. In contrast, exogenously applied NAC increased GSH content. The results suggest that exogenous SNP and NAC may protect algae by different mechanisms: SNP may play double roles as both sources of reactive free radicals as well as ROS scavengers in mediating the protective role of PSII on algae under UV-B radiation. On the other hand, NAC functions as an antioxidant or precursor of glutathione, which could protect PSII directly from UV-B radiation. (c) 2007 COSPAR, Published by Elsevier Ltd. All rights reserved.

Microcystin-RR-induced accumulation of reactive oxygen species and alteration of antioxidant systems in tobacco BY-2 cells

Microcystins are cyclic heptapeptide hepatoxins produced by cyanobacteria. It has been shown that microcystins have adverse effects on animals and on plants as well. Previous researches also indicated that microcystins were capable of inducing oxidative damage in animals both in vivo and in vitro. In this study, tobacco BY-2 suspension cell line was applied to examine the effects of microcystin-RR on plant cells. Cell viability and five biochemical parameters including reactive oxygen species (ROS), superoxide dismutase (SOD), catalase (CAT), glutathione peroxide (GPX) and peroxide dismutase (POD) were investigated when cells were exposed to 50 mg/L microcystin-RR. Results showed that microcystin-RR evoked decline of the cell viability to approximately 80% after treating for 144 h. ROS levels, POD and GPX activities of the treated cells were gradually increased with a time dependent manner. Changes of SOD and CAT activities were also detected in BY-2 cells. After 168 h recovery, ROS contents, POD, GPX and CAT activities returned to normal levels. These results suggest that the microcystin-RR can cause the increase of ROS contents in plant cells and these changes led to oxidant stress, at the same time, the plant cells would improve their antioxidant abilities to combat mirocystin-RR induced oxidative injury. (c) 2005 Elsevier Ltd. All rights reserved.

Responses of antioxidant systems in the hepatocytes of common carp (Cyprinus carpio L.) to the toxicity of microcystin-LR

The freshwater, bloom-forming cyanobacterium (blue-green alga) Microcystis aeruginosa produces a peptide hepatotoxin, which causes the damage of animal liver. Recently, toxic Microcystis blooms frequently occur in the eutrophic Dianchi Lake (300 km(2) and located in the South-Westem of China). Microcystin-LR from Microcystis in Dianchi was isolated and purified by high performance liquid chromatography (HPLC) and its toxicity to mouse and fish liver was studied (Li et al., 2001). In this study, six biochemical parameters (reactive oxygen species, glutathione, superoxide dismutase, catalase, glutathione peroxide and glutathione S-transferase) were determined in common carp hepatocytes when the cells were exposed to 10 mug microcystin-LR per litre. The results showed that reactive oxygen species (ROS) contents increased by more than one-time compared with the control after 6 h exposure to the toxin. In contrast, glutathione (GSH) levels in the hepatocytes exposed to microcystin-LR decreased by 47% compared with the control. The activities of superoxide dismutase (SOD), catalase (CAT) and glutathione peroxide (GSH-Px) increased significantly after 6 h exposure to microcystin-LR, but glutathione S-transferase (GST) activity showed no difference from the control. These results suggested that the toxicity of microcystin-LR caused the increase of ROS contents and the depletion of GSH in hepatocytes exposed to the toxin and these changes led to oxidant shock in hepatocytes. Increases of SOD, CAT and GSH-Px activities revealed that these three kinds of antioxidant enzymes might play important roles in eliminating the excessive ROS. This paper also examined the possible toxicity mechanism of microcystin-LR on the fish hepatocytes and the results were similar to those with mouse hepatocytes. (C) 2003 Elsevier Science Ltd. All rights reserved.