Improved robust control of nonlinear stochastic systems using uncertain models

We introduce a technique for quantifying and then exploiting uncertainty in nonlinear stochastic control systems. The approach is suboptimal though robust and relies upon the approximation of the forward and inverse plant models by neural networks, which also estimate the intrinsic uncertainty. Sampling from the resulting Gaussian distributions of the inversion based neurocontroller allows us to introduce a control law which is demonstrably more robust than traditional adaptive controllers.

Multi-valued control problems and mixture density network

We have proposed a novel robust inversion-based neurocontroller that searches for the optimal control law by sampling from the estimated Gaussian distribution of the inverse plant model. However, for problems involving the prediction of continuous variables, a Gaussian model approximation provides only a very limited description of the properties of the inverse model. This is usually the case for problems in which the mapping to be learned is multi-valued or involves hysteritic transfer characteristics. This often arises in the solution of inverse plant models. In order to obtain a complete description of the inverse model, a more general multicomponent distributions must be modeled. In this paper we test whether our proposed sampling approach can be used when considering an arbitrary conditional probability distributions. These arbitrary distributions will be modeled by a mixture density network. Importance sampling provides a structured and principled approach to constrain the complexity of the search space for the ideal control law. The effectiveness of the importance sampling from an arbitrary conditional probability distribution will be demonstrated using a simple single input single output static nonlinear system with hysteretic characteristics in the inverse plant model.

Robust control of nonlinear stochastic systems by modelling conditional distributions of control signals

We introduce a novel inversion-based neuro-controller for solving control problems involving uncertain nonlinear systems that could also compensate for multi-valued systems. The approach uses recent developments in neural networks, especially in the context of modelling statistical distributions, which are applied to forward and inverse plant models. Provided that certain conditions are met, an estimate of the intrinsic uncertainty for the outputs of neural networks can be obtained using the statistical properties of networks. More generally, multicomponent distributions can be modelled by the mixture density network. In this work a novel robust inverse control approach is obtained based on importance sampling from these distributions. This importance sampling provides a structured and principled approach to constrain the complexity of the search space for the ideal control law. The performance of the new algorithm is illustrated through simulations with example systems.

Voltage control on an uninhabited autonomous vehicle electrical distribution system

More-electric vehicle technology is becoming prevalent in a number of transportation systems because of its ability to improve efficiency and reduce costs. This paper examines the specific case of an Uninhabited Autonomous Vehicle (UAV), and the system topology and control elements required to achieve adequate dc distribution voltage bus regulation. Voltage control methods are investigated and a droop control scheme is implemented on the system. Simulation results are also presented.

Exploiting uncertainty in nonlinear stochastic control problem

This work introduces a novel inversion-based neurocontroller for solving control problems involving uncertain nonlinear systems which could also compensate for multi-valued systems. The approach uses recent developments in neural networks, especially in the context of modelling statistical distributions, which are applied to forward and inverse plant models. Provided that certain conditions are met, an estimate of the intrinsic uncertainty for the outputs of neural networks can be obtained using the statistical properties of networks. More generally, multicomponent distributions can be modelled by the mixture density network. Based on importance sampling from these distributions a novel robust inverse control approach is obtained. This importance sampling provides a structured and principled approach to constrain the complexity of the search space for the ideal control law. The developed methodology circumvents the dynamic programming problem by using the predicted neural network uncertainty to localise the possible control solutions to consider. Convergence of the output error for the proposed control method is verified by using a Lyapunov function. Several simulation examples are provided to demonstrate the efficiency of the developed control method. The manner in which such a method is extended to nonlinear multi-variable systems with different delays between the input-output pairs is considered and demonstrated through simulation examples.

A probabilistic indirect adaptive control for systems with input-dependent noise

A probabilistic indirect adaptive controller is proposed for the general nonlinear multivariate class of discrete time system. The proposed probabilistic framework incorporates input–dependent noise prediction parameters in the derivation of the optimal control law. Moreover, because noise can be nonstationary in practice, the proposed adaptive control algorithm provides an elegant method for estimating and tracking the noise. For illustration purposes, the developed method is applied to the affine class of nonlinear multivariate discrete time systems and the desired result is obtained: the optimal control law is determined by solving a cubic equation and the distribution of the tracking error is shown to be Gaussian with zero mean. The efficiency of the proposed scheme is demonstrated numerically through the simulation of an affine nonlinear system.

