Systematic Design of Type-2 Fuzzy Logic Systems for Modeling and Control with Applications to Modular and Reconfigurable Robots

Fuzzy logic systems (FLSs) are well known in the literature for their ability to model linguistics and system uncertainties. Due to this ability, FLSs have been successfully used in modeling and control applications such as medicine, finance, communications, and operations research. Moreover, the ability of higher order fuzzy systems to handle system uncertainty has become an interesting topic of research in the field. In particular, type-2 FLSs (T2 FLSs), systems consisting of fuzzy sets with fuzzy grades of membership, a feature that type-1 (T1) does not offer, are most well-known for this capability. The structure of T2 FLSs allows for the incorporation of uncertainty in the input membership grades, a common situation in reasoning with physical systems. General T2 FLSs have a complex structure, thus making them difficult to adopt on a large scale. As a result, interval T2 FLSs (IT2 FLSs), a special class of T2 FLSs, have recently shown great potential in various applications with input-output (I/O) system uncertainties. Due to the sophisticated mathematical structure of IT2 FLSs, little to no systematic analysis has been reported in the literature to use such systems in control design. Moreover, to date, designers have distanced themselves from adopting such systems on a wide scale because of their design complexity. Furthermore, the very few existing control methods utilizing IT2 fuzzy logic control systems (IT2 FLCSs) do not guarantee the stability of their system. Therefore, this thesis presents a systematic method for designing stable IT2 Takagi-Sugeno-Kang (IT2 TSK) fuzzy systems when antecedents are T2 fuzzy sets and consequents are crisp numbers (A2-C0). Five new inference mechanisms are proposed that have closed-form I/O mappings, making them more feasible for FLCS stability analysis. The thesis focuses on control applications for when (a) both plant and controller use A2-C0 TSK models, and (b) the plant uses T1 Takagi-Sugeno (T1 TS) and the controller uses IT2 TS models. In both cases, sufficient stability conditions for the stability of the closed-loop system are derived. Furthermore, novel linear matrix inequality-based algorithms are developed for satisfying the stability conditions. Numerical analyses are included to validate the effectiveness of the new inference methods. Case studies reveal that a well-tuned IT2 TS FLCS using the proposed inference engine can potentially outperform its T1 TSK counterpart, a result of IT2 having greater structural flexibility than T1. Moreover, due to the simple nature of the proposed inference engine, it is easy to implement in real-time control systems. In addition, a novel design methodology is proposed for IT2 TSK FLC for modular and reconfigurable robot (MRR) manipulators with uncertain dynamic parameters. A mathematical framework for the design of IT2 TSK FLCs is developed for tracking purposes that can be effectively used in real-time applications. To verify the effectiveness of the proposed controller, experiments are performed on an MRR with two degrees of freedom which exhibits dynamic coupling behavior. Results show that the developed controller can outperform some well-known linear and nonlinear controllers for different configurations. Therefore, the proposed structure can be adopted for the position control of MRRs with unknown dynamic parameters in trajectory-tracking applications. Finally, a rigorous mathematical analysis of the robustness of FLSs (both T1 and IT2) is presented in the thesis and entails a formulation of the robustness of FLSs as a constraint multi-objective optimization problem. Consequently, a procedure is proposed for the design of robust IT2 FLSs. Several examples are presented to demonstrate the effectiveness of the proposed methodologies. It was concluded that both T1 and IT2 FLSs can be designed to achieve robust behavior in various applications. IT2 FLSs, having a more flexible structure than T1 FLSs, exhibited relatively small approximation errors in the several examples investigated. The rigorous methodologies presented in this thesis lay the mathematical foundations for analyzing the stability and facilitating the design of stabilizing IT2 FLCSs. In addition, the proposed control technique for tracking purposes of MRRs will provide control engineers with tools to control dynamic systems with uncertainty and changing parameters. Finally, the systematic approach developed for the analysis and design of robust T1 and IT2 FLSs is of great practical value in various modeling and control applications

Modelação e controlo de sistemas com incertezas baseados em lógica difusa de tipo-2

