LEE- Kontrol ve Otomasyon Mühendisliği-Doktora
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ÖgeDiscrete-time adaptive control of port controlled hamiltonian systems(Fen Bilimleri Enstitüsü, 2020)In control theory, the design of the adaptive controllers in the discrete-time setting for nonlinear systems has been an interesting area of research. The adaptive controller deals with the problem of finding an appropriate and efficient control structure with an adaptation mechanism to preserve stability and an acceptable closed-loop performance in the existence of a considerable amount of uncertainties or time-varying parameters. It is well known that nonlinear systems are sensitive to disturbances, unknown noises, and parameter perturbations. For these kinds of perturbed systems, adaptive control theory is a powerful tool to establish compensation procedures in an effective way that automatically updates the controller to improve the performance of the controlled systems. This thesis study considers adaptive control of an important class of nonlinear systems so-called Port-controlled Hamiltonian systems (PCH) with uncertainty in their energy function and proposes adaptive discrete-time controllers with novel construction of parameter estimators for the multiplicative uncertainty case, the linearly parametrized case, and the nonlinearly parameterized case. The proposed method adopts the Interconnection and Damping Assignment Passivity-based control (IDA-PBC) as the control design method and the Immersion and Invariance (I&I) for parameter(s) estimation. Therefore, the two approaches, namely, the IDA-PBC and I&I techniques, are combined in a discrete-time framework such that all the trajectories of the closed-loop system are bounded, and system states successfully converge to the stable desired equilibrium points, namely the minimum of the desired energy function. As mentioned previously, the Immersion and Invariance (I&I) approach is considered to develop an automatic tuning mechanism for the adaptive IDA-PBC controller. To comply with I&I conditions, for each case, the estimation error dynamic is defined such that it includes a free design function of the system states, and then the parameter estimator is constructed by establishing a parameter update rule and by presenting a novel function for the mentioned free design function such that Lyapunov stability of the estimator error dynamics is ensured. This novel design function includes some parameters, that can vary in a determined range, to provide the ability to assign desired dynamics to the estimator error system. By replacing the uncertain terms with the values obtained by the I&I estimator, the closed-loop system is immersed in the desired closed-loop system which would be obtained with the IDA-PBC controller with true parameters. In the multiplicative uncertainty case, and as an initial formulation of this study, the uncertainties in energy function appear as multiplicative uncertainties to the gradient of the Hamiltonian function. Unlike the other two formulation cases, no specific perturbation is considered in the system parameters and instead, a general multiplicative uncertainty is presented to the gradient of the Hamiltonian function and thus the adaptive IDA-PBC controller is constructed considering this multiplicative uncertainty formulation. The I&I based estimator is designed by selecting an update rule and presenting a general structure for the free design function such that the estimator error dynamics are Lyapunov asymptotically stable. The proposed general structure includes a free parameter that enables to assign different desired dynamics to the estimator. By including the proposed estimator in the constructed adaptive IDA-PBC controller, the local asymptotic stability of the obtained closed-loop system is shown in a sufficiently large set. One underactuated Hamiltonian system example is considered. In the linear parameterized case, the uncertainties of system parameters appear linearly in the energy function and thus the uncertain system dynamics are formulated such that these uncertainties appear in linearly parameterized form in the gradient of the Hamiltonian function. By considering this formulation of the linear parameterization of the uncertain system parameters, the adaptive IDA-PBC controller is constructed. Since PCH is linearly parameterized in the proposed formulation, the gradient of the Hamiltonian function could be factorized in two terms such as one of the terms becomes a matrix that includes all the known terms of system states and system parameters while the other term is a vector of unknown parameters. The mentioned matrix can be a full column rank or not. In the case where this matrix is full rank, the Lyapunov asymptotic stability of the estimator is proved while the Lyapunov stability of the estimator is shown for the case when it is not full rank. It is also shown that, for the case of having not full rank matrix, the term representing the effect of uncertainties in the closed-loop system dynamics obtained with the IDA-PBC controller that uses the estimated parameters approaches