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The purpose of this paper is to develop the multi-objective optimization approach and its numerical implementation to synthesise the model-base control for the part curing at autoclave processing, which supplies the stability and uniformity of the structure and mechanical properties of the material within the cured composite part.

The approach includes conversion of the cured part and mold geometry from their computer-aided design (CAD) to computer-aided engineering (CAE) representation, a finite element (FE) formulation of the coupled forward heat transfer/thermal kinetic problem with the parameters of prepreg, which should be determined by the thermal analysis, and, finally, a mapping of the area of 4D design space (thermal control parameters) to 2D objective space, whose coordinates are the maximum deviations of degree of cure and temperature within the cured part calculated at each call of the FE model.

The present modeling and optimization approach to the cure process control of the prepreg with thermosetting resin, as well as the means of visualizing optimization results, allow providing insight into complex curing phenomena, estimating the best achievable quality indicators of manufactured composite parts, finding satisfactory parameters of the control law and deciding considering all manufacturing constraints.

The research can be effectively used to optimize the cure process control for a wide class of polymeric composite parts, even with a complex geometry, but it requires the exact conversion of the geometry of the modeled part from the CAD to CAE environment, which implies the need for excluding all topological imperfections of original CAD model to eliminate the possible formation of void elements and other reasons that do not allow the correct FE meshing. Because thermal, rheological and kinetics parameters, which include the governing equations of cure process, depend on the reinforcing fibers, and especially on the resin properties, the thermal testing for the new modeled prepreg needs to be performed.

Computer implementation of the proposed approach and numerical method for model-based optimal control synthesis for composite part cure process can be used in aircraft, rotorcraft, ship and automotive technologies at the design of manufacturing process of the large composite parts with complex shape.

This will allow much better quality for large-scale composite parts, excluding very expensive, time-, energy- and material-consuming multiple cure process testing.

This is first time the problem of optimal control synthesis for curing the large-scale composite parts of complex shape was solved.

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.

Obstacle and wind field are common environmental factors for mini unmanned helicopter (MUH) flight. This paper aims to develop a trajectory planning approach guiding MUH to avoid static and dynamic obstacles and to fly in steady uniform or boundary-layer wind field.

An optimal control model including a nonlinear flight dynamics model and a cubic obstacle model is established for MUH trajectory planning. Radau pseudospectral method is used to generate the optimal trajectory.

The approach can plan reasonable obstacle-avoiding trajectories in obstacle and windy environments. The simulation results show that high-speed wind fields increase the flight time and fluctuation of control inputs. If boundary-layer wind field exists, the trajectory deforms significantly and gets closer to the ground to escape from the strong wind.

The key innovations in this paper include a cubic obstacle model which is straightforward and practical for trajectory planning and MUH trajectory planning in steady uniform wind field and boundary-layer wind field. This study provides an efficient solution to the trajectory planning for MUH in obstacle and windy environments.

The conflict between economic growth and sustainable development is foregone and there is prodigious literature examining the nature and causes of such trade-off. Keeping with this dispensation, the current chapter examines the dynamics of such trade-off in Ramsey–Cass–Koopmans (R–C–K) optimal growth-theoretic lines. The model developed in the chapter departs from the fundamental feature of R–C–K framework in as much as the capital is considered on a broader spectrum having its marginal productivity being increasing in nature and it considers a centralised economy with the planner maximising discounted utility over per capita consumption (private good) and pollution (public bad) over the infinite horizon of time. The study reveals potential trade-off between consumption and environmental emission quiet emphatically for the developed, developing and less developed countries, in both single equilibrium and multiple equilibrium cases. Besides, the study examines the impact of rise in population growth and fuel price on the steady-state equilibrium with respect to per capita capital, relative intensity of energy usage, emission and consumption using comparative static exercise.

The aim of this paper is to provide a review of recent developments in the application of swarm intelligence to robotics.

This paper initially considers swarm intelligence and then discusses its application to robotics through reference to a number of recent research programmes.

Based on the principles of swarm intelligence, which is derived from the swarming behaviour of biological entities, swarm robotics research is widespread but still at an early stage. Much aims to gain an understanding of biological swarming and apply it to autonomous, mobile multi‐robot systems. European activities are particularly strong and several large, collaborative projects are underway. Research in the USA has a military bias and much is funded by defence agencies.

The paper provides an up‐to‐date insight into swarm robot research and development.