A mixture density network approach to modelling and exploiting uncertainty in nonlinear control problems

In nonlinear and stochastic control problems, learning an efficient feed-forward controller is not amenable to conventional neurocontrol methods. For these approaches, estimating and then incorporating uncertainty in the controller and feed-forward models can produce more robust control results. Here, we introduce a novel inversion-based neurocontroller for solving control problems involving uncertain nonlinear systems which could also compensate for multi-valued systems. The approach uses recent developments in neural networks, especially in the context of modelling statistical distributions, which are applied to forward and inverse plant models. Provided that certain conditions are met, an estimate of the intrinsic uncertainty for the outputs of neural networks can be obtained using the statistical properties of networks. More generally, multicomponent distributions can be modelled by the mixture density network. Based on importance sampling from these distributions a novel robust inverse control approach is obtained. This importance sampling provides a structured and principled approach to constrain the complexity of the search space for the ideal control law. The developed methodology circumvents the dynamic programming problem by using the predicted neural network uncertainty to localise the possible control solutions to consider. A nonlinear multi-variable system with different delays between the input-output pairs is used to demonstrate the successful application of the developed control algorithm. The proposed method is suitable for redundant control systems and allows us to model strongly non-Gaussian distributions of control signal as well as processes with hysteresis. © 2004 Elsevier Ltd. All rights reserved.

Generalised Riccati solution and pinning control of complex stochastic networks

This paper considers the global synchronisation of a stochastic version of coupled map lattices networks through an innovative stochastic adaptive linear quadratic pinning control methodology. In a stochastic network, each state receives only noisy measurement of its neighbours' states. For such networks we derive a generalised Riccati solution that quantifies and incorporates uncertainty of the forward dynamics and inverse controller in the derivation of the stochastic optimal control law. The generalised Riccati solution is derived using the Lyapunov approach. A probabilistic approximation type algorithm is employed to estimate the conditional distributions of the state and inverse controller from historical data and quantifying model uncertainties. The theoretical derivation is complemented by its validation on a set of representative examples.

A Bayesian perspective on stochastic neurocontrol

Control design for stochastic uncertain nonlinear systems is traditionally based on minimizing the expected value of a suitably chosen loss function. Moreover, most control methods usually assume the certainty equivalence principle to simplify the problem and make it computationally tractable. We offer an improved probabilistic framework which is not constrained by these previous assumptions, and provides a more natural framework for incorporating and dealing with uncertainty. The focus of this paper is on developing this framework to obtain an optimal control law strategy using a fully probabilistic approach for information extraction from process data, which does not require detailed knowledge of system dynamics. Moreover, the proposed control method framework allows handling the problem of input-dependent noise. A basic paradigm is proposed and the resulting algorithm is discussed. The proposed probabilistic control method is for the general nonlinear class of discrete-time systems. It is demonstrated theoretically on the affine class. A nonlinear simulation example is also provided to validate theoretical development.

Suppression and summation in contrast gain control for human vision

Over the last ten years our understanding of early spatial vision has improved enormously. The long-standing model of probability summation amongst multiple independent mechanisms with static output nonlinearities responsible for masking is obsolete. It has been replaced by a much more complex network of additive, suppressive, and facilitatory interactions and nonlinearities across eyes, area, spatial frequency, and orientation that extend well beyond the classical recep-tive field (CRF). A review of a substantial body of psychophysical work performed by ourselves (20 papers), and others, leads us to the following tentative account of the processing path for signal contrast. The first suppression stage is monocular, isotropic, non-adaptable, accelerates with RMS contrast, most potent for low spatial and high temporal frequencies, and extends slightly beyond the CRF. Second and third stages of suppression are difficult to disentangle but are possibly pre- and post-binocular summation, and involve components that are scale invariant, isotropic, anisotropic, chromatic, achromatic, adaptable, interocular, substantially larger than the CRF, and saturated by contrast. The monocular excitatory pathways begin with half-wave rectification, followed by a preliminary stage of half-binocular summation, a square-law transducer, full binocular summation, pooling over phase, cross-mechanism facilitatory interactions, additive noise, linear summation over area, and a slightly uncertain decision-maker. The purpose of each of these interactions is far from clear, but the system benefits from area and binocular summation of weak contrast signals as well as area and ocularity invariances above threshold (a herd of zebras doesn't change its contrast when it increases in number or when you close one eye). One of many remaining challenges is to determine the stage or stages of spatial tuning in the excitatory pathway.

