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Brazil’s regional inequality is an important topic due to the large and persistent differences in development between states and the high levels of inequality in the country. These variations in development can potentially render survey data inaccurate since the significance of capital income varies across the states. Besides, previous studies incorporating tax and national accounts data globally have mainly focused on measuring the income distribution at the country-level. This approach can limit the understanding of inequality, especially when considering large countries such as Brazil.

The methodology used to construct these estimates follows the guidelines of the Distributional National Accounts, whose core goal is to provide income distribution measures consistent with macroeconomic aggregates and harmonized across countries and time. The procedure has three main steps: first, it corrects the survey’s underrepresentation of top incomes using tax data. Then, it accounts for national income items not included in the survey or tax data, such as imputed rents and undistributed profits. Finally, it ensures that all components match the national income.

Compared to survey-based estimations, the results reveal a new angle on the state-level inequality. This study indicates that Amazonas, Rio de Janeiro and São Paulo have a more concentrated income distribution. The top 1\% of earners in these states receives around 28\% of total pre-tax income, while the top 10\% receive nearly 60\%. On the other end, Amapá (AP), Acre (AC), Rondônia (RO) and Santa Catarina (SC) are the states where the income distribution is less concentrated. There were no significant changes in the income distribution across the states during the period analyzed.

This study combines survey, tax and national accounts data to construct new estimates of Brazil’s state-level income distribution from 2006 to 2019. Previous results only considered income captured in surveys, which usually misses a significant part of capital incomes. This limitation may bias comparisons as capital income has different importance across the states. The new estimates represent the income of top groups more accurately, account for the entire national income and enable to compare regional inequality levels consistently with other countries.

The purpose of this paper is to investigate the impact of changes in credit stock on real and financial indicators in Turkey with a focus on conditional and time-varying dynamics.

In addition to lag-augmented vector autoregression (LA-VAR) based time-varying Granger causality tests, threshold models and a research setting that identifies high/low states of credit growth based on 24-month moving averages are used to explore regime-dependent behavior. For investigating the asymmetric dynamics, the authors use a methodology that identifies good/bad news in credit growth based on 24-month moving averages and standard deviations.

Results strongly suggest that the impact of changes in credit stock induces conditional responses. Moreover, we find evidence for asymmetric responses. In the case of Turkey, efforts to spur growth through credit produce a strong negative byproduct, a depreciation in the exchange rate. The authors also find that changes in credit stock have become more relevant for uncertainties in inflation and exchange rate expectations, particularly in the era after mid-2018 in which credit growth volatility has increased noticeably.

This study provides a comprehensive analysis of time-varying and conditional responses to a change in credit stock in a major emerging economy. Using a moving threshold based only on the available information in the analysis of state-dependency represents a new approach.

The purpose of this paper is to design an output-feedback algorithm based on low-power observer (LPO), robust chattering-free controller and nonlinear disturbance observer (DO) to achieve trajectory tracking of quadrotor in the Cartesian plane.

To achieve trajectory tracking control, firstly the decoupled rotational and translational model of quadrotor are modified by introducing backstepped state-space variables. In the second step, robust integral sliding mode control is designed based on the proportional-integral-derivative (PID) technique. In the third step, a DO is constructed. In next step, the measurable outputs, i.e. rotational and translational state variables, are used to design the LPO. Finally, in the control algorithm all state variables and its rates are replaced with its estimates obtained using the state-observer.

The finding includes output-feedback control (OFC) algorithm designed by using a LPO. A modified backstepping model for rotational and rotational systems is developed prior to the design of integral sliding mode control based on PID technique. Unlike traditional high-gain observers (HGO), this paper used the LPO for state estimation of quadrotor systems to solve the problem of peaking phenomenon in HGO. Furthermore, a nonlinear DO is designed such that it attenuates disturbance with unknown magnitude and frequency. Moreover, a chattering reduction criterion has been introduced to solve the inherited chattering issue of controllers based on sliding mode technique.

This paper presents input and output data-driven model-free control algorithm. That is, only input and output of the quadrotor model are required to achieve the trajectory tracking control. Therefore, for practical implementation, the number of on-board sensor is reduced.

Although extensive research has been done for designing OFC algorithms for quadrotor, LPO has never been implemented for the rotational and translational state estimations of quadrotor. Furthermore, the mathematical model of rotational and translational systems is modified by using backstepped variables followed by the controller designed using PID and integral sliding mode control technique. Moreover, a DO is developed for attenuation of disturbance with unknown bound, magnitude and frequency.