Doutoramento em Engenharia EletrotécnicaA última fronteira da Inteligência Artificial será o desenvolvimento de um sistema computacional autónomo capaz de "rivalizar" com a capacidade de aprendizagem e de entendimento humana. Ainda que tal objetivo não tenha sido até hoje atingido, da sua demanda resultam importantes contribuições para o estado-da-arte tecnológico atual. A Lógica Difusa é uma delas que, influenciada pelos princípios fundamentais da lógica proposicional do raciocínio humano, está na base de alguns dos sistemas computacionais "inteligentes" mais usados da atualidade. A teoria da Lógica Difusa é uma ferramenta fundamental na suplantação de algumas das limitações inerentes à representação de informação incerta em sistemas computacionais. No entanto esta apresenta ainda algumas lacunas, pelo que diversos melhoramentos à teoria original têm sido introduzidos ao longo dos anos, sendo a Lógica Difusa de Tipo-2 uma das mais recentes propostas. Os novos graus de liberdade introduzidos por esta teoria têm-se demonstrado vantajosos, particularmente em aplicações de modelação de sistemas não-lineares complexos. Uma das principais vantagens prende-se com o aumento da robustez dos modelos assim desenvolvidos comparativamente àqueles baseados nos princípios da Lógica Difusa de Tipo-1 sem implicar necessariamente um aumento da sua dimensão. Tal propriedade é particularmente vantajosa considerando que muitas vezes estes modelos são utilizados como suporte ao desenvolvimento de sistemas de controlo que deverão ser capazes de assegurar o comportamento ótimo de um processo em condições de operação variáveis. No entanto, o estado-da-arte da teoria de controlo de sistemas baseada em modelos não tem integrado todos os melhoramentos proporcionados pelo desenvolvimento de modelos baseados nos princípios da Lógica Difusa de Tipo-2. Por essa razão, a presente tese propõe-se a abordar este tópico desenvolvendo uma metodologia de síntese de Controladores Preditivos baseados em modelos Takagi-Sugeno seguindo os princípios da Lógica Difusa de Tipo-2. De modo a cumprir este objetivo, quatro linhas de investigação serão debatidas neste trabalho.Primeiramente proceder-se-á ao desenvolvimento de uma metodologia de treino de Modelos Difusos de Tipo-2 simplificada, focada em dois paradigmas: manter a clareza dos intervalos de incerteza introduzidos sobre um Modelo Difuso de Tipo-1; assegurar a validade dos diversos modelos localmente lineares que constituem a estrutura Takagi- Sugeno, de modo a torná-los adequados a métodos de síntese de controladores baseados em modelos. O modelo desenvolvido é tipicamente utilizado para extrapolar o comportamento do sistema numa janela temporal futura. No entanto, quando usados em aproximações de sistemas não lineares, os modelos do tipo Takagi-Sugeno estabelecem um compromisso entre exatidão e complexidade computacional. Assim, é proposta a utilização dos princípios da Lógica Difusa de Tipo-2 para reduzir a influência dos erros de modelação nas estimações obtidas através do ajuste dos intervalos de incerteza dos parâmetros do modelo. Com base na estrutura Takagi-Sugeno, um método de linearização local de modelos não-lineares será utilizado em cada ponto de funcionamento do sistema de modo a obter os parâmetros necessários para a síntese de um controlador otimizado numa janela temporal futura de acordo com os princípios da teoria de Controlo Preditivo Generalizado - um dos algoritmos de Controlo Preditivo mais utilizado na indústria. A qualidade da resposta do sistema em malha fechada e a sua robustez a perturbações serão então comparadas com implementações do mesmo algoritmo baseadas em métodos de modelação mais simples. Para concluir, o controlador proposto será implementado num System-on-Chip baseado no core ARM Cortex-M4. Com o propósito de facilitar a realização de testes de implementação de algoritmos de controlo em sistemas embutidos, será apresentada também uma plataforma baseada numa arquitetura Processor-In-the-Loop, que permitirá avaliar a execução do algoritmo proposto em sistemas computacionais com recursos limitados, aferindo a existência de possíveis limitações antes da sua aplicação em cenários reais. A validade do novo método proposto é avaliada em dois cenários de simulação comummente utilizados em testes de sistemas de controlo não-lineares: no Controlo da Temperatura de uma Cuba de Fermentação e no Controlo do Nível de Líquidos num Sistema de Tanques Acoplados. É demonstrado que o algoritmo de controlo