Fuzzy Controllers

Trying to meet the requirements in the field, present book treats different fuzzy control architectures both in terms of the theoretical design and in terms of comparative validation studies in various applications, numerically simulated or experimentally developed. Through the subject matter and through the inter and multidisciplinary content, this book is addressed mainly to the researchers, doctoral students and students interested in developing new applications of intelligent control, but also to the people who want to become familiar with the control concepts based on fuzzy techniques. Bibliographic resources used to perform the work includes books and articles of present interest in the field, published in prestigious journals and publishing houses, and websites dedicated to various applications of fuzzy control. Its structure and the presented studies include the book in the category of those who make a direct connection between theoretical developments and practical applications, thereby constituting a real support for the specialists in artificial intelligence, modelling and control fields

Fitted Q-Function Control Methodology Based on Takagi-Sugeno Systems

"© 2020 IEEE. Personal use of this material is permitted. Permissíon from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertisíng or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works."[EN] This paper presents a combined identification/ Q-function fitting methodology that involves identification of a Takagi-Sugeno model, computation of (sub)optimal controllers from linear matrix inequalities (LMIs), and subsequent data-based fitting of the Q-function via monotonic optimization. The LMI-based initialization provides a conservative solution, but it is a sensible starting point to avoid convergence/local-minima issues in raw data-based fitted Q-iteration or Bellman residual minimization. An inverted-pendulum experimental case study illustrates the approach.This work was supported in part by the Spanish Ministry of Economy and European Union (AEI/FEDER, UE) under Grant DPI2016-81002-R and in part by the Government of Ecuador through the Ph.D. Grant SENESCYT.Diaz-Iza, HP.; Armesto, L.; Sala, A. (2020). Fitted Q-Function Control Methodology Based on Takagi-Sugeno Systems. IEEE Transactions on Control Systems Technology. 28(2):477-488. https://doi.org/10.1109/TCST.2018.2885689S47748828

Real time control of nonlinear dynamic systems using neuro-fuzzy controllers

The problem of real time control of a nonlinear dynamic system using intelligent control techniques is considered. The current trend is to incorporate neural networks and fuzzy logic into adaptive control strategies. The focus of this work is to investigate the current neuro-fuzzy approaches from literature and adapt them for a specific application. In order to achieve this objective, an experimental nonlinear dynamic system is considered. The motivation for this comes from the desire to solve practical problems and to create a test-bed which can be used to test various control strategies. The nonlinear dynamic system considered here is an unstable balance beam system that contains two fluid tanks, one at each end, and the balance is achieved by pumping the fluid back and forth from the tanks. A popular approach, called ANFIS (Adaptive Networks-based Fuzzy Inference Systems), which combines the structure of fuzzy logic controllers with the learning aspects from neural networks is considered as a basis for developing novel techniques, because it is considered to be one of the most general framework for developing adaptive controllers. However, in the proposed new method, called Generalized Network-based Fuzzy Inferencing Systems (GeNFIS), more conventional fuzzy schemes for the consequent part are used instead of using what is called the Sugeno type rules. Moreover, in contrast to ANFIS which uses a full set of rules, GeNFIS uses only a limited number of rules based on certain expert knowledge. GeNFIS is tested on the balance beam system, both in a real- time actual experiment and the simulation, and is found to perform better than a comparable ANFIS under supervised learning. Based on these results, several modifications of GeNFIS are considered, for example, synchronous defuzzification through triangular as well as bell shaped membership functions. Another modification involves simultaneous use of Sugeno type as well as conventional fuzzy schemes for the consequent part, in an effort to create a more flexible framework. Results of testing different versions of GeNFIS on the balance beam system are presented

Adaptive dynamic programming with eligibility traces and complexity reduction of high-dimensional systems

This dissertation investigates the application of a variety of computational intelligence techniques, particularly clustering and adaptive dynamic programming (ADP) designs especially heuristic dynamic programming (HDP) and dual heuristic programming (DHP). Moreover, a one-step temporal-difference (TD(0)) and n-step TD (TD(λ)) with their gradients are utilized as learning algorithms to train and online-adapt the families of ADP. The dissertation is organized into seven papers. The first paper demonstrates the robustness of model order reduction (MOR) for simulating complex dynamical systems. Agglomerative hierarchical clustering based on performance evaluation is introduced for MOR. This method computes the reduced order denominator of the transfer function by clustering system poles in a hierarchical dendrogram. Several numerical examples of reducing techniques are taken from the literature to compare with our work. In the second paper, a HDP is combined with the Dyna algorithm for path planning. The third paper uses DHP with an eligibility trace parameter (λ) to track a reference trajectory under uncertainties for a nonholonomic mobile robot by using a first-order Sugeno fuzzy neural network structure for the critic and actor networks. In the fourth and fifth papers, a stability analysis for a model-free action-dependent HDP(λ) is demonstrated with batch- and online-implementation learning, respectively. The sixth work combines two different gradient prediction levels of critic networks. In this work, we provide a convergence proofs. The seventh paper develops a two-hybrid recurrent fuzzy neural network structures for both critic and actor networks. They use a novel n-step gradient temporal-difference (gradient of TD(λ)) of an advanced ADP algorithm called value-gradient learning (VGL(λ)), and convergence proofs are given. Furthermore, the seventh paper is the first to combine the single network adaptive critic with VGL(λ). --Abstract, page iv

