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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.

This paper aims to propose a new neural-based enhanced extreme learning machine (EELM) algorithm, used as an online adaptive estimation model, regarding undetermined system dynamics and containing internal/external perturbations.

The EELM structure bases on the single layer feed-forward neural (SLFN) model in which the hidden weighting coefficients are initiated in random and the weighting outputs of the SLFN are online modified using an online adaptive rule implemented from Lyapunov stability concept.

Four different benchmark uncertain chaotic system tests have been satisfactorily investigated for demonstrating the superiority of proposed EELM technique.

Authors confirm that this manuscript is original.

This study aims to improve the muscle model control performance of a tendon-driven musculoskeletal system (TDMS) to overcome disadvantages such as multisegmentation and strong coupling. An adaptive network controller (ANC) with a disturbance observer is established to reduce the modeling error of the musculoskeletal model and improve its antidisturbance ability.

In contrast to other control technologies adopted for musculoskeletal humanoids, which use geometric relationships and antagonist inhibition control, this study develops a method comprising of three parts. (1) First, a simplified musculoskeletal model is constructed based on the Taylor expansion, mean value theorem and Lagrange–d’Alembert principle to complete the decoupling of the muscle model. (2) Next, for this simplified musculoskeletal model, an adaptive neuromuscular controller is designed to acquire the muscle-activation signal and realize stable tracking of the endpoint of the muscle-driven robot relative to the desired trajectory in the TDMS. For the ANC, an adaptive neural network controller with a disturbance observer is used to approximate dynamical uncertainties. (3) Using the Lyapunov method, uniform boundedness of the signals in the closed-loop system is proved. In addition, a tracking experiment is performed to validate the effectiveness of the adaptive neuromuscular controller.

The experimental results reveal that compared with other control technologies, the proposed design techniques can effectively improve control accuracy. Moreover, the proposed controller does not require extensive considerations of the geometric and antagonistic inhibition relationships, and it demonstrates anti-interference ability.

Musculoskeletal robots with humanoid structures have attracted considerable attention from numerous researchers owing to their potential to avoid danger for humans and the environment. The controller based on bio-muscle models has shown great performance in coordinating the redundant internal forces of TDMS. Therefore, adaptive controllers with disturbance observers are designed to improve the immunity of the system and thus directly regulate the internal forces between the bio-muscle models.

The paper is concerned with the different aspects of mathematical modelling and analysis in dynamics of complex non‐linear systems, that are generated by applied problems of engineering practice. Main aims are the problems of optimal (in some sense) mechanical‐mathematical modelling and the regular schemes of decomposition. The critical step in the use of mathematics for solving complex engineering problems is the building of a suitable mathematical model, that, generally speaking, is the result of combining the mathematical formalized procedures as well as heuristic (non‐formalized) manners (conjunction of rigorous science and free art). This work advocates a novel approach to the building process of mathematical models, presenting an overview of concepts and techniques needed for modelling, via comprehension of modelling problem as singularly perturbed one. Here uniform methodology, based on methods of Lyapunov theory, Perturbations theory [Asymptotic method in theory of non‐linear oscillations (1963)] in accordance with Stability postulate and Singularity postulate is developed. This asymptotic approach (called – LPSS approach) allows to elaborate the general conception of the modelling; to determine the conditions of qualitative equivalence between full model and simplified model. As applications, the different examples of concrete physical nature are considered.

The purpose of this paper is to find the efficient iterative methods for solving the general matrix equation A1X+ XA2+A3XH+XHA4=B (including Lyapunov and Sylvester matrix equations as special cases) with the unknown complex (reflexive) matrix X.

By applying the principle of hierarchical identification and the Hermitian/skew‐Hermitian splitting of the coefficient matrix quadruplet A1; A2; A3; A4 the authors propose a shift‐splitting hierarchical identification (SSHI) method to solve the general linear matrix equation A1X+XA2+A3XH+XHA4=B. Also, the proposed algorithm is extended for finding the reflexive solution to this matrix equation.

The authors propose two iterative methods for finding the solution and reflexive solution of the general linear matrix equation, respectively. The proposed algorithms have a simple, neat and elegant structure. The convergence analysis of the methods is also discussed. Some numerical results are given which illustrate the power and effectiveness of the proposed algorithms.

So far, several methods have been presented and used for solving the matrix equations by using vec operator and Kronecker product, generalized inverse, generalized singular value decomposition (GSVD) and canonical correlation decomposition (CCD) of matrices. In several cases, it is difficult to find the solutions by using matrix decomposition and generalized inverse. Also vec operator and Kronecker product enlarge the size of the matrix greatly therefore the computations are very expensive in the process of finding solutions. To overcome these complications and drawbacks, by using the hierarchical identification principle and the Hermitian=skew‐Hermitian splitting of the coefficient matrix quadruplet (A1; A2; A3; A4), the authors propose SSHI methods for solving the general matrix equation.

A tension leg platform (TLP) is a vertically moored, floating structure which is normally used for offshore oil/gas production. However, these types of structures can be damaged by vibration responses that are too large. The purpose of this paper is to consider the influence of the external waves on oceanic structures.

A mathematical model of an ocean environment was constructed, in which wave‐induced flow fields cause structural surge motion, then solutions to the mathematical model were analytically derived.

The Takagi‐Sugeno (T‐S) fuzzy model is employed in the approximation of the oceanic structure. The stability analysis of the TLP system is carried out using the Lyapunov direct method.