desenvolvido permite uma melhoria da performance dos processos supramencionados, particularmente em casos de mudança rápida dos regimes de funcionamento e na presença de perturbações ao processo não medidas.The development of an autonomous system capable of matching human knowledge and learning capabilities embedded in a compact yet transparent way has been one of the most sought milestones of Artificial Intelligence since the invention of the first mechanical general purpose computers. Such accomplishment is yet to come but, in its pursuit, important contributions to the state-of-the-art of current technology have been made. Fuzzy Logic is one of such, supporting some of the most used frameworks for embedding human-like knowledge in computational systems. The theory of Fuzzy Logic overcame some of the difficulties that the inherent uncertainty in information representations poses to the development of computational systems. However, it does present some limitations so, aiming to further extend its capabilities, several improvements over its original formalization have been proposed over the years such as Type-2 Fuzzy Logic - one of its most recent advances. The additional degrees of freedom of Type-2 Fuzzy Logic are showing greater potential to supplant its original counterpart, especially in complex non-linear modeling tasks. One of its main outcomes is its capability of improving the developed model’s robustness without necessarily increasing its dimensionality comparatively to a Type-1 Fuzzy Model counterpart. Such feature is particularly advantageous if one considers these model as a support for developing control systems capable of maintaining a process’s optimal performance over changing operating conditions. However, state-of-the art model-based control theory does not seem to be taking full advantage of the improvements achieved with the development of Type-2 Fuzzy Logic based models. Therefore, this thesis proposes to address this problem by developing a Model Predictive Control system supported by Interval Type-2 Takagi- Sugeno Fuzzy Models. To accomplish this goal, four main research directions are covered in this work.Firstly, a simpler method for training a Type-2 Takagi-Sugeno Fuzzy Model focused on two main paradigms is proposed: maintaining a meaningful interpretation of the uncertainty intervals embedded over an estimated Type-1 Fuzzy Model; ensuring the validity of several locally linear models that constitute the Takagi-Sugeno structure in order to make them suitable for model-based control approaches. Based on the developed model, a multi-step ahead estimation of the process behavior is extrapolated. However, as Takagi-Sugeno Fuzzy Models establish a trade-off between accuracy and computational complexity when used as a non-linear process approximation, it is proposed to apply the principles of Type-2 Fuzzy Logic to reduce the influence of modeling uncertainties on the obtained estimations by adjusting the model parameters’ uncertainty intervals. Supported by the developed Type-2 Takagi-Sugeno Fuzzy Model, a locally linear approximation of each current operation point is used to obtain the optimal control law over a prediction horizon according to the principles of Generalized Predictive Control - one of the most used Model Predictive Control algorithms in Industry. The improvements in terms of closed loop tracking performance and robustness to unmodeled operation conditions are then assessed comparatively to Generalized Predictive Control implementations based on simpler modeling approaches. Ultimately, the proposed control system is implemented in a general purpose System-on-a-Chip based on a ARM Cortex-M4 core. A Processor-In-the-Loop testing framework, developed to support the implementation of control loops in embedded systems, is used to evaluate the algorithm’s turnaround time when executed in such computationally constrained platform, assessing its possible limitations before deployment in real application scenarios. The applicability of the new methods introduced in this thesis is illustrated in two simulated processes commonly used in non-linear control benchmarking: the Temperature Control of a Fermentation Reactor and the Liquid Level Control of a Coupled Tanks System. It is shown that the developed control system achieves an improved closed loop performance of the above mentioned processes, particularly in the cases of quick changes in the operation regime and in presence of unmeasured external disturbances