Intelligent System Synthesis for Dynamic Locomotion Behavior in Multi-legged Robots

Robot technology has been implemented in many fields of our life, such as entertainment, security, rescue, rehabilitation, social life, the military, and etc. Multi-legged robot always exist in many fields, therefore it is important to be developed. Motion capabilities of the robot will be a main focus to be developed. Current development or conventional model of motion capabilities have several issues in saturation of development. There are some limitation in dynamic factors such as, locomotion generator, flexibility of motion planning, and smoothness of movement. Therefore, in this research, natural based computation are implemented as the basic model. There are three subsystems to be developed and integrated, (1) locomotion behavior model, (2) stability behavior model, and (3) motion planning model. Since individual people has different walking behavior in each walking direction and walking speed, locomotion behavior learning model of omni-directional bio-inspired locomotion which is generating different walking behavior in different walking provision are required to be developed. Step length in sagital and coronal direction, and degree of turning are considered parameters in walking provision. In proposed omni-directional walking model, interconnection structures composed by 16 neurons where 1 leg is represented by 4 joints and 1 joint is represented by 2 motor neurons. In order to acquire walking behavior in certain walking provision, the interconnection structure is optimized by multi-objectives evolutionary algorithm. For acquiring the diversity of references, several optimized interconnection structures are generated in optimization processes in different walking provisions. Learning models are proposed for solving non-linearity of relationship between walking input and walking output representing the synaptic weight of interconnection structure, where one learning model representing one walking parameter. Furthermore, by using optimized model, walking behavior can be generated with unsealed walking provision. Smooth walking transition with low error of desired walking provision was proved based on several numerical experiments in physical computer simulation. In stability behavior model, neuro-based push recovery controller is applied in multi-legged robot in order to keep the stability with minimum energy required. There are three motion patterns in individual people behavior when it gets external perturbation, those are ankle behavior, hip behavior, and step behavior. We propose a new model of Modular Recurrent Neural Network (MRNN) for performing online learning system in each motion behavior. MRNN consists of several recurrent neural networks (RNNs) working alternatively depending on the condition. MRNN performs online learning process of each motion behavior controller independently. The aim of push recovery controller is to manage the motion behavior controller by minimizing the energy required for responding to the external perturbation. This controller selects the appropriate motion behavior and adjusts the gain that represent the influence of the motion behavior to certain push disturbance based on behavior graphs which is generated by adaptive regression spline. We applied the proposed controller to the humanoid robot that has small footprint in open dynamics engine. Experimental result shows the effectiveness of the push controller stabilizing the external perturbation with minimum energy required. Proposed motion planning model presents a natural mechanism of the human brain for generating a dynamic path planning in 3-D rough terrain. The proposed model not only emphasizes the inner state process of the neuron but also the development process of the neurons in the brain. There are two information transmission processes in this proposed model, the forward transmission activity for constructing the neuron connections to find the possible way and the synaptic pruning activity with backward neuron transmission for finding the best pathway from current position to target position and reducing inefficient neuron with its synaptic connections. In order to respond and avoid the unpredictable obstacle, dynamic path planning is also considered in this proposed model. An integrated system for applying the proposed model in the actual experiments is also presented. In order to confirm the effectiveness of the proposed model, we applied the integrated system in