to zero. Furthermore, the Lyapunov asymptotic stability of the obtained closed-loop system is shown in a sufficiently large local set either the matrix is full rank or not. For the I&I based estimator design, a general structure for the free design function that includes some free parameters is presented that makes the estimator error dynamics Lyapunov stable where these free parameters are in a determined specific range. So that, by selecting different values for these free parameters in the determined range, different desired dynamics can be assigned to the estimation of each unknown parameter. Three linearly parameterized examples are considered; two fully actuated systems (One has a formulation with a full rank matrix while the other has a formulation with a not full rank matrix), and one underactuated system. In the nonlinear parametrized case, the parameter uncertainties that appear nonlinearly in the energy function are considered. A proper formulation for uncertain system dynamics is presented such that the uncertainties appear in non-linearly parameterized form in the gradient of the Hamiltonian function and the adaptive IDA-PBC controller is constructed considering this formulation. The conditions on the Lyapunov asymptotic stability of the estimator dynamics are derived. Namely, it is proved that if these conditions are satisfied, the estimator error dynamics become asymptotically stable. Assuming these conditions are satisfied, local asymptotic stability of the closed-loop system, which is obtained when the proposed estimator is used with the adaptive IDA-PBC controller, in a sufficiently large set is proved. For the I&I based estimator design, a structure for the free design function of the estimator is proposed including some other free design functions to satisfy these conditions however it is seen that it is not easy to give general suggestions for these last free functions. It is concluded that for each example, a special selection of these functions is needed. Two nonlinearly parameterized examples are considered and proper selections of the free design functions in the proposed structure is performed. One of the example is a fully actuated mechanical system while the other one is under-actuated. The simulation results for each of the previously mentioned systems illustrated the effectiveness of the proposed adaptive controller in comparison to the non-adaptive controller for the same test conditions. The estimator successfully estimates the uncertain parameters and the adaptive IDA-PBC controller that utilizing these parameters stabilizes the closed-loop system and preserves the performance of the stable desired Hamiltonian systems.
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ÖgeAnalysis and design of general type-2 fuzzy logic controllers(Fen Bilimleri Enstitüsü, 2020)This thesis presents new interpretations on the design parameters of the general type-2 fuzzy logic controllers by investigating their internal structures, proposes novel systematic design approaches for the general type-2 fuzzy logic controllers based on comprehensive and comparative analyses, and validates theoretical findings as well as proposed tuning methods via simulation and real-time experiments. The fuzzy systems have been successfully realized in a wide variety of engineering areas such as controls, image processing, data processing, decision making, estimation, modeling, and robotics. The fuzzy logic systems provide complex mappings from inputs to outputs, and this benefit usually results in better performances in comparison to non-fuzzy counterparts. Due to this, the fuzzy logic controllers have been applied to numerous challenging control problems for decades. Nowadays, more attention has been given to a new research direction of the fuzzy sets and systems, the general type-2 fuzzy logic controllers, which is the main motivation of this thesis. The internal structures of a class of Takagi-Sugeno-Kang type fuzzy logic controllers are first examined in detail. In this context, three fuzzy logic controller types (type-1, interval type-2, and general type 2) and two kinds of controller configurations (single-input and double-input) are considered. The baseline controllers, i.e. type-1 and interval type-2 fuzzy logic controllers, are presented in the preliminaries section. The fuzzy sets, fuzzy relations, fuzzy rules, fuzzy operators, and PID forms of these fuzzy logic controllers are explained in detail. The design assumptions and design parameters are given, also the most common design approaches are listed. Afterward, the general type-2 fuzzy sets and the general type-2 fuzzy logic controllers are presented. The general type-2 fuzzy logic controllers are described with α-plane associated horizontal slices because the α-plane representation provides useful advantages on the handling of the secondary membership function of the general type-2 fuzzy sets and the calculation of the general type-2 fuzzy logic controller output. It is shown that the α-plane based general type-2 fuzzy logic controller output calculation is accomplished through the well-known interval