Admittance control is a typical complaint control methodology. Traditionally, admittance control systems are based on a dynamical relationship described by Voigt model. By contrast, after changing connection of spring and damper, Maxwell model produces different dynamics and has shown better impact absorption performance. This paper aims to design a novel compliant control method based on Maxwell model and implement it in a robot catching scenario.

To achieve this goal, this paper proposed a Maxwell model based admittance control scheme. Considering several motion stages involved in one catching attempt, the following approaches are adopted. First, Kalman filter is used to process the position data stream acquired from motion capture system and predict the subsequent object flying trajectory. Then, a linear segments with parabolic blends reaching motion is generated to achieve time-optimal movement under kinematic and joint inherent constraints. After robot reached the desired catching point, the proposed Maxwell model based admittance controller performs such as a cushion to moderate the impact between robot end-effector and flying object.

This paper has experimentally demonstrated the feasibility and effectiveness of the proposed method. Compared with typical Voigt model based compliant catching, less object bounding away from end-effector happens and the success rate of catching has been improved.

The authors proposed a novel Maxwell model based admittance control method and demonstrated its effectiveness in a robot catching scenario. The author’s approach may inspire other related researchers and has great potential of practical usage in a widespread of robot applications.

The purpose of this paper is to design a model-based bilateral teleoperation method to improve the feedback force and velocity/position tracking for robotic-assisted tasks (such as palpation, etc.) under constant and/or varying time delay with environment dynamic property. Time delay existing in bilateral teleoperation easily destabilizes the system. Proper control strategies are able to make the system stable, but at the cost of compromised performance. Model-based bilateral teleoperation is designed to achieve enhanced performance of this time-delayed system, but an accurate model is required.

Viscoelastic model has been used to describe the robot tool-soft tissue interaction behavior. Kevin-Boltzmann (K-B) model is selected to model the soft tissue behavior due to its good accuracy, transient and linearity properties among several viscoelastic models. In this work, the K-B model is designed at the master side to generate a virtual environment of remote robotic tool-soft tissue interaction. In order to obtain improved performance, a self perturbing recursive least square (SPRLS) algorithm is developed to on-line update the necessary parameters of the environment with varying dynamics.

With fast and optimal on-line estimation of primary parameters of the K-B model, the reflected force of the model-based bilateral teleoperation at the master side is improved as well as the position/velocity tracking performance. This model-based design in the bilateral teleoperation avoids the stability issue caused by time delay in the communication channel since the exchanged information become position/velocity and estimated parameters of the used model. Even facing with big and varying time delay, the system keeps stably and enhanced tracking performance. Besides, the fast convergence of the SPRLS algorithm helps to track the time-varying dynamic of the environment, which satisfies the surgical applications as the soft tissue properties usually are not static.

The originality of this work lies in that an enhanced perception of bilateral teleoperation structure under constant/varying time delay that benefits robotic assisted tele-palpation (time varying environment dynamic) tasks is developed. With SPRLS algorithm to on-line estimate the main parameters of environment, the feedback perception of system can be enhanced with stable velocity/position tracking. The superior velocity/position and force tracking performance of the developed method makes it possible for future robotic-assisted tasks with long-distance communication.

Smog seriously affects the ecological environment and poses a threat to public health. Therefore, smog control has become a key task in China, which requires reliable prediction.

This paper establishes a novel time-lag GM(1,N) model based on interval grey number sequences. Firstly, calculating kernel and degree of greyness of the interval grey number sequence respectively. Then, establishing the time-lag GM(1,N) model of kernel and degree of greyness sequences respectively to obtain their values after determining the time-lag parameters of two models. Finally, the upper and lower bounds of interval grey number sequences are obtained by restoring the values of kernel and degree of greyness.

In order to verify the validity and practicability of the model, the monthly concentrations of PM2.5, SO2 and NO2 in Beijing during August 2017 to September 2018 are selected to establish the time-lag GM(1,3) model for kernel and degree of greyness sequences respectively. Compared with three existing models, the proposed model in this paper has better simulation accuracy. Therefore, the novel model is applied to forecast monthly PM2.5 concentration for October to December 2018 in Beijing and provides a reference basis for the government to formulate smog control policies.

The proposed model can simulate and forecast system characteristic data with the time-lag effect more accurately, which shows that the time-lag GM(1,N) model proposed in this paper is practical and effective.

Based on interval grey number sequences, the traditional GM(1,N) model neglects the time-lag effect of driving terms, hence this paper introduces the time-lag parameters into driving terms of the traditional GM(1,N) model and proposes a novel time-lag GM(1,N) model.

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.