the pathway of a four-legged robot on rough terrain in computer simulation. For analyzing and proving the flexibility of proposed model, unpredictable collision is also performed in those experiments. The model can find the best pathway and facilitate the safe movement of the robot. When the robot found an unpredictable collision, the path planner dynamically changed the pathway. The proposed path planning model is capable to be applied in further advance implementation. In order to implement the motion capabilities in real cases, all subsystem should be integrated into one interconnected motion capabilities model. We applied small quadruped robot equipped with IMU, touch sensor, and dual ultrasonic sensor for performing motion planning in real terrain from starting point to goal point. Before implemented, topological map is generated by Kinect camera. In this implementation, all subsystem were analyzed and performed well and the robot able to stop in the goal point. These implementation proved the effectiveness of the system integration, the motion planning model is able to generate safe path planning, the locomotion model is able to generate flexible movement depending on the walking provision from motion planning model, and the stability model can stabilize the robot on rough terrain. Generally, the proposed model can be expected to bring a great contribution to the motion capabilities development and can be used as alternative model for acquiring the dynamism and efficient model in the future instead of conventional model usage. In the future, the proposed model can be applied into any legged robot as navigation, supporter, or rescue robot in unstable environmental condition. In addition, we will realize a cognitive locomotion that generates multiple gaits depending on the 3 aspects, embodiment, locomotion generator, and cognition model. A dynamic neuro-locomotion integrated with internal and external sensory information for correlating with the environmental condition will be designed.ロボット技術は、エンターテイメント、セキュリティ、救助、リハビリ、社会生活、軍事などの様々な生活分野に実現さている。多脚ロポットは常に多くの分野に存在するため開発することが重要である。ロボットの運動能力が開発の主要となっている。現状の開発されている動作能力は,飽和状態にある。いくつかの動的な要因により、歩行生成器、動作計画の柔軟性、および動作の滑らかさ等に制限がある。そこで、本研究では、基本的なモデルとして自然計算に基づく方法論を実装する、また、本研究では、歩行動作モデル、安定動作モデル、や運動計画モデルからなる3つのサブシステムを開発し統合する。人間は歩行方向と速度に応じて歩行動作が異なるため、異なる歩行軸では異なる歩行動作を生成するという全方位生物的な運動の歩行動作学習モデルが開発には要求される。球欠および制御方向のステップ長や旋回の度合いは,歩行軸のパラメータとして考慮される。提案した全方位歩行モデルでは,1肢につき16個のニューロンによって構成される相互接続構造を4つの関節によって表現する。また、1つの関節は,2個のモータニューロンによって表現する。一定の歩行軸での歩行動作を獲得するために,本研究では,多目的進化アルゴリズムによって最適化を行う。提案手法では、参照点の多様性を獲得するために,異なる歩行軸においていくつかの最適な相互接続構造が生成される。相互接続構造のシナプス重みを表現している歩行入力と出力間の非線形な関係を解くための学習モデルを構築する。本手法では,1つの学習モデルが1つの歩行パラメータで表現され、最適化されたモデルを用いることにより,歩行動作は,スケーリングされていない歩行軸を生成することが可能となる,物理演算シミュレーションを用いた実験により,誤差の少ない歩行軸の滑らかな歩行遷移を本実験では示している。安定動作モデルでは、必要最小限のエネルギーで安定性を維持するため多足歩行ロボットにニューロベースプッシュリカバリ制御器を適用した。外力をを受けたとき,人間の行動には足首の動作・股関節の動作・踏み動作の3つの動作パターンが存在する。本研究では,各運動動作におけるオンライン学習システムを実現するために、モジュラーリカレントニューラルネットワーク(MRNN)を用いた新たな学習モデルを提案する。MRNNは状況に応じて選択される複数のリカレントニューラルネットワーク(RNN)によって構成される。MRNNは各運動動作コントローラのオンライン学習プロセスを独立して実行する。プッシュリカバリ制御器の目的は、外乱に応じてエネルギー最小化を行うことによって運動動作制御器を管理することである。この制御器は適切な運動動作を選択し,適応回帰スプラインにより生成された動作グラフに基づき押し動作に対して最も影響を及ぼす運動動作のゲインの調整を行う。提案した制御器をOpen Dynamics Engine(ODE)上で小さな足の長さを持つヒューマノイドロボットに適用し,必要最小限のエネルギーで外力に対して安定させるプッシュリカバリ制御器の有効性を示している。3次元の不整地における動的な経路計画を生成するために,人間の自然な脳機能に基づいた動作計画手法を提案する。本モデルは、ニューロンの内部状態過程だけでなく、脳内のニューロンの発達過程も重視している。本モデルは二つのアルゴリズムに構成される。1つは、通過可能な道を見つけるために構築される接続的なニューロン活動である順方向伝達活動であり,もう1つは、現在位置から最適経路を見つけるために、シナプス結合を用いて非効率的なニューロンを減少させる逆方向にニューロン伝達を行うシナプスプルーニング活動である。また,予測不可能な衝突を回避するために,動的な経路計画も実行される。さらに、実環境において提案されたモデルを実現するための統合システムも提示される。提案モデルの有効性を検証するために,コンピュータシミュレーション上で、不整地環境の4足歩行ロボットに関するシミュレーション環境を実装した。これらの実験では,予測不能な衝突に関する実験も行った。本モデルは、最適経路を見つけ出しロボットの安全な移動を実現できた。さらに、ロボットが予測できない衝突を検出した場合,経路計画アルゴリズムが経路を動的に変更可能であることを示している。これらのことから、提案された経路計画モデルはさらなる先進的な展開が実現可能であると考えられる。実環境における運動能力を実装するためには、すべてのサブシステムを1つの運動能力モデルに統合する必要がある。そこで本研究では、IMU、タッチセンサ、2つの超音波センサを搭載した小型の4足歩行ロポットを用いた実環境において出発地点から目的地点までの運動計画を行った、本実装では、3次元距離計測センサであるKinecを用い3次元空間の位相構造を生成する。また、本実装では、すべてのサブシステムが分析され、ロボットは目的地点で停止することができた。さらに、安全な経路計画を生成することができたことからシステム統合の有効性が確認できた。また、歩行モデルにより歩行軸に応じた柔軟な動きが生成されることで、この安定性モデルは不整地環撹でもロボットの歩行を安定させることができた。これらのことから、本提案モデルは運動能力への多大な貢献が期待され、ダイナミクスを獲得するための代替モデルとして使用することができ,現在よく使用されているモデルに代わる効率的なモデルとなることが考えられる。今後の課題としては,不安定な環境下におけるナビゲーション・支援・レスキューロボットといった任意の肢の数を持つ多足歩行ロボットへの本提案モデルの適用があげられる。さらに,身体性,歩行生成,認知モデルの3つの観点から複数の歩容を生成する認知的歩行を実現することを考えている。環境と相互作用するためのモデルとして、内界センサと外界センサ情報を統合した動的ニューロ歩行を実現する予定である。首都大学東京, 2018-03-25, 修士（工学）首都大学東