type-2 fuzzy logic computations. The secondary membership functions are further detailed in terms of their mathematical definitions and design options. The structure analysis on the general type-2 fuzzy sets shows the interactions between non-fuzzy, type-1 fuzzy, interval type-2 fuzzy, and general type-2 fuzzy sets happen in the secondary membership function. It is shown that the general type-2 fuzzy logic controller can easily transform into interval type-2 fuzzy, or type-1 fuzzy counterparts based on the secondary membership function definitions. As an outcome of this structural analysis, a new representation of the trapezoid secondary membership function is proposed based on a novel parameterization of the parameters that form the trapezoid shape. It is shown that the parameterized trapezoid secondary membership function is capable to construct trapezoid, triangle, interval, and singleton shapes so that the general type-2 fuzzy logic controllers are further capable to transform into interval type-2 fuzzy, or type-1 fuzzy counterparts. It is also shown that the proposed parameterization of the trapezoid secondary membership functions allows designing the control curves/surfaces of the general type-2 fuzzy logic controllers with a single tuning parameter. Moreover, the structural design suggestions are presented not only to construct fuzzy controllers in a straightforward manner but also to ease the design of the controllers with few design parameters. The design parameters of the general type-2 fuzzy logic controllers are grouped as the shape and the sensitivity design parameters with respect to their effects on the accuracy and the shape of the resulting fuzzy mapping. Accordingly, the tuning parameter of the secondary membership functions and the total number of α-planes are interpreted and as the sensitivity and shape design parameters, respectively. The shape analyses of the general type-2 fuzzy logic controllers show the effects of the proposed shape design parameter on the control curves/surfaces. In this context, the resulting fuzzy mappings of single input and double input general type-2 fuzzy logic controller structures are compared for various design settings of the shape design parameter. The comparative analyses provide interpretable and practical explanations on the potential advances of the shape design parameter. Based on the shape analyses, novel design approaches are proposed to tune the shape design parameter in a systematic way. In this context, it is suggested constructing the general type-2 fuzzy logic controllers over their type-1 and interval type-2 baselines and tuning them via the shape design parameter by providing a tunable tradeoff between robustness and performance. Therefore, it is aimed to combine benefits of baseline type-1 (relatively more aggressive control curves/surfaces better performance measures) and interval type 2 (relatively smoother control curves/surfaces, better robustness measures) fuzzy logic controllers. To enhance the control performance, two scheduling mechanisms are also proposed for online-tuning of the shape design parameter with respect to the steady-state operating points as well as transient-state dynamics. The sensitivity analyses of the general type-2 fuzzy logic controllers show the effects of the proposed sensitivity design parameter on the accuracy of the control curves/ surfaces. In this context, the resulting fuzzy mappings of single input and double input general type-2 fuzzy logic controller structures are also compared for various design settings of the sensitivity design parameter. The comparative sensitivity analyses show interpretable and practical explanations of the sensitivity design parameter in terms of calculation accuracy and computation burden. Therefore, it is suggested tuning the sensitivity design parameter by considering the limitations of hardware components such as resolution and processing speed. To accomplish the design in accordance with a tradeoff between sensitivity and computational time, a novel iterative algorithm is proposed to tune the sensitivity design parameter. The simulation and real-time experimental control studies validate the proposed design recommendations, systematic design approaches, and tuning methods for the general type-2 fuzzy logic controllers on benchmark control systems. In these control studies, the general type-2 fuzzy logic controllers are designed based on the proposed design methods. In order to show the performance improvements on the control systems, the general type-2 fuzzy logic controllers (tuned either online or offline) are compared with type-1 fuzzy and interval type-2 fuzzy counterparts. The performance measures clearly show that the online-tuned general type-2 fuzzy logic controllers outperform all general type-2, interval type-2, and type-1 counterparts on account of the proposed scheduling mechanisms over the proposed systematic design rules. The results also show that the systematic design of the general type-2 fuzzy logic controllers is simply accomplished by following the proposed tuning steps of the shape and sensitivity design parameters.