Interval type-2 Atanassov-intuitionistic fuzzy logic for uncertainty modelling

This thesis investigates a new paradigm for uncertainty modelling by employing a new class of type-2 fuzzy logic system that utilises fuzzy sets with membership and non-membership functions that are intervals. Fuzzy logic systems, employing type-1 fuzzy sets, that mark a shift from computing with numbers towards computing with words have made remarkable impacts in the field of artificial intelligence. Fuzzy logic systems of type-2, a generalisation of type-1 fuzzy logic systems that utilise type-2 fuzzy sets, have created tremendous advances in uncertainty modelling. The key feature of the type-2 fuzzy logic systems, with particular reference to interval type-2 fuzzy logic systems, is that the membership functions of interval type-2 fuzzy sets are themselves fuzzy. These give interval type-2 fuzzy logic systems an advantage over their type-1 counterparts which have precise membership functions. Whilst the interval type-2 fuzzy logic systems are effective in modelling uncertainty, they are not able to adequately handle an indeterminate/neutral characteristic of a set, because interval type-2 fuzzy sets are only specified by membership functions with an implicit assertion that the non-membership functions are complements of the membership functions (lower or upper). In a real life scenario, it is not necessarily the case that the non-membership function of a set is complementary to the membership function. There may be some degree of hesitation arising from ignorance or a complete lack of interest concerning a particular phenomenon. Atanassov intuitionistic fuzzy set, another generalisation of the classical fuzzy set, captures this thought process by simultaneously defining a fuzzy set with membership and non-membership functions such that the sum of both membership and non-membership functions is less than or equal to 1. In this thesis, the advantages of both worlds (interval type-2 fuzzy set and Atanassov intuitionistic fuzzy set) are explored and a new and enhanced class of interval type-2 fuzzy set namely, interval type-2 Atanassov intuitionistic fuzzy set, that enables hesitation, is introduced. The corresponding fuzzy logic system namely, interval type-2 Atanassov intuitionistic fuzzy logic system is rigorously and systematically formulated. In order to assess this thesis investigates a new paradigm for uncertainty modelling by employing a new class of type-2 fuzzy logic system that utilises fuzzy sets with membership and non-membership functions that are intervals. Fuzzy logic systems, employing type-1 fuzzy sets, that mark shift from computing with numbers towards computing with words have made remarkable impacts in the field of artificial intelligence. Fuzzy logic systems of type-2, a generalisation of type-1 fuzzy logic systems that utilise type-2 fuzzy sets, have created tremendous advances in uncertainty modelling. The key feature of the type-2 fuzzy logic systems, with particular reference to interval type-2 fuzzy logic systems, is that the membership functions of interval type-2 fuzzy sets are themselves fuzzy. These give interval type-2 fuzzy logic systems an advantage over their type-1 counterparts which have precise membership functions. Whilst the interval type-2 fuzzy logic systems are effective in modelling uncertainty, they are not able to adequately handle an indeterminate/neutral characteristic of a set, because interval type-2 fuzzy sets are only specified by membership functions with an implicit assertion that the non-membership functions are complements of the membership functions (lower or upper). In a real life scenario, it is not necessarily the case that the non-membership function of a set is complementary to the membership function. There may be some degree of hesitation arising from ignorance or a complete lack of interest concerning a particular phenomenon. Atanassov intuitionistic fuzzy set, another generalisation of the classical fuzzy set, captures this thought process by simultaneously defining a fuzzy set with membership and non-membership functions such that the sum of both membership and non-membership functions is less than or equal to 1. In this thesis, the advantages of both worlds (interval type-2 fuzzy set and Atanassov intuitionistic fuzzy set) are explored and a new and enhanced class of interval type-2 fuzz set namely, interval type-2 Atanassov intuitionistic fuzzy set, that enables hesitation, is introduced. The corresponding fuzzy logic system namely, interval type-2 Atanassov intuitionistic fuzzy logic system is rigorously and systematically formulated. In order to assess the viability and efficacy of the developed framework, the possibilities of the optimisation of the parameters of this class of fuzzy systems are rigorously examined. First, the parameters of the developed model are optimised using one of the most popular fuzzy logic optimisation algorithms such as gradient descent (first-order derivative) algorithm and evaluated on publicly available benchmark datasets from diverse domains and characteristics. It is shown that the new interval type-2 Atanassov intuitionistic fuzzy logic system is able to handle uncertainty well through the minimisation of the error of the system compared with other approaches on the same problem instances and performance criteria. Secondly, the parameters of the proposed framework are optimised using a decoupledextended Kalman filter (second-order derivative) algorithm in order to address the shortcomings of the first-order gradient descent method. It is shown statistically that the performance of this new framework with fuzzy membership and non-membership functions is significantly better than the classical interval type-2 fuzzy logic systems which have only the fuzzy membership functions, and its type-1 counterpart which are specified by single membership and non-membership functions. The model is also assessed using a hybrid learning of decoupled extended Kalman filter and gradient descent methods. The proposed framework with hybrid learning algorithm is evaluated by comparing it with existing approaches reported in the literature on the same problem instances and performance metrics. The simulation results have demonstrated the potential benefits of using the proposed framework in uncertainty modelling. In the overall, the fusion of these two concepts (interval type-2 fuzzy logic system and Atanassov intuitionistic fuzzy logic system) provides a synergistic capability in dealing with imprecise and vague information

