Search results

To study these issues, the authors chose a GFSC with one producer and one material supplier as research object, the supplier will offer green material to the producer and the producer will make green food using green production technology. Then, the authors proposed that consumers' perceived value was determined by the trustworthiness levels of the related green and quality-safety information provided by the supplier and the producer. Then, considering the trustworthiness levels of the green and quality information provided by the supplier and the producer, the authors improved the demand function. Afterwards, we constructed four investment models and their income models are built and then a cost-sharing and revenue-sharing contract (hereafter, CSRS) was adopted to coordinate the GFSC.

With the growth of consumers environmental awareness and life level, consumers' requirements for green and high quality food are growing. In recently years, to increase consumers' perceived trustworthiness on the product greenness and quality levels, stakeholders in green food supply chain (hereafter, GFSC) start to adopt the blockchain-based traceability system (hereafter, BLTS). For investors, they need to know the investment conditions and how to coordinate the GFSC.

(1) When the revenue-sharing coefficient is less than three-fourths and higher then a certain vaule, the cost-sharing and revenue-sharing contract can make the GFSC coordinate. (2) The investment cost threshold of the BLTS has a positive relationship with the trustworthiness improvement levels of the green and quality information, the green degree of food products and the quality of food products. (3) In the proposed four investment situations, as the growth of consumers perceived credibility coefficient about the greenness information and the quality information, chain members' revenues will increase. In addition, comparing with co-investing the BLTS, benefits of chain members are lower than them in the sole investment model.

(1) The demand function we proposed can help chain members forecast market demand to support production or ordering decisions. (2) The investment decision policies can offer a theoretical reference for chain members to use the BLTS. (3) The CSRS will offer the theoretical reference for coordinating the supply chain after using the BLTS. Furthermore, our study method can be referenced by other scholars. (4) The study method can offer a method reference for researchers who do a similar discussion in a manufacturing supply chain. Although, our research cannot guide the industrial practices, it can serve as a reference of the similar research in industry.

The purpose of this study is to improve the computational efficiency and accuracy of fatigue reliability analysis.

By absorbing the advantages of Markov chain and active Kriging model into the hierarchical collaborative strategy, an enhanced active Kriging-based hierarchical collaborative model (DCEAK) is proposed.

The analysis results show that the proposed DCEAK method holds high accuracy and efficiency in dealing with fatigue reliability analysis with high nonlinearity and small failure probability.

The effectiveness of the presented method in more complex reliability analysis problems (i.e. noisy problems, high-dimensional issues etc.) should be further validated.

The current efforts can provide a feasible way to analyze the reliability performance and identify the sensitive variables in aeroengine mechanisms.

To improve the computational efficiency and accuracy of fatigue reliability analysis, an enhanced active DCEAK is proposed and the corresponding fatigue reliability framework is established for the first time.

This paper aims to present an adaptive sliding mode control (ASMC) for tunnel boring machine cutterhead telescopic system with uncertainties to achieve a high-precision trajectory in complex strata. This method could be applied to solve the problems caused by linear and nonlinear model uncertainties.

First, an integral-type sliding surface is defined to reduce the static tracking error. Second, a projection type adaptation law is designed to approximate the linear and nonlinear redefined parameters of the electrohydraulic system. Third, a nonlinear robust term with a continuous approximation function is presented for handling load force uncertainty and reducing sliding mode chattering. Moreover, Lyapunov theory is applied to guarantee the stability of the closed-loop system. Finally, the effectiveness of the proposed controller is proved by comparative experiments on a scaled test rig.

The linear and nonlinear model uncertainties lead to large variations in the dynamics of the mechanism and the tracking error. To achieve precise position tracking, an adaptation law was integrated into the sliding mode control which compensated for model uncertainties. Besides, the inherent sliding mode chattering was reduced by a continuous approximation function, while load force uncertainty was solved by a nonlinear robust feedback. Therefore, a novel ASMC for tunnel boring machine cutterhead telescopic system with uncertainties can improve its tracking precision and reduce the sliding mode chattering.

To the best of the authors’ knowledge, the ASMC is proposed for the first time to control the tunnel boring machine cutterhead telescopic system with uncertainties. The presented control is effective not only in control accuracy but also in parameter uncertainty.

Permanent magnet synchronous spherical motors can have wide use in robotics and industrial automation. They enable three-DOF omnidirectional motion of their rotor. They are suitable for several applications, such as actuation in robotics, traction in electric vehicles and use in several automation systems. Unlike conventional synchronous motors, permanent magnet synchronous spherical motors consist of a fixed inner shell, which is the stator, and a rotating outer shell, which is the rotor. Their dynamic model is multivariable and strongly nonlinear. The treatment of the associated control problem is important.