This study aims to introduce a novel technique for nonlinear sensor time constant estimation and sensor dynamic compensation in hot-bar soldering using an extended Kalman filter (EKF) to estimate the temperature of the thermocouple.

Temperature optimal control is combined with a closed-loop proportional integral differential (PID) control method based on an EKF. Different control methods for measuring the temperature of the thermode in terms of temperature control, error and antidisturbance are studied. A soldering process in a semi-industrial environment is performed. The proposed control method was applied to the soldering of flexible printed circuits and circuit boards. An infrared camera was used to measure the top-surface temperature.

The proposed method can not only estimate the soldering temperature but also eliminate the noise of the system. The performance of this methodology was exemplary, characterized by rapid convergence and negligible error margins. Compared with the conventional control, the temperature variability of the proposed control is significantly attenuated.

An EKF was designed to estimate the temperature of the thermocouple during hot-bar soldering. Using the EKF and PID controller, the nonlinear properties of the system could be effectively overcome and the effects of disturbances and system noise could be decreased. The proposed method significantly enhanced the temperature control performance of hot-bar soldering, effectively suppressing overshoot and shortening the adjustment time, thereby achieving precise temperature control of the controlled object.

Background: Geostatistics focuses on spatial or spatiotemporal datasets. Geostatistics was initially developed to generate probability distribution predictions of ore grade in the mining industry; however, it has been successfully applied in diverse scientific disciplines. This technique includes univariate, multivariate, and simulations. Kriging geostatistical methods, simple, ordinary, and universal Kriging, are not multivariate models in the usual statistical function. Notwithstanding, simple, ordinary, and universal kriging techniques utilize random function models that include unlimited random variables while modeling one attribute. The coKriging technique is a multivariate estimation method that simultaneously models two or more attributes defined with the same domains as coregionalization.

Objective: This study investigates the impact of populations on traffic volumes as a variable. The additional variable determines the strength or accuracy obtained when data integration is adopted. In addition, this is to help improve the estimation of annual average daily traffic (AADT).

Methods procedures, process: The investigation adopts the coKriging technique with AADT data from 2009 to 2016 from Montana, Minnesota, and Washington as primary attributes and population as a controlling factor (second variable). CK is implemented for this study after reviewing the literature and work completed by comparing it with other geostatistical methods.

Results, observations, and conclusions: The Investigation employed two variables. The data integration methods employed in CK yield more reliable models because their strength is drawn from multiple variables. The cross-validation results of the model types explored with the CK technique successfully evaluate the interpolation technique's performance and help select optimal models for each state. The results from Montana and Minnesota models accurately represent the states' traffic and population density. The Washington model had a few exceptions. However, the secondary attribute helped yield an accurate interpretation. Consequently, the impact of tourism, shopping, recreation centers, and possible transiting patterns throughout the state is worth exploring.

Background: The annual average daily traffic (AADT) data from road segments are critical for roadway projects, especially with the decision-making processes about operations, travel demand, safety-performance evaluation, and maintenance. Regular updates help to determine traffic patterns for decision-making. Unfortunately, the luxury of having permanent recorders on all road segments, especially low-volume roads, is virtually impossible. Consequently, insufficient AADT information is acquired for planning and new developments. A growing number of statistical, mathematical, and machine-learning algorithms have helped estimate AADT data values accurately, to some extent, at both sampled and unsampled locations on low-volume roadways. In some cases, roads with no representative AADT data are resolved with information from roadways with similar traffic patterns.

Methods: This study adopted an integrative approach with a combined systematic literature review (SLR) and meta-analysis (MA) to identify and to evaluate the performance, the sources of error, and possible advantages and disadvantages of the techniques utilized most for estimating AADT data. As a result, an SLR of various peer-reviewed articles and reports was completed to answer four research questions.

Results: The study showed that the most frequent techniques utilized to estimate AADT data on low-volume roadways were regression, artificial neural-network techniques, travel-demand models, the traditional factor approach, and spatial interpolation techniques. These AADT data-estimating methods' performance was subjected to meta-analysis. Three studies were completed: R squared, root means square error, and mean absolute percentage error. The meta-analysis results indicated a mixed summary effect: 1. all studies were equal; 2. all studies were not comparable. However, the integrated qualitative and quantitative approach indicated that spatial-interpolation (Kriging) methods outperformed the others.