Interval type-2 Atanassov-intuitionistic fuzzy logic for uncertainty modelling

This thesis investigates a new paradigm for uncertainty modelling by employing a new class of type-2 fuzzy logic system that utilises fuzzy sets with membership and non-membership functions that are intervals. Fuzzy logic systems, employing type-1 fuzzy sets, that mark a shift from computing with numbers towards computing with words have made remarkable impacts in the field of artificial intelligence. Fuzzy logic systems of type-2, a generalisation of type-1 fuzzy logic systems that utilise type-2 fuzzy sets, have created tremendous advances in uncertainty modelling. The key feature of the type-2 fuzzy logic systems, with particular reference to interval type-2 fuzzy logic systems, is that the membership functions of interval type-2 fuzzy sets are themselves fuzzy. These give interval type-2 fuzzy logic systems an advantage over their type-1 counterparts which have precise membership functions. Whilst the interval type-2 fuzzy logic systems are effective in modelling uncertainty, they are not able to adequately handle an indeterminate/neutral characteristic of a set, because interval type-2 fuzzy sets are only specified by membership functions with an implicit assertion that the non-membership functions are complements of the membership functions (lower or upper). In a real life scenario, it is not necessarily the case that the non-membership function of a set is complementary to the membership function. There may be some degree of hesitation arising from ignorance or a complete lack of interest concerning a particular phenomenon. Atanassov intuitionistic fuzzy set, another generalisation of the classical fuzzy set, captures this thought process by simultaneously defining a fuzzy set with membership and non-membership functions such that the sum of both membership and non-membership functions is less than or equal to 1. In this thesis, the advantages of both worlds (interval type-2 fuzzy set and Atanassov intuitionistic fuzzy set) are explored and a new and enhanced class of interval type-2 fuzzy set namely, interval type-2 Atanassov intuitionistic fuzzy set, that enables hesitation, is introduced. The corresponding fuzzy logic system namely, interval type-2 Atanassov intuitionistic fuzzy logic system is rigorously and systematically formulated. In order to assess this thesis investigates a new paradigm for uncertainty modelling by employing a new class of type-2 fuzzy logic system that utilises fuzzy sets with membership and non-membership functions that are intervals. Fuzzy logic systems, employing type-1 fuzzy sets, that mark shift from computing with numbers towards computing with words have made remarkable impacts in the field of artificial intelligence. Fuzzy logic systems of type-2, a generalisation of type-1 fuzzy logic systems that utilise type-2 fuzzy sets, have created tremendous advances in uncertainty modelling. The key feature of the type-2 fuzzy logic systems, with particular reference to interval type-2 fuzzy logic systems, is that the membership functions of interval type-2 fuzzy sets are themselves fuzzy. These give interval type-2 fuzzy logic systems an advantage over their type-1 counterparts which have precise membership functions. Whilst the interval type-2 fuzzy logic systems are effective in modelling uncertainty, they are not able to adequately handle an indeterminate/neutral characteristic of a set, because interval type-2 fuzzy sets are only specified by membership functions with an implicit assertion that the non-membership functions are complements of the membership functions (lower or upper). In a real life scenario, it is not necessarily the case that the non-membership function of a set is complementary to the membership function. There may be some degree of hesitation arising from ignorance or a complete lack of interest concerning a particular phenomenon. Atanassov intuitionistic fuzzy set, another generalisation of the classical fuzzy set, captures this thought process by simultaneously defining a fuzzy set with membership and non-membership functions such that the sum of both membership and non-membership functions is less than or equal to 1. In this thesis, the advantages of both worlds (interval type-2 fuzzy set and Atanassov intuitionistic fuzzy set) are explored and a new and enhanced class of interval type-2 fuzz set namely, interval type-2 Atanassov intuitionistic fuzzy set, that enables hesitation, is introduced. The corresponding fuzzy logic system namely, interval type-2 Atanassov intuitionistic fuzzy logic system is rigorously and systematically formulated. In order to assess the viability and efficacy of the developed framework, the possibilities of the optimisation of the parameters of this class of fuzzy systems are rigorously examined. First, the parameters of the developed model are optimised using one of the most popular fuzzy logic optimisation algorithms such as gradient descent (first-order derivative) algorithm and evaluated on publicly available benchmark datasets from diverse domains and characteristics. It is shown that the new interval type-2 Atanassov intuitionistic fuzzy logic system is able to handle uncertainty well through the minimisation of the error of the system compared with other approaches on the same problem instances and performance criteria. Secondly, the parameters of the proposed framework are optimised using a decoupledextended Kalman filter (second-order derivative) algorithm in order to address the shortcomings of the first-order gradient descent method. It is shown statistically that the performance of this new framework with fuzzy membership and non-membership functions is significantly better than the classical interval type-2 fuzzy logic systems which have only the fuzzy membership functions, and its type-1 counterpart which are specified by single membership and non-membership functions. The model is also assessed using a hybrid learning of decoupled extended Kalman filter and gradient descent methods. The proposed framework with hybrid learning algorithm is evaluated by comparing it with existing approaches reported in the literature on the same problem instances and performance metrics. The simulation results have demonstrated the potential benefits of using the proposed framework in uncertainty modelling. In the overall, the fusion of these two concepts (interval type-2 fuzzy logic system and Atanassov intuitionistic fuzzy logic system) provides a synergistic capability in dealing with imprecise and vague information