In this paper, the multivariable dynamic model of permanent magnet synchronous spherical motors is analysed, and a nonlinear optimal (H-infinity) control method is developed for it. Differential flatness properties are proven for the spherical motors’ state-space model. Next, the motors’ state-space description undergoes approximate linearization with the use of first-order Taylor series expansion and through the computation of the associated Jacobian matrices. The linearization process takes place at each sampling instance around a time-varying operating point, which is defined by the present value of the motors’ state vector and by the last sampled value of the control input vector. For the approximately linearized model of the permanent magnet synchronous spherical motors, a stabilizing H-infinity feedback controller is designed. To compute the controller’s gains, an algebraic Riccati equation has to be repetitively solved at each time-step of the control algorithm. The global stability properties of the control scheme are proven through Lyapunov analysis. Finally, the performance of the nonlinear optimal control method is compared against a flatness-based control approach implemented in successive loops.

Due to the nonlinear and multivariable structure of the state-space model of spherical motors, the solution of the associated nonlinear control problem is a nontrivial task. In this paper, a novel nonlinear optimal (H-infinity) control approach is proposed for the dynamic model of permanent magnet synchronous spherical motors. The method is based on approximate linearization of the motor’s state-space model with the use of first-order Taylor series expansion and the computation of the associated Jacobian matrices. Furthermore, the paper has introduced a different solution to the nonlinear control problem of the permanent magnet synchronous spherical motor, which is based on flatness-based control implemented in successive loops.

The presented control approaches do not exhibit any limitations, but on the contrary, they have specific advantages. In comparison to global linearization-based control schemes (such as Lie-algebra-based control), they do not make use of complicated changes of state variables (diffeomorphisms) and transformations of the system's state-space description. The computed control inputs are applied directly to the initial nonlinear state-space model of the permanent magnet spherical motor without the intervention of inverse transformations and thus without coming against the risk of singularities.

The motion control problem of spherical motors is nontrivial because of the complicated nonlinear and multivariable dynamics of these electric machines. So far, there have been several attempts to apply nonlinear feedback control to permanent magnet-synchronous spherical motors. However, due to the model’s complexity, few results exist about the associated nonlinear optimal control problem. The proposed nonlinear control methods for permanent magnet synchronous spherical motors make more efficient, precise and reliable the use of such motors in robotics, electric traction and several automation systems.

The treated research topic is central for robotic and industrial automation. Permanent magnet synchronous spherical motors are suitable for several applications, such as actuation in robotics, traction in electric vehicles and use in several automation systems. The solution of the control problem for the nonlinear dynamic model of permanent magnet synchronous spherical motors has many industrial applications and therefore contributes to economic growth and development.

The proposed nonlinear optimal control method is novel compared to past attempts to solve the optimal control problem for nonlinear dynamical systems. Unlike past approaches, in the new nonlinear optimal control method, linearization is performed 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 and not at points that belong to the desirable trajectory (setpoints). Besides, the Riccati equation which is used for computing the feedback gains of the controller is new, and so is the global stability proof for this control method. Compared to nonlinear model predictive control, which is a popular approach for treating the optimal control problem in industry, the new nonlinear optimal (H-infinity) control scheme is of proven global stability, and the convergence of its iterative search for the optimum does not depend on initial conditions and trials with multiple sets of controller parameters. It is also noteworthy that 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 into the linear parameter varying 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. Furthermore, the second control method proposed in this paper, which is flatness-based control in successive loops, is also novel and demonstrates substantial contribution to nonlinear control for robotics and industrial automation.

Voltage source inverter-fed permanent magnet synchronous motors (VSI-PMSMs) are widely used in industrial actuation and mechatronic systems in water pumping stations, as well as in the traction of transportation systems (such as electric vehicles and electric trains or ships with electric propulsion). The dynamic model of VSI-PMSMs is multivariable and exhibits complicated nonlinear dynamics. The inverters’ currents, which are generated through a pulsewidth modulation process, are used to control the stator currents of the PMSM, which in turn control the rotational speed of this electric machine. So far, several nonlinear control schemes for VSI-PMSMs have been developed, having as primary objectives the precise tracking of setpoints by the system’s state variables and robustness to parametric changes or external perturbations. However, little has been done for the solution of the associated nonlinear optimal control problem. The purpose of this study/paper is to provide a novel nonlinear optimal control method for VSI-fed three-phase PMSMs.