Conclusions: Spatial-interpolation methods may be selected over others to generate accurate AADT data by practitioners at all levels for decision making. Besides, the resulting cross-validation statistics give statistics like the other methods' performance measures.

This study was carried out to analyze the importance of consumer preference data in forecasting demand in apparel retailing.

To collect preference data, 729 hypothetical stock keeping units (SKU) were derived using a full factorial design, from a combination of six attributes and three levels each. From the hypothetical SKU's, 63 practical SKU's were selected for further analysis. Two hundred two responses were collected from a store intercept survey. Respondents' utility scores for all 63 SKUs were calculated using conjoint analysis. In estimating aggregate demand, to allow for consumer substitution and to make the SKU available when a consumer wishes to buy more than one item in the same SKU, top three highly preferred SKU's utility scores of each individual were selected and classified using a decision tree and was aggregated. A choice rule was modeled to include substitution; by applying this choice rule, aggregate demand was estimated.

The respondents' utility scores were calculated. The value of Kendall's tau is 0.88, the value of Pearson's R is 0.98 and internal predictive validity using Kendall's tau is 1.00, and this shows the high quality of data obtained. The proposed model was used to estimate the demand for 63 SKUs. The demand was estimated at 6.04 per cent for the SKU cotton, regular style, half sleeve, medium priced, private label. The proposed model for estimating demand using consumer preference data gave better estimates close to actual sales than expert opinion data. The Spearman's rank correlation between actual sales and consumer preference data is 0.338 and is significant at 5 per cent level. The Spearman's rank correlation between actual sales and expert opinion is −0.059, and there is no significant relation between expert opinion data and actual sales. Thus, consumer preference model proves to be better in estimating demand than expert opinion data.

There has been a considerable amount of work done in choice-based models. There is a lot of scope in working in deterministic models.

The proposed consumer preference-based demand estimation model can be beneficial to the apparel retailers in increasing their profit by reducing stock-out and overstocking situations. Though conjoint analysis is used in demand estimation in other industries, it is not used in apparel for demand estimations and can be greater use in its simplest form.

This research is the first one to model consumer preferences-based data to estimate demand in apparel. This research was practically tested in an apparel retail store. It is original.

To provide high torques needed to move a robot’s links, electric actuators are followed by a transmission system with a high transmission rate. For instance, gear ratios of 100:1 are often used in the joints of a robotic manipulator. This results into an actuator with large mechanical impedance (also known as nonback-drivable actuator). This in turn generates high contact forces when collision of the robotic mechanism occur and can cause humans’ injury. Another disadvantage of electric actuators is that they can exhibit overheating when constant torques have to be provided. Comparing to electric actuators, pneumatic actuators have promising properties for robotic applications, due to their low weight, simple mechanical design, low cost and good power-to-weight ratio. Electropneumatically actuated robots usually have better friction properties. Moreover, because of low mechanical impedance, pneumatic robots can provide moderate interaction forces which is important for robotic surgery and rehabilitation tasks. Pneumatic actuators are also well suited for exoskeleton robots. Actuation in exoskeletons should have a fast and accurate response. While electric motors come against high mechanical impedance and the risk of causing injuries, pneumatic actuators exhibit forces and torques which stay within moderate variation ranges. Besides, unlike direct current electric motors, pneumatic actuators have an improved weight-to-power ratio and avoid overheating problems.

The aim of this paper is to analyze a nonlinear optimal control method for electropneumatically actuated robots. A two-link robotic exoskeleton with electropneumatic actuators is considered as a case study. The associated nonlinear and multivariable state-space model is formulated and its differential flatness properties are proven. The dynamic model of the electropneumatic robot is linearized at each sampling instance with the use of first-order Taylor series expansion and through the computation of the associated Jacobian matrices. Within each sampling period, the time-varying linearization point is defined by the present value of the robot’s state vector and by the last sampled value of the control inputs vector. An H-infinity controller is designed for the linearized model of the robot aiming at solving the related optimal control problem under model uncertainties and external perturbations. An algebraic Riccati equation is solved at each time-step of the control method to obtain the stabilizing feedback gains of the H-infinity controller. Through Lyapunov stability analysis, it is proven that the robot’s control scheme satisfies the H-infinity tracking performance conditions which indicate the robustness properties of the control method. Moreover, global asymptotic stability is proven for the control loop. The method achieves fast convergence of the robot’s state variables to the associated reference trajectories, and despite strong nonlinearities in the robot’s dynamics, it keeps moderate the variations of the control inputs.