Development of advanced autonomous learning algorithms for nonlinear system identification and control

Identification of nonlinear dynamical systems, data stream analysis, etc. is usually handled by autonomous learning algorithms like evolving fuzzy and evolving neuro-fuzzy systems (ENFSs). They are characterized by the single-pass learning mode and open structure-property. Such features enable their effective handling of fast and rapidly changing natures of data streams. The underlying bottleneck of ENFSs lies in its design principle, which involves a high number of free parameters (rule premise and rule consequent) to be adapted in the training process. This figure can even double in the case of the type-2 fuzzy system. From this literature gap, a novel ENFS, namely Parsimonious Learning Machine (PALM) is proposed in this thesis. To reduce the number of network parameters significantly, PALM features utilization of a new type of fuzzy rule based on the concept of hyperplane clustering, where it has no rule premise parameters. PALM is proposed in both type-1 and type-2 fuzzy systems where all of them characterize a fully dynamic rule-based system. Thus, it is capable of automatically generating, merging, and tuning the hyperplane-based fuzzy rule in a single-pass manner. Moreover, an extension of PALM, namely recurrent PALM (rPALM), is proposed and adopts the concept of teacher-forcing mechanism in the deep learning literature. The efficacy of both PALM and rPALM have been evaluated through numerical study with data streams and to identify nonlinear unmanned aerial vehicle system. The proposed models showcase significant improvements in terms of computational complexity and the number of required parameters against several renowned ENFSs while attaining comparable and often better predictive accuracy. The ENFSs have also been utilized to develop three autonomous intelligent controllers (AICons) in this thesis. They are namely Generic (G) controller, Parsimonious controller (PAC), and Reduced Parsimonious Controller (RedPAC). All these controllers start operating from scratch with an empty set of fuzzy rules, and no offline training is required. To cope with the dynamic behavior of the plant, these controllers can add, merge or prune the rules on demand. Among three AICons, the G-controller is built by utilizing an advanced incremental learning machine, namely Generic Evolving Neuro-Fuzzy Inference System. The integration of generalized adaptive resonance theory provides a compact structure of the G-controller. Consequently, the faster evolution of structure is witnessed, which lowers its computational cost. Another AICon namely, PAC is rooted with PALM's architecture. Since PALM has a dependency on user-defined thresholds to adapt the structure, these thresholds are replaced with the concept of bias- variance trade-off in PAC. In RedPAC, the network parameters have further reduced in contrast with PALM-based PAC, where the number of consequent parameters has reduced to one parameter per rule. These AICons work with very minor expert domain knowledge and developed by incorporating the sliding mode control technique. In G-controller and RedPAC, the control law and adaptation laws for the consequent parameters are derived from the SMC algorithm to establish a stable closed-loop system, where the stability of these controllers are guaranteed by using the Lyapunov function and the uniform asymptotic convergence of tracking error to zero is witnessed through the implication of an auxiliary robustifying control term. While using PAC, the boundedness and convergence of the closed-loop control system's tracking error and the controller's consequent parameters are confirmed by utilizing the LaSalle-Yoshizawa theorem. Their efficacy is evaluated by observing various trajectory tracking performance of unmanned aerial vehicles. The accuracy of these controllers is comparable or better than the benchmark controllers where the proposed controllers incur significantly fewer parameters to attain similar or better tracking performance