The present article proposes a nonlinear optimal control approach for VSI-PMSMs. The nonlinear dynamic model of VSI-PMSMs undergoes approximate linearization around a temporary operating point, which is recomputed at each iteration of the control method. This temporary operating point is defined by the present value of the voltage source inverter-fed PMSM state vector and by the last sampled value of the motor’s control input vector. The linearization relies on Taylor series expansion and the calculation of the system’s Jacobian matrices. For the approximately linearized model of the voltage source inverter-fed PMSM, an H-infinity feedback controller is designed. For the computation of the controller’s feedback gains, an algebraic Riccati equation is iteratively solved at each time-step of the control method. The global asymptotic stability properties of the control method are proven through Lyapunov analysis. Finally, to implement state estimation-based control for this system, the H-infinity Kalman filter is proposed as a state observer. The proposed control method achieves fast and accurate tracking of the reference setpoints of the VSI-fed PMSM under moderate variations of the control inputs.

The proposed H-infinity controller provides the solution to the optimal control problem for the VSI-PMSM system under model uncertainty and external perturbations. Actually, this controller represents a min–max differential game taking place between the control inputs, which try to minimize a cost function that contains a quadratic term of the state vector’s tracking error, the model uncertainty, and exogenous disturbance terms, which try to maximize this cost function. To select the feedback gains of the stabilizing feedback controller, an algebraic Riccati equation is repetitively solved at each time-step of the control algorithm. To analyze the stability properties of the control scheme, the Lyapunov method is used. It is proven that the VSI-PMSM loop has the H-infinity tracking performance property, which signifies robustness against model uncertainty and disturbances. Moreover, under moderate conditions, the global asymptotic stability properties of this control scheme are proven. The proposed control method achieves fast tracking of reference setpoints by the VSI-PMSM state variables, while keeping also moderate the variations of the control inputs. The latter property indicates that energy consumption by the VSI-PMSM control loop can be minimized.

The proposed nonlinear optimal control method for the VSI-PMSM system exhibits several advantages: Comparing to global linearization-based control methods, such as Lie algebra-based control or differential flatness theory-based control, the nonlinear optimal control scheme avoids complicated state variable transformations (diffeomorphisms). Besides, its control inputs are applied directly to the initial nonlinear model of the VSI-PMSM system, and thus inverse transformations and the related singularity problems are also avoided. Compared with backstepping control, the nonlinear optimal control scheme does not require the state-space description of the controlled system to be found in the triangular (backstepping integral) form. Compared with sliding-mode control, there is no need to define in an often intuitive manner the sliding surfaces of the controlled system. Finally, compared with local model-based control, the article’s nonlinear optimal control method avoids linearization around multiple operating points and does not need the solution of multiple Riccati equations or LMIs. As a result of this, the nonlinear optimal control method requires less computational effort.

Voltage source inverter-fed permanent magnet synchronous motors (VSI-PMSMs) are widely used in industrial actuation and mechatronic systems in water pumping stations, as well as in the traction of transportation systems (such as electric vehicles and electric trains or ships with electric propulsion), The solution of the associated nonlinear control problem enables reliable and precise functioning of VSI-fd PMSMs. This in turn has a positive impact in all related industrial applications and in tasks of electric traction and propulsion where VSI-fed PMSMs are used. It is particularly important for electric transportation systems and for the wide use of electric vehicles as expected by green policies which aim at deploying electromotion and at achieving the Net Zero objective.

Unlike past approaches, in the new nonlinear optimal control method, linearization is performed 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 input vector and not at points that belong to the desirable trajectory (setpoints). Besides, the Riccati equation, which is used for computing the feedback gains of the controller, is new, as is the global stability proof for this control method. Comparing with nonlinear model predictive control, which is a popular approach for treating the optimal control problem in industry, the new nonlinear optimal (H-infinity) control scheme is of proven global stability, and the convergence of its iterative search for the optimum does not depend on initial conditions and trials with multiple sets of controller parameters. It is also noteworthy that 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 that can be transformed to the linear parameter varying 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.

This paper aims to refine the mechanisms affecting the two-way technology spillover and carbon transfer interactions between supply chain enterprises, and to guide their reduction of carbon emissions.

This study formulates a supplier-led Stackelberg game model to explore the effects of the interactions between two-way technology spillover effects and carbon transfers in decentralized and centralized decision-making scenarios. The optimized Shapley value is introduced to coordinate across the supply chain and determine the overall profits lost in the decentralized scenario.

Emission reductions by the low-carbon manufacturer are negatively correlated with the carbon transfers. Vertical technology spillovers promote carbon reduction, whereas horizontal technology spillovers inhibit it. The vertical technology spillovers amplify the negative effects of the carbon transfers, whereas the horizontal technology spillovers alleviate these negative effects. When the vertical technology spillover effect is strong or the horizontal technology spillover effect is weak in the centralized scenario, the carbon reduction is negatively correlated with the carbon transfers. Conversely, when the vertical technology spillover effect is weak or the horizontal technology spillover effect is strong, the enterprise’s carbon reduction is positively correlated with the carbon transfers. An optimized Shapley value can coordinate the supply chain.