Hierarchical Optimization-Based Model Predictive Control for a Class of Discrete Fuzzy Large-Scale Systems Considering Time-Varying Delays and Disturbances

Altres ajuts: Acord transformatiu CRUE-CSICIn this manuscript, model predictive control for class of discrete fuzzy large-scale systems subjected to bounded time-varying delay and disturbances is studied. The considered method is Razumikhin for time-varying delay large-scale systems, in which it includes a Lyapunov function associated with the original non-augmented state space of system dynamics in comparison with the Krasovskii method. As a rule, the Razumikhin method has a perfect potential to avoid the inherent complexity of the Krasovskii method especially in the presence of large delays and disturbances. The considered large-scale system in this manuscript is decomposed into several subsystems, each of which is represented by a fuzzy Takagi-Sugeno (TS) model and the interconnection between any two subsystems is considered. Because the main section of the model predictive control is optimization, the hierarchical scheme is performed for the optimization problem. Furthermore, persistent disturbances are considered that robust positive invariance and input-to-state stability under such circumstances are studied. The linear matrix inequalities (LMIs) method is performed for our computations. So the closed-loop large-scale system is asymptotically stable. Ultimately, by two examples, the effectiveness of the proposed method is illustrated, and a comparison with other papers is made by remarks

Development of Self-Learning Type-2 Fuzzy Systems for System Identification and Control of Autonomous Systems