Advances in fuzzy rule-based system for pattern classification

Ph.DDOCTOR OF PHILOSOPH

Improving risk-adjusted performance in high-frequency trading: The role of fuzzy logic systems

In recent years, algorithmic and high-frequency trading have been the subject of increasing risk concerns. A general theme that we adopt in this thesis is that trading practitioners are predominantly interested in risk-adjusted performance. Likewise, regulators are demanding stricter risk controls. First, we scrutinise conventional AI model design approaches with the aim to increase the risk-adjusted trading performance of the proposed fuzzy logic models. We show that applying risk-return objective functions and accounting for transaction costs improve out-of-sample results. Our experiments identify that neuro-fuzzy models exhibit superior performance stability across multiple risk regimes when compared to popular neural network models identified in AI literature. Moreover, we propose an innovative ensemble model approach which combines multiple risk-adjusted objective functions and dynamically adapts risk- tolerance according to time-varying risk. Next, we extend our findings to the money management aspects of trading algorithms. We introduce an effective fuzzy logic approach which dynamically discriminates across different regions in the trend and volatility space. The model prioritises higher performing regions at an intraday level and adapts capital allocation policies with the objective to maximise global risk-adjusted performance. Finally, we explore trading improvements that can be attained by advancing our type-1 fuzzy logic ideas to higher order fuzzy systems in view of the increased noise (uncertainty) that is inherent in high-frequency data. We propose an innovative approach to design type-2 models with minimal increase in design and computational complexity. As a further step, we identify a relationship between the increased trading performance benefits of the proposed type-2 model and higher levels of trading frequencies. In conclusion, this thesis sets a framework for practitioners, researchers and regulators in the design of fuzzy logic systems for better management of risk in the field of algorithmic and high-frequency trading

Join and Meet Operations for Interval-Valued Complex Fuzzy Logic

DMU Interdisciplinary Group in Intelligent Transport SystemsInterval-valued complex fuzzy logic is able to handle scenarios where both seasonality and uncertainty feature. The interval-valued complex fuzzy set is defined, and the interval valued complex fuzzy inferencing system outlined. Highly pertinent to complex fuzzy logic operations is the concept of rotational invariance, which is an intuitive and desirable characteristic. Interval-valued complex fuzzy logic is driven by interval-valued join and meet operations. Four pairs of alternative algorithms for these operations are specified; three pairs possesses the attribute of rotational invariance, whereas the other pair lacks this characteristic

Intelligent Control Strategies for an Autonomous Underwater Vehicle

The dynamic characteristics of autonomous underwater vehicles (AUVs) present a control problem that classical methods cannot often accommodate easily. Fundamentally, AUV dynamics are highly non-linear, and the relative similarity between the linear and angular velocities about each degree of freedom means that control schemes employed within other flight vehicles are not always applicable. In such instances, intelligent control strategies offer a more sophisticated approach to the design of the control algorithm. Neurofuzzy control is one such technique, which fuses the beneficial properties of neural networks and fuzzy logic in a hybrid control architecture. Such an approach is highly suited to development of an autopilot for an AUV. Specifically, the adaptive network-based fuzzy inference system (ANFIS) is discussed in Chapter 4 as an effective new approach for neurally tuning course-changing fuzzy autopilots. However, the limitation of this technique is that it cannot be used for developing multivariable fuzzy structures. Consequently, the co-active ANFIS (CANFIS) architecture is developed and employed as a novel multi variable AUV autopilot within Chapter 5, whereby simultaneous control of the AUV yaw and roll channels is achieved. Moreover, this structure is flexible in that it is extended in Chapter 6 to perform on-line control of the AUV leading to a novel autopilot design that can accommodate changing vehicle pay loads and environmental disturbances. Whilst the typical ANFIS and CANFIS structures prove effective for AUV control system design, the well known properties of radial basis function networks (RBFN) offer a more flexible controller architecture. Chapter 7 presents a new approach to fuzzy modelling and employs both ANFIS and CANFIS structures with non-linear consequent functions of composite Gaussian form. This merger of CANFIS and a RBFN lends itself naturally to tuning with an extended form of the hybrid learning rule, and provides a very effective approach to intelligent controller development.The Sea Systems and Platform Integration Sector, Defence Evaluation and Research Agency, Winfrit