This study examines the effects of carbon transfers on enterprises from a micro-perspective and distinguishes between vertical and horizontal technology spillovers to explore how carbon transfers and different types of technology spillovers affect enterprises’ decisions to reduce carbon emissions.

A combination of highly conductive porous media and nanofluids is an efficient way for improving thermal performance of relevant applications. For precisely predicting the flow and thermal transport of nanofluids in porous media, the purpose of this paper is to explore the inter-phase coupling numerical methods.

Based on the lattice Boltzmann (LB) method, this study combines the convective flow, non-equilibrium thermal transport and phase interactions of nanofluids in porous matrix and proposes a new multi-phase LB model. The micro-scale momentum and heat interactions are especially analyzed for nanoparticles, base fluid and solid matrix. A set of three-phase LB equations for the flow/thermal coupling of base fluid, nanoparticles and solid matrix is established.

Distributions of nanoparticles, velocities for nanoparticles and the base fluid, temperatures for three phases and interaction forces are analyzed in detail. Influences of parameters on the nanofluid convection in the porous matrix are examined. Thermal resistance of nanofluid convective transport in porous structures are comprehensively discussed with the models of multi-phases. Results show that the Rayleigh number and the Darcy number have significant influences on the convective characteristics. The result with the three-phase model is mildly larger than that with the local thermal non-equilibrium model.

This paper first creates the multi-phase theoretical model for the complex coupling process of nanofluids in porous structures, which is useful for researchers and technicians in fields of thermal science and computational fluid dynamics.

The purpose of this paper is to research the induced flashover laws of different insulation materials under electrostatic electromagnetic pulse, and the induced flashover characteristics of different electrode structures are further explored.

According to standard IEC 61000–4-2, an experimental system of electrostatic electromagnetic pulse flashover for insulation materials is established. The induction flashover laws of polytetrafluoroethylene, epoxy resin and polymethyl methacrylate surface-mounted finger electrodes under the different intensity of electrostatic electromagnetic pulse are researched. The influence of the finger electrode, needle–needle electrode and needle–plate electrode on insulation flashover was compared. Secondary electron emission avalanche (SEEA) and field superposition theory are used to analyze the experimental results of electrostatic electromagnetic pulse induced flashover.

The larger the dielectric strength of insulation materials, the more difficult flashover occurs on the surface. The field superposition enhances collision ionization between electrons and gas molecules, which leads to the insulation materials surface induced flashover easily by electrostatic electromagnetic pulse. The sharper the electrode shapes on the insulation materials surface, the stronger the electric field intensity at the cathode triple junction, more initial electrons are excited to form the discharge channel, which easily leads to flashover on the surface of the insulating material.

The proposed field superposition combined with the SEEA method provides a new study perspective and enables a more rational, comprehensive analysis of electrostatic electromagnetic pulse induced flashover of insulation materials. The work of this paper can provide a reference for the safety protection of spacecraft in orbit under a strong electromagnetic field environment, increase the service life of spacecraft and improve the reliability of spacecraft’s safe operation in orbit. It provides a basis for the selection of insulation materials for equipment under the different intensities of the external electromagnetic environment.

The main purpose of this paper is to investigate the adsorption properties of CoFe_1.9Mo_0.1O₄ magnetic nanoparticles (CFMo MNPs) using, anionic dye “congo red (CR)” as a model of water pollutants.

The magnetic nano-adsorbent was synthesized via sol-gel process. Different techniques including; Fourier transform infrared spectroscopy, point of zero charge, scanning electron microscope and X-ray powder diffraction were used to characterize the prepared adsorbent. Adsorption experiments were conducted in batch mode under various conditions (contact time, shaking speed, initial dye concentration, initial solution pH, solution temperature and adsorbent amount) to investigate the adsorption capability of CFMo MNPs for CR.

The results showed that, CFMo MNPs could successfully remove more than 90% of CR dye within 20 min. Adsorption kinetics and isotherms were better described using pseudo-second-order (PSO) and Langmuir models, respectively. The maximum adsorbed amount (q_max) of CR dye was 135.14 mg/g. The adsorption process was found to be endothermic and spontaneous in nature as demonstrated by the thermodynamics ( ΔGo, ΔHoand ΔSo).

This study provided a good example of using an easily separated magnetic nano-adsorbent for fast removal of a very toxic organic pollutant, congo red, from the aquatic environment

The employment of Mo-doped cobalt ferrite for the first time for removing hazardous anionic dyes such as congo red from their aqueous solutions.

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.