In this paper, a novel solution has been proposed for the nonlinear optimal control problem of robotic exoskeletons with electropneumatic actuators. As a case study, the dynamic model of a two-link lower-limb robotic exoskeleton with electropneumatic actuators has been considered. The dynamic model of this robotic system undergoes first approximate linearization at each iteration of the control algorithm around a temporary operating point. Within each sampling period, this linearization point is defined by the present value of the robot’s state vector and by the last sampled value of the control inputs vector. The linearization process relies on first-order Taylor series expansion and on the computation of the associated Jacobian matrices. The modeling error which is due to the truncation of higher-order terms from the Taylor series is considered to be a perturbation which is asymptotically compensated by the robustness of the control algorithm. To stabilize the dynamics of the electropneumatically actuated robot and to achieve precise tracking of reference setpoints, an H-infinity (optimal) feedback controller is designed. Actually, the proposed H-infinity controller for the model of the two-link electropneumatically actuated exoskeleton achieves the solution of the associated optimal control problem under model uncertainty and external disturbances. This controller implements a min-max differential game taking place between: (i) the control inputs which try to minimize a cost function which comprises a quadratic term of the state vector’s tracking error and (ii) the model uncertainty and perturbation inputs which try to maximize this cost function. To select the stabilizing feedback gains of this H-infinity controller, an algebraic Riccati equation is being repetitively solved at each time-step of the control method. The global stability properties of the H-infinity control scheme are proven through Lyapunov analysis.

Pneumatic actuators are characterized by high nonlinearities which are due to air compressibility, thermodynamics and valves behavior and thus pneumatic robots require elaborated nonlinear control schemes to ensure their fast and precise positioning. Among the control methods which have been applied to pneumatic robots, one can distinguish differential geometric approaches (Lie algebra-based control, differential flatness theory-based control, nonlinear model predictive control [NMPC], sliding-mode control, backstepping control and multiple models-based fuzzy control). Treating nonlinearities and fault tolerance issues in the control problem of robotic manipulators with electropneumatic actuators has been a nontrivial task.

The novelty of the proposed control method is outlined as follows: preceding results on the use of H-infinity control to nonlinear dynamical systems were limited to the case of affine-in-the-input systems with drift-only dynamics. These results considered that the control inputs gain matrix is not dependent on the values of the system’s state vector. Moreover, in these approaches the linearization was performed around points of the desirable trajectory, whereas in the present paper’s control method the linearization points are related with the value of the state vector at each sampling instance as well as with the last sampled value of the control inputs vector. The Riccati equation which has been proposed for computing the feedback gains of the controller is novel, so is the presented global stability proof through Lyapunov analysis. This paper’s scientific contribution is summarized as follows: (i) the presented nonlinear optimal control method has improved or equally satisfactory performance when compared against other nonlinear control schemes that one can consider for the dynamic model of robots with electropneumatic actuators (such as Lie algebra-based control, differential flatness theory-based control, nonlinear model-based predictive control, sliding-mode control and backstepping control), (ii) it achieves fast and accurate tracking of all reference setpoints, (iii) despite strong nonlinearities in the dynamic model of the robot, it keeps moderate the variations of the control inputs and (iv) unlike the aforementioned alternative control approaches, this paper’s method is the only one that achieves solution of the optimal control problem for electropneumatic robots.

The use of electropneumatic actuation in robots exhibits certain advantages. These can be the improved weight-to-power ratio, the lower mechanical impedance and the avoidance of overheating. At the same time, precise positioning and accurate execution of tasks by electropneumatic robots requires the application of elaborated nonlinear control methods. In this paper, a new nonlinear optimal control method has been developed for electropneumatically actuated robots and has been specifically applied to the dynamic model of a two-link robotic exoskeleton. The benefit from using this paper’s results in industrial and biomedical applications is apparent.

