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.

A model for motion sharpening: contrast gain control precedes compressive nonlinearity

Blurred edges appear sharper in motion than when they are stationary. We have previously shown how such distortions in perceived edge blur may be explained by a model which assumes that luminance contrast is encoded by a local contrast transducer whose response becomes progressively more compressive as speed increases. To test this model further, we measured the sharpening of drifting, periodic patterns over a large range of contrasts, blur widths, and speeds Human Vision. The results indicate that, while sharpening increased with speed, it was practically invariant with contrast. This contrast invariance cannot be explained by a fixed compressive nonlinearity since that predicts almost no sharpening at low contrasts.We show by computational modelling of spatiotemporal responses that, if a dynamic contrast gain control precedes the static nonlinear transducer, then motion sharpening, its speed dependence, and its invariance with contrast can be predicted with reasonable accuracy.

Pragmatic approach to the development of robust real-time protocols

This research is concerned with the development of distributed real-time systems, in which software is used for the control of concurrent physical processes. These distributed control systems are required to periodically coordinate the operation of several autonomous physical processes, with the property of an atomic action. The implementation of this coordination must be fault-tolerant if the integrity of the system is to be maintained in the presence of processor or communication failures. Commit protocols have been widely used to provide this type of atomicity and ensure consistency in distributed computer systems. The objective of this research is the development of a class of robust commit protocols, applicable to the coordination of distributed real-time control systems. Extended forms of the standard two phase commit protocol, that provides fault-tolerant and real-time behaviour, were developed. Petri nets are used for the design of the distributed controllers, and to embed the commit protocol models within these controller designs. This composition of controller and protocol model allows the analysis of the complete system in a unified manner. A common problem for Petri net based techniques is that of state space explosion, a modular approach to both the design and analysis would help cope with this problem. Although extensions to Petri nets that allow module construction exist, generally the modularisation is restricted to the specification, and analysis must be performed on the (flat) detailed net. The Petri net designs for the type of distributed systems considered in this research are both large and complex. The top down, bottom up and hybrid synthesis techniques that are used to model large systems in Petri nets are considered. A hybrid approach to Petri net design for a restricted class of communicating processes is developed. Designs produced using this hybrid approach are modular and allow re-use of verified modules. In order to use this form of modular analysis, it is necessary to project an equivalent but reduced behaviour on the modules used. These projections conceal events local to modules that are not essential for the purpose of analysis. To generate the external behaviour, each firing sequence of the subnet is replaced by an atomic transition internal to the module, and the firing of these transitions transforms the input and output markings of the module. Thus local events are concealed through the projection of the external behaviour of modules. This hybrid design approach preserves properties of interest, such as boundedness and liveness, while the systematic concealment of local events allows the management of state space. The approach presented in this research is particularly suited to distributed systems, as the underlying communication model is used as the basis for the interconnection of modules in the design procedure. This hybrid approach is applied to Petri net based design and analysis of distributed controllers for two industrial applications that incorporate the robust, real-time commit protocols developed. Temporal Petri nets, which combine Petri nets and temporal logic, are used to capture and verify causal and temporal aspects of the designs in a unified manner.

The design of robust protocols for distributed real-time systems

Modern distributed control systems comprise of a set of processors which are interconnected using a suitable communication network. For use in real-time control environments, such systems must be deterministic and generate specified responses within critical timing constraints. Also, they should be sufficiently robust to survive predictable events such as communication or processor faults. This thesis considers the problem of coordinating and synchronizing a distributed real-time control system under normal and abnormal conditions. Distributed control systems need to periodically coordinate the actions of several autonomous sites. Often the type of coordination required is the all or nothing property of an atomic action. Atomic commit protocols have been used to achieve this atomicity in distributed database systems which are not subject to deadlines. This thesis addresses the problem of applying time constraints to atomic commit protocols so that decisions can be made within a deadline. A modified protocol is proposed which is suitable for real-time applications. The thesis also addresses the problem of ensuring that atomicity is provided even if processor or communication failures occur. Previous work has considered the design of atomic commit protocols for use in non time critical distributed database systems. However, in a distributed real-time control system a fault must not allow stringent timing constraints to be violated. This thesis proposes commit protocols using synchronous communications which can be made resilient to a single processor or communication failure and still satisfy deadlines. Previous formal models used to design commit protocols have had adequate state coverability but have omitted timing properties. They also assumed that sites communicated asynchronously and omitted the communications from the model. Timed Petri nets are used in this thesis to specify and design the proposed protocols which are analysed for consistency and timeliness. Also the communication system is mcxielled within the Petri net specifications so that communication failures can be included in the analysis. Analysis of the Timed Petri net and the associated reachability tree is used to show the proposed protocols always terminate consistently and satisfy timing constraints. Finally the applications of this work are described. Two different types of applications are considered, real-time databases and real-time control systems. It is shown that it may be advantageous to use synchronous communications in distributed database systems, especially if predictable response times are required. Emphasis is given to the application of the developed commit protocols to real-time control systems. Using the same analysis techniques as those used for the design of the protocols it can be shown that the overall system performs as expected both functionally and temporally.