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ÖgeActive slam with informative path planning for heterogeneous robot teams(Fen Bilimleri Enstitüsü, 2020)Recently, heterogeneous teams consisting of unmanned ground vehicles and unmanned aerial vehicles are being used for different types of missions such as surveillance, tracking, and exploration, etc. Exploration missions with heterogeneous robot teams should acquire a common map for understanding the surroundings better. The unique approach presented in this dissertation with cooperative use of agents provides a well-detailed observation over the environment where challenging details and complex structures are involved. Also, the presented method is suitable for real-time applications and autonomous path planning for exploration. Lidar Odometry and Mapping with various similarity metrics such as Shannon Entropy, Kullback-Liebler Divergence, Jeffrey Divergence, K Divergence, Topsoe Divergence, Jensen-Shannon Divergence and Jensen Divergence are used to construct a common height map of the environment. Furthermore, the given layering method that provides more accuracy and a better understanding of the common map. All of the given similarity metrics are compared, and the advantage of utilizing the layering method is shown. The best similarity metric for constructing a heterogeneous robot team common map of the experimental area was obtained by using the Jensen Divergence similarity metric and layering method. Moreover, Extended Kalman Filter localization and OctoMap techniques are utilized to create an adaptive simultaneous localization and mapping infrastructure for informative path planning. Optimal parameter tuning for the specified simulation environment provides adjustable memory allocation and exploration performance, such as; duration, collected information and effort. The information seeking controller obtained with the use of relative entropy ensures exploration of the given area to minimize the uncertainty between observed states and environmental states. Robots move to the volumetric spaces' center under given rules and collect measurements by proprioceptive and exteroceptive sensors. With the use of heterogeneous robot teams, the measurements collected by the Lidar provide an advantage in perceiving complex details that can not be done by homogeneous robot teams. Constructing common map part of the theoretical approaches in this thesis are experimentally validated. In addition, the complete demonstration of this dissertation is done with six different cases by simulation studies. The theoretical background of active simultaneous localization and mapping with informative path planning for heterogeneous robot teams are validated, and the advantages of this study are remarked.
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ÖgeMulti-agent coverage control with adaptation to performance variations and imprecise localization( 2020)In this thesis, an adaptive collaboration approach for a multi-agent system consisting of nonholonomic wheeled mobile robots is proposed. The positions of the agents are not known precisely but their locations are known to be within uncertainty circles. For the collaboration among the robots, the workspace partitioning algorithm is chosen as Guaranteed Power Voronoi Diagram (GPVD or GPD) which not only takes the localization uncertainty into account but also is capable of changing the regions of the generator points with respect to corresponding weight parameters. Also, the assumption is that the actuation capabilities of the robots are different from each other. The agents do not know those parameters related to their actuation performances beforehand. The contribution of the thesis is that the performance parameters of the agents are learned online by the proposed adaptive estimator algorithm and Hopfield Neural Network (HNN) estimator under localization uncertainty. The proposed algorithm is based on the coverage control which performs collaboration among the robots by assigning the regions from the workspace according to their actuation performances automatically. The definition of the actuation performances is different capabilities of the agents. The examples of strong actuation performances may include powerful motors and favorable terrain while wheel slip and weak motors can be counted as examples for the weak actuator performances. The proposed multi-agent collaborative coverage algorithm learns the performance parameters of the robots by using two approaches proposed in the thesis. The first approach is based on an adaptive estimator with a non-holonomic estimation model. The second method uses an HNN estimator. The theoretical proof, analysis and verification of the aforementioned methods are given in the related sections. After estimating the performance parameters, the weights are calculated using a neighbor based weight estimation algorithm. The weight variables are utilized in the GPD algorithm so that the workspace is partitioned according to the performance parameters of the agents in a guaranteed sense. At the end, the agents take regions from the workspace according to their actuation performances and achieve the optimal collaborative coverage so that the agents with strong actuators take larger regions from the environment than the agents with poor actuators. Thus, the collaborative coverage algorithm enables the robots to deploy themselves to an optimal configuration which minimizes the total coverage cost by taking imprecise localization into account. Moreover, a multi-agent coverage collaboration method with an energy-efficient optimal coverage control law and Hopfield networks is proposed in the related section. By using the algorithm a trade-off between coverage time and energy consumption among agents can be done. Meanwhile, the collaboration is achieved according to the actuation performances of the agents. The theoretical results are verified with MATLAB and ROS/Gazebo simulations and experiments that show the efficiency of the algorithm. The ROS implementation of the algorithm is explained. The experimental results are given in the related section.