A comparison of the proposed nonlinear optimal (H-infinity) control method against other linear and nonlinear control schemes for electropneumatically actuated robots shows the following: (1) Unlike global linearization-based control approaches, such as Lie algebra-based control and differential flatness theory-based control, the optimal control approach does not rely on complicated transformations (diffeomorphisms) of the system’s state variables. Besides, the computed control inputs are applied directly on the initial nonlinear model of the electropneumatic robot and not on its linearized equivalent. The inverse transformations which are met in global linearization-based control are avoided and consequently one does not come against the related singularity problems. (2) Unlike model predictive control (MPC) and NMPC, the proposed control method is of proven global stability. It is known that MPC is a linear control approach that if applied to the nonlinear dynamics of the electropneumatic robot, the stability of the control loop will be lost. Besides, in NMPC the convergence of its iterative search for an optimum depends on initialization and parameter values selection and consequently the global stability of this control method cannot be always assured. (3) Unlike sliding-mode control and backstepping control, the proposed optimal control method does not require the state-space description of the system to be found in a specific form. About sliding-mode control, it is known that when the controlled system is not found in the input-output linearized form the definition of the sliding surface can be an intuitive procedure. About backstepping control, it is known that it cannot be directly applied to a dynamical system if the related state-space model is not found in the triangular (backstepping integral) form. (4) Unlike PID control, the proposed nonlinear optimal control method is of proven global stability, the selection of the controller’s parameters does not rely on a heuristic tuning procedure, and the stability of the control loop is assured in the case of changes of operating points. (5) Unlike multiple local models-based control, the nonlinear optimal control method uses only one linearization point and needs the solution of only one Riccati equation so as to compute the stabilizing feedback gains of the controller. Consequently, in terms of computation load the proposed control method for the electropneumatic actuator’s dynamics is much more efficient.

The purpose of this study is to improve the control performance of wind energy conversion systems (WECSs) by proposing a new sensorless, robust control strategy based on a Smith predictor active disturbance rejection control (SP-ADRC) associated with a speed/position estimator.

The estimator consists of a sliding mode observer (SMO) in combination with a phase-locked loop (PLL) to estimate the permanent magnet synchronous generator (PMSG) rotor position and speed. At the same time, the SP-ADRC is applied to the speed control loop of the variable-speed WECS control system to adapt strongly to dynamic characteristics under parameter uncertainties and disturbances.

Numerical simulations are conducted to evaluate the speed tracking performances under various wind speed profiles. The results show that the proposed sensorless speed control improves the accuracy of rotor speed and position estimation and provides better power tracking performance than a regular ADRC controller under fast wind speed variations.

This paper offers a new approach for designing sensorless, robust control for PMSG-based WECSs.

A new sensorless, robust control is proposed to improve the stability and tracking performance of PMSG-based WECSs. The SP-ADRC control attenuates the effects of parameter uncertainties and disturbances and eliminates the time-delay impact. The sensorless control design based on SMO and PLL improves the accuracy of rotor speed estimation and reduces the chattering problem of traditional SMO. The obtained results support the theoretical findings.

A distinctive feature of tilt-rotor UAVs is that they can be fully actuated, whereas in fixed-angle rotor UAVs (e.g. common-type quadrotors, octorotors, etc.), the associated dynamic model is characterized by underactuation. Because of the existence of more control inputs, in tilt-rotor UAVs, there is more flexibility in the solution of the associated nonlinear control problem. On the other side, the dynamic model of the tilt-rotor UAVs remains nonlinear and multivariable and this imposes difficulty in the drone's controller design. This paper aims to achieve simultaneously precise tracking of trajectories and minimization of energy dissipation by the UAV's rotors. To this end elaborated control methods have to be developed.

A solution of the nonlinear control problem of tilt-rotor UAVs is attempted using a novel nonlinear optimal control method. This method is characterized by computational simplicity, clear implementation stages and proven global stability properties. At the first stage, approximate linearization is performed on the dynamic model of the tilt-rotor UAV with the use of first-order Taylor series expansion and through the computation of the system's Jacobian matrices. This linearization process is carried out at each sampling instance, around a temporary operating point which is defined by the present value of the tilt-rotor UAV's state vector and by the last sampled value of the control inputs vector. At the second stage, an H-infinity stabilizing controller is designed for the approximately linearized model of the tilt-rotor UAV. To find the feedback gains of the controller, an algebraic Riccati equation is repetitively solved, at each time-step of the control method. Lyapunov stability analysis is used to prove the global stability properties of the control scheme. Moreover, the H-infinity Kalman filter is used as a robust observer so as to enable state estimation-based control. The paper's nonlinear optimal control approach achieves fast and accurate tracking of reference setpoints under moderate variations of the control inputs. Finally, the nonlinear optimal control approach for UAVs with tilting rotors is compared against flatness-based control in successive loops, with the latter method to be also exhibiting satisfactory performance.