Interocular masking and summation indicate two stages of divisive contrast gain control

Our understanding of early spatial vision owes much to contrast masking and summation paradigms. In particular, the deep region of facilitation at low mask contrasts is thought to indicate a rapidly accelerating contrast transducer (eg a square-law or greater). In experiment 1, we tapped an early stage of this process by measuring monocular and binocular thresholds for patches of 1 cycle deg-1 sine-wave grating. Threshold ratios were around 1.7, implying a nearly linear transducer with an exponent around 1.3. With this form of transducer, two previous models (Legge, 1984 Vision Research 24 385 - 394; Meese et al, 2004 Perception 33 Supplement, 41) failed to fit the monocular, binocular, and dichoptic masking functions measured in experiment 2. However, a new model with two-stages of divisive gain control fits the data very well. Stage 1 incorporates nearly linear monocular transducers (to account for the high level of binocular summation and slight dichoptic facilitation), and monocular and interocular suppression (to fit the profound 42 Oral presentations: Spatial vision Thursday dichoptic masking). Stage 2 incorporates steeply accelerating transduction (to fit the deep regions of monocular and binocular facilitation), and binocular summation and suppression (to fit the monocular and binocular masking). With all model parameters fixed from the discrimination thresholds, we examined the slopes of the psychometric functions. The monocular and binocular slopes were steep (Weibull ߘ3-4) at very low mask contrasts and shallow (ߘ1.2) at all higher contrasts, as predicted by all three models. The dichoptic slopes were steep (ߘ3-4) at very low contrasts, and very steep (ß>5.5) at high contrasts (confirming Meese et al, loco cit.). A crucial new result was that intermediate dichoptic mask contrasts produced shallow slopes (ߘ2). Only the two-stage model predicted the observed pattern of slope variation, so providing good empirical support for a two-stage process of binocular contrast transduction. [Supported by EPSRC GR/S74515/01]

Ownership concentration:'Private benefits of control' and debt financing

Building on the ‘law and economics’ literature, this paper analyses corporate governance implications of debt financing in an environment where a dominant owner is able to extract ex ante ‘private benefits of control’. Ownership concentration may result in lower efficiency, measured as a ratio of a firm’s debt to investment, and this effect depends on the identity of the largest shareholder. Moreover, entrenched dominant shareholder(s) may be colluding with fixed-claim holders in extracting ‘control premium’. One of possible outcomes is a ‘crowding out’ of entrepreneurial firms from the debt market, and this is supported by evidence from the transition economies.

O2 v Hutchison 3G comparative advertising:European trade mark law beyond compare?

Legislation: Directive 89/104 on trade marks art.5 Directive 84/450 on misleading advertising Directive 97/55 amending Directive 84/450 concerning misleading advertising so as to include comparative advertising Case: O2 Holdings Ltd v Hutchison 3G UK Ltd (C-533/06) [2008] E.C.R. I-4231 (ECJ (1st Chamber)) *Comms. L. 155 Long, long ago a trade mark allowed a craftsman to be identified and held accountable for shoddy goods. Today in the era of the ‘Lovemark,’1 due to extensive advertising hopes and aspirations a lifestyle can be purchased with a brand. For many products a trademark is no longer merely a badge of origin but has a commercial value of its own. Through advertising an emotional attachment is created in the heart of the consumer for particular brands. Brand owners are determined that the value of this attachment be preserved and protected against any encroachment into the aura that has been painstakingly created. Comparative advertising, the allusive use of a mark, is seen by the owners of such emotive brands as likely to jeopardise the character of the brand that they have so carefully nurtured. As they have invested so heavily in creating their concept these owners want to control its use by others. There is an issue however as to how far this control ought to extend when the image is used in the marketing of a rival's goods or services.

International trade law, plain packaging and tobacco industry political activity:the Trans-Pacific Partnership

Tobacco companies are increasingly turning to trade and investment agreements to challenge measures aimed at reducing tobacco use. This study examines their efforts to influence the Trans-Pacific Partnership (TPP), a major trade and investment agreement which may eventually cover 40% of the world's population; focusing on how these efforts might enhance the industry's power to challenge the introduction of plain packaging. Specifically, the paper discusses the implications for public health regulation of Philip Morris International's interest in using the TPP to: shape the bureaucratic structures and decision-making processes of business regulation at the national level; introduce a higher standard of protection for trademarks than is currently provided under the Agreement on Trade Related Aspects of Intellectual Property Rights; and expand the coverage of Investor-State Dispute Settlement which empowers corporations to litigate directly against governments where they are deemed to be in breach of investment agreements. The large number of countries involved in the TPP underlines its risk to the development of tobacco regulation globally.