Modelling and control of dynamic systems are faced by multiple technical challenges, mainly due to the nature of uncertain complex, nonlinear, and time-varying systems. Traditional modelling techniques require a complete understanding of system dynamics and obtaining comprehensive mathematical models is not always achievable due to limited knowledge of the systems as well as the presence of multiple uncertainties in the environment. As universal approximators, fuzzy logic systems (FLSs), neural networks (NNs) and neuro-fuzzy systems have proved to be successful computational tools for representing the behaviour of complex dynamical systems. Moreover, FLSs, NNs and learning-based techniques have been gaining popularity for controlling complex, ill-defined, nonlinear, and time-varying systems in the face of uncertainties. However, fuzzy rules derived by experts can be too ad-hoc, and the performance is less than optimum. In other words, generating fuzzy rules and membership functions in fuzzy systems is a potential challenge especially for systems with many variables. Moreover, under the umbrella of FLSs, although type-1 fuzzy logic control systems (T1-FLCs) have been applied to control various complex nonlinear systems, they have limited capability to handle uncertainties. Aiming to accommodate uncertainties, type-2 fuzzy logic control systems (T2-FLCs) were established. This thesis aims to address the shortcomings of existing fuzzy techniques by utilisation of type-2 FLCs with novel adaptive capabilities. The first contribution of this thesis is a novel online system identification technique by means of a recursive interval type-2 Takagi-Sugeno fuzzy C-means clustering technique (IT2-TS-FC) to accommodate the footprint-of-uncertainties (FoUs). This development is meant to specifically address the shortcomings of type-1 fuzzy systems in capturing the footprint-of-uncertainties such as mechanical wear, rotor damage, battery drain and sensor and actuator faults. Unlike previous type-2 TS fuzzy models, the proposed method constructs two fuzzifiers (upper and lower) and two regression coefficients in the consequent part to handle uncertainties. The weighted least square method is employed to compute the regression coefficients. The proposed method is validated using two benchmarks, namely, real flight test data of a quadcopter drone and Mackey-Glass time series data. The algorithm has the capability to model uncertainties (e.g., noisy dataset). The second contribution of this thesis is the development of a novel self-adaptive interval type-2 fuzzy controller named the SAF2C for controlling multi-input multi-output (MIMO) nonlinear systems. The adaptation law is derived using sliding mode control (SMC) theory to reduce the computation time so that the learning process can be expedited by 80% compared to separate single-input single-output (SISO) controllers. The system employs the `Enhanced Iterative Algorithm with Stop Condition' (EIASC) type-reduction method, which is more computationally efficient than the `Karnik-Mendel' type-reduction algorithm. The stability of the SAF2C is proven using the Lyapunov technique. To ensure the applicability of the proposed control scheme, SAF2C is implemented to control several dynamical systems, including a simulated MIMO hexacopter unmanned aerial vehicle (UAV) in the face of external disturbance and parameter variations. The ability of SAF2C to filter the measurement noise is demonstrated, where significant improvement is obtained using the proposed controller in the face of measurement noise. Also, the proposed closed-loop control system is applied to control other benchmark dynamic systems (e.g., a simulated autonomous underwater vehicle and inverted pendulum on a cart system) demonstrating high accuracy and robustness to variations in system parameters and external disturbance. Another contribution of this thesis is a novel stand-alone enhanced self-adaptive interval type-2 fuzzy controller named the ESAF2C algorithm, whose type-2 fuzzy parameters are tuned online using the SMC theory. This way, we expect to design a computationally efficient adaptive Type-2 fuzzy system, suitable for real-time applications by introducing the EIASC type-reducer. The proposed technique is applied on a quadcopter UAV (QUAV), where extensive simulations and real-time flight tests for a hovering QUAV under wind disturbances are also conducted to validate the efficacy of the ESAF2C. Specifically, the control performance is investigated in the face of external wind gust disturbances, generated using an industrial fan. Stability analysis of the ESAF2C control system is investigated using the Lyapunov theory. Yet another contribution of this thesis is the development of a type-2 evolving fuzzy control system (T2-EFCS) to facilitate self-learning (either from scratch or from a certain predefined rule). T2-EFCS has two phases, namely, the structure learning and the parameters learning. The structure of T2-EFCS does not require previous information about the fuzzy structure, and it can start the construction of its rules from scratch with only one rule. The rules are then added and pruned in an online fashion to achieve the desired set-point. The proposed technique is applied to control an unmanned ground vehicle (UGV) in the presence of multiple external disturbances demonstrating the robustness of the proposed control systems. The proposed approach turns out to be computationally efficient as the system employs fewer fuzzy parameters while maintaining superior control performance

Fuzzy Systems

This book presents some recent specialized works of theoretical study in the domain of fuzzy systems. Over eight sections and fifteen chapters, the volume addresses fuzzy systems concepts and promotes them in practical applications in the following thematic areas: fuzzy mathematics, decision making, clustering, adaptive neural fuzzy inference systems, control systems, process monitoring, green infrastructure, and medicine. The studies published in the book develop new theoretical concepts that improve the properties and performances of fuzzy systems. This book is a useful resource for specialists, engineers, professors, and students

Optimized state feedback regulation of 3DOF helicopter system via extremum seeking

In this paper, an optimized state feedback regulation of a 3 degree of freedom (DOF) helicopter is designed via extremum seeking (ES) technique. Multi-parameter ES is applied to optimize the tracking performance via tuning State Vector Feedback with Integration of the Control Error (SVFBICE). Discrete multivariable version of ES is developed to minimize a cost function that measures the performance of the controller. The cost function is a function of the error between the actual and desired axis positions. The controller parameters are updated online as the optimization takes place. This method significantly decreases the time in obtaining optimal controller parameters. Simulations were conducted for the online optimization under both fixed and varying operating conditions. The results demonstrate the usefulness of using ES for preserving the maximum attainable performance