So far, nonlinear model predictive control (NMPC) methods have been of questionable performance in treating the nonlinear optimal control problem for tilt-rotor UAVs because NMPC's convergence to optimum depends often on the empirical selection of parameters while also lacking a global stability proof. In the present paper, a novel nonlinear optimal control method is proposed for solving the nonlinear optimal control problem of tilt rotor UAVs. Firstly, by following the assumption of small tilting angles, the state-space model of the UAV is formulated and conditions of differential flatness are given about it. Next, to implement the nonlinear optimal control method, the dynamic model of the tilt-rotor UAV undergoes approximate linearization at each sampling instance around a temporary operating point which is defined by the present value of the system's state vector and by the last sampled value of the control inputs vector. The linearization process is based on first-order Taylor series expansion and on the computation of the associated Jacobian matrices. The modelling error, which is due to the truncation of higher-order terms from the Taylor series, is considered to be a perturbation that is asymptotically compensated by the robustness of the control scheme. For the linearized model of the UAV, an H-infinity stabilizing feedback controller is designed. To select the feedback gains of the H-infinity controller, an algebraic Riccati equation has to be repetitively solved at each time-step of the control method. The stability properties of the control scheme are analysed with the Lyapunov method.

There are no research limitations in the nonlinear optimal control method for tilt-rotor UAVs. The proposed nonlinear optimal control method achieves fast and accurate tracking of setpoints by all state variables of the tilt-rotor UAV under moderate variations of the control inputs. Compared to past approaches for treating the nonlinear optimal (H-infinity) control problem, the paper's approach is applicable also to dynamical systems which have a non-constant control inputs gain matrix. Furthermore, it uses a new Riccati equation to compute the controller's gains and follows a novel Lyapunov analysis to prove global stability for the control loop.

There are no practical implications in the application of the nonlinear optimal control method for tilt-rotor UAVs. On the contrary, the nonlinear optimal control method is applicable to a wider class of dynamical systems than approaches based on the solution of state-dependent Riccati equations (SDRE). The SDRE approaches can be applied only to dynamical systems which can be transformed to the linear parameter varying (LPV) form. Besides, the nonlinear optimal control method performs better than nonlinear optimal control schemes which use approximation of the solution of the Hamilton–Jacobi–Bellman equation by Galerkin series expansions. The stability properties of the Galerkin series expansion-based optimal control approaches are still unproven.

The proposed nonlinear optimal control method is suitable for using in various types of robots, including robotic manipulators and autonomous vehicles. By treating nonlinear control problems for complicated robotic systems, the proposed nonlinear optimal control method can have a positive impact towards economic development. So far the method has been used successfully in (1) industrial robotics: robotic manipulators and networked robotic systems. One can note applications to fully actuated robotic manipulators, redundant manipulators, underactuated manipulators, cranes and load handling systems, time-delayed robotic systems, closed kinematic chain manipulators, flexible-link manipulators and micromanipulators and (2) transportation systems: autonomous vehicles and mobile robots. Besides, one can note applications to two-wheel and unicycle-type vehicles, four-wheel drive vehicles, four-wheel steering vehicles, articulated vehicles, truck and trailer systems, unmanned aerial vehicles, unmanned surface vessels, autonomous underwater vessels and underactuated vessels.

The proposed nonlinear optimal control method is a novel and genuine result and is used for the first time in the dynamic model of tilt-rotor UAVs. The nonlinear optimal control approach exhibits advantages against other control schemes one could have considered for the tilt-rotor UAV dynamics. For instance, (1) compared to the global linearization-based control schemes (such as Lie algebra-based control or flatness-based control), it does not require complicated changes of state variables (diffeomorphisms) and transformation of the system's state-space description. Consequently, it also avoids inverse transformations which may come against singularity problems, (2) compared to NMPC, the proposed nonlinear optimal control method is of proven global stability and the convergence of its iterative search for an optimum does not depend on initialization and controller's parametrization, (3) compared to sliding-mode control and backstepping control the application of the nonlinear optimal control method is not constrained into dynamical systems of a specific state-space form. It is known that unless the controlled system is found in the input–output linearized form, the definition of the associated sliding surfaces is an empirical procedure. Besides, unless the controlled system is found in the backstepping integral (triangular) form, the application of backstepping control is not possible, (4) compared to PID control, the nonlinear optimal control method is of proven global stability and its performance is not dependent on heuristics-based selection of parameters of the controller and (5) compared to multiple-model-based optimal control, the nonlinear optimal control method requires the computation of only one linearization point and the solution of only one Riccati equation.