The dependence of the wave‐induced flow field and its resonant frequency on the wave characteristics and the structural properties of the platform, which include width, thickness and mass, can be drawn using a parametric approach.

Mathematical modeling is applied to find the wave‐induced displacement due to the surge motion. The vibration of the mechanical motion of the platform structure caused by wave force is also discussed.

The purpose of this study is to improve vehicles’ brake stability, the problem of constraint control for an antilock braking system (ABS) with asymmetric slip ratio constraints is concerned. A nonlinear control method based on barrier Lyapunov function (BLF) is proposed not only to track the optimal slip ratio but also to guarantee no violation on slip ratio constraints.

A quarter vehicle braking model and Burckhardt’s tire model are considered. The asymmetric BLF is introduced into the controller for solving asymmetric slip ratio constraint problems.

The proposed controller can implement ABS zero steady-state error tracking of the optimal wheel slip ratio and make slip ratio constraints flexible for various runway surfaces and runway transitions. Simulation and experimental results show that the control scheme can guarantee no violation on slip ratio constraints and avoid self-locking.

The slip rate equation with uncertainties is established, and BLF is introduced into the design process of the constrained controller to realize the slip rate constrained control.

This purpose of this paper is to discuss a linear fractional representation (LFR) of parameter‐dependent systems which are linear in the parameters but uncertain, being eventually time‐varying real‐rational nonlinear parameterizations, and dynamics with constant point delays.

The formulation is made in terms of Lyapunov's second method whereby the Lyapunov function candidate is confirmed to be a Lyapunov function by testing a finite number of linear‐matrix inequalities when the uncertain parameter vector, which might be time‐varying, lies within a known polytope which characterizes the uncertainties. The tests are performed only on the set of vertices associated with polytopes.

Sufficient conditions for global asymptotic stability are obtained. Conditions constraining the system to be slowly time‐varying around a stable nominal parameterization are not imposed in order to guarantee the stability.

The formulation is applied to a class of systems whose uncertainties might be parameterized through time‐varying real‐rational nonlinear parameterizations and which include point‐delayed dynamics with constant delays. However, such a class includes certain classes of neural networks with delays, systems with switched parameterizations and systems whose uncertain dynamics evolve arbitrarily in regions defined by known polytopes.

The stability tests are less involved than usual for time‐varying systems since only a finite number of them is necessary to investigate the stability.

LFR descriptions of linear time‐varying systems are extended to a wide class of systems with constant point delays. Also, the real‐rational nonlinear parameterizations of the uncertainties are admitted in both the delay‐free and delayed dynamics.

The study aims to equip robots with the ability to precisely maintain interaction forces, which is crucial for tasks such as polishing in highly dynamic environments with unknown and varying stiffness and geometry, including those found in airplane wings or thin, soft materials. The purpose of this study is to develop a novel adaptive force-tracking admittance control scheme aimed at achieving a faster response rate with higher tracking accuracy for robot force control.

In the proposed method, the traditional admittance model is improved by introducing a pre-proportional-derivative controller to accelerate parameter convergence. Subsequently, the authors design an adaptive law based on fuzzy logic systems (FLS) to compensate for uncertainties in the unknown environment. Stability conditions are established for the proposed method through Lyapunov analysis, which ensures the force tracking accuracy and the stability of the coupled system consisting of the robot and the interaction environment. Furthermore, the effectiveness and robustness of the proposed control algorithm are demonstrated by simulation and experiment.

A variety of unstructured simulations and experimental scenarios are designed to validate the effectiveness of the proposed algorithm in force control. The outcomes demonstrate that this control strategy excels in providing fast response, precise tracking accuracy and robust performance.

In real-world applications spanning industrial, service and medical fields where accurate force control by robots is essential, the proposed method stands out as both practical and straightforward, delivering consistently satisfactory performance across various scenarios.

This research introduces a novel adaptive force-tracking admittance controller based on FLS and validated through both simulations and experiments. The proposed controller demonstrates exceptional performance in force control within environments characterized by unknown and varying.

This paper aims to present an intelligent motion attitude control algorithm, which is used to solve the poor precision problems of motion-manipulation control and the problems of motion balance of humanoid robots. Aiming at the problems of a few physical training samples and low efficiency, this paper proposes an offline pre-training of the attitude controller using the identification model as a priori knowledge of online training in the real physical environment.

The deep reinforcement learning (DRL) of continuous motion and continuous state space is applied to motion attitude control of humanoid robots and the robot motion intelligent attitude controller is constructed. Combined with the stability analysis of the training process and control process, the stability constraints of the training process and control process are established and the correctness of the constraints is demonstrated in the experiment.

Comparing with the proportion integration differentiation (PID) controller, PID + MPC controller and MPC + DOB controller in the humanoid robots environment transition walking experiment, the standard deviation of the tracking error of robots’ upper body pitch attitude trajectory under the control of the intelligent attitude controller is reduced by 60.37 per cent, 44.17 per cent and 26.58 per cent.

Using an intelligent motion attitude control algorithm to deal with the strong coupling nonlinear problem in biped robots walking can simplify the control process. The offline pre-training of the attitude controller using the identification model as a priori knowledge of online training in the real physical environment makes up the problems of a few physical training samples and low efficiency. The result of using the theory described in this paper shows the performance of the motion-manipulation control precision and motion balance of humanoid robots and provides some inspiration for the application of using DRL in biped robots walking attitude control.