This paper proposes a robust control approach to achieve high-precision trajectory tracking for permanent magnet linear motor (PMLM) system containing uncertainties by describing the dynamic model of PMLM based on the Udwadia-Kalaba equation combined with constraint-following method. First, the system of PMLM is described as a constraint-following system by adding the generalized constraint force to the unconstrained Udwadia-Kalaba equation of PMLM system. Second, the robust constraint-following controller is designed based on the proposed model after uncertainty analysis. Moreover, the proposed controller is verified to guarantee deterministic performance for uncertain systems: uniformly bounded and uniformly ultimately bounded. Third, the numerical simulation and experimental validation demonstrate the effectiveness of proposed controller. Finally, the design approach of constraint-following can be applied to other systems with uncertainties.

As shown in previous work, in some cases closed quantum systems exhibit a non-conventional absence of trade-off between performance and robustness in the sense that controllers with the highest fidelity can also provide the best robustness to parameter uncertainty. As the dephasing induced by the interaction of the system with the environment guides the evolution to a more classically mixed state, it is worth investigating what effect the introduction of dephasing has on the relationship between performance and robustness. In this paper we analyze the robustness of the fidelity error, as measured by the logarithmic sensitivity function, to dephasing processes. We show that introduction of dephasing as a perturbation to the nominal unitary dynamics requires a modification of the log-sensitivity formulation used to measure robustness about an uncertain parameter with nonzero nominal value used in previous work. We consider controllers optimized for a number of target objectives ranging from fidelity under coherent evolution to fidelity under dephasing dynamics to determine the extent to which optimizing for a specific regime has desirable effects in terms of robustness. Our analysis is based on two independent computations of the log-sensitivity: a statistical Monte Carlo approach and an analytic calculation. We show that despite the different log-sensitivity calculations employed in this study, both demonstrate that the log-sensitivity of the fidelity error to dephasing results in a conventional trade-off between performance and robustness.

The design and analysis of controllers to regulate excitation transport in quantum spin rings presents challenges in the application of classical feedback control techniques to synthesize effective control and generates results in contradiction to the expectations of classical control theory. This paper examines the robustness of controllers designed to optimize the fidelity of an excitation transfer to uncertainty in system and control parameters. We use the logarithmic sensitivity of the fidelity error as the robustness measure, drawing on the classical control analog of the sensitivity of the tracking error. Our analysis shows that quantum systems optimized for coherent transport demonstrate significantly different correlation between error and the log-sensitivity depending on whether the controller is optimized for readout at an exact time T or over a time-window T ± Δ/2.

Technology is the product of understanding physical processes and learning how to control them in order to achieve desired objectives. To be practically usable, technology requires a degree of reliability, which can be achieved by robust system design and control [1].

Robust control of non-linear systems is a challenging task, notably in the presence of external disturbances and uncertain parameters. The main focus of this paper is to solve the trajectory tracking problem of an unconventional quadrotor with rotating arms (also known as a foldable drone), while overcoming some of the challenges associated with this type of vehicle. Therefore, in a first step, the model of this vehicle is presented, taking into account the change of the inertia, the centre of gravity, and the control matrix. The theoretical foundations of backstepping control, based on the finite time Lyapunov stability theory and enhanced by a Super-Twisting algorithm, are then discussed. Numerical simulations are performed to demonstrate the efficiency of the suggested control approach. Finally, a qualitative and quantitative comparative study of the proposed controller with the conventional backstepping controller is performed. Overall, the obtained results show that the proposed control strategy outperforms in terms of accuracy and resilience.

This article investigates the fixed-time trajectory tracking control of a free-flying rigid space manipulator perturbed by model uncertainties and external disturbances. A novel robust fixed-time integrated controller is developed by integrating a nominal fixed-time proportional–differential-like controller with a fixed-time disturbance observer. It is strictly proved that the proposed controller can ensure the position and velocity tracking errors regulate to zero in fixed time even subject to lumped disturbance. Benefiting from the feedforward compensation, the proposed controller has the strong robustness and excellent disturbance attenuation capability. The effectiveness and advantages of the proposed control approach are validated through simulations and comparisons.

For robot manipulators, there are two types of disturbances. One is model parametric uncertainty; the other is unmodelled parameters such as joint friction forces and external disturbances. Unmodelled joint frictions and external disturbances reduce performance in terms of positioning accuracy and repeatability. In order to compensate for unmodelled parameters, the design of a new controller is considered. First, the modelled and unmodelled parameters are included in a dynamic model. Then, based on the dynamic model, a new Lyapunov function is developed. After that, new nonlinear joint friction and external disturbance estimation laws are derived as an analytic solution from the Lyapunov function; thus, the stability of the closed system is guaranteed. Better values of the adaptive dynamic compensators can be extracted by fuzzy rules according to the tracking error. Limitations and knowledge about friction and external disturbances are not required for the design of the controller. The controller compensates for all possible model parameter uncertainties, all possible unknown joint frictions and external disturbances.

During the last two decades, parallel robots have become more ubiquitous, employed in a great variety of sectors, from food to aerospace industries. In fact, they are much more efficient than their serial counterparts in terms of performing fast motions and consuming less energy. However, due to their mechanical complexity, they present a highly complex non-linear dynamics, which makes the modelling and control tasks difficult. Aiming to improve the performance and robustness of the control laws already used to control this type of mechanisms, this paper proposes two hybrid control techniques. The first hybrid control is derived from the combination of a pure PD control with a modified Sliding Mode control. The second hybrid control, in its turn, combines a pure Computed Torque with the altered Sliding Mode control. The proposed modifications in the Sliding Mode control aim to achieve a considerable reduction of the tracking errors and chattering. A stability analysis of the proposed control techniques and an experimental validation are carried out, comparing the performance of the pure and hybrid control laws in a 5R parallel mechanism. Moreover, simulations are also conducted to evaluate the behaviour of a 3-dof spatial parallel robot, when performing a 3D-path. Analysing the simulations and the experimental results, it is possible to observe a significant reduction of the path tracking and steady-state errors in both hybrid control strategies.

Turbulence and gusts cause variations in the aerodynamic forces and moments applied to the structure of aircraft, resulting in passenger discomfort and dynamic loads on the structure that it must be designed to support. By designing Gust Load Alleviation (GLA) systems, two objectives can be achieved: first, realizing higher passenger comfort; and second, reducing the dynamic structural loads, which allows the design of lighter structures. In this paper, a methodology for designing combined feedback/feedforward GLA systems is proposed. The methodology relies on the availability of a wind profile ahead of the aircraft measured by a Doppler LIDAR sensor, and is based on $H_{\infty}$-optimal control techniques and a discrete-time preview-control problem formulation. Moreover, to allow design trade-offs between those two objectives (to achieve design flexibility) as well as to allow specification of robustness criteria, a variant of the problem using multi-channel $H_{\infty}$-optimal control techniques is introduced. The methodology developed in this paper is intended to be applied to large aircraft, e.g. transport aircraft or business jets. The simulation results show the effectiveness of the proposed design methodology in accounting for the measured wind profile to achieve the two mentioned objectives, while ensuring both design flexibility and controller robustness and optimality.

This paper proposes a new design of robust control combining feedback linearization, backstepping, and sliding mode control called FLBS applied to the locomotion of five-link biped robot. Due to the underactuated robot’s model, the system has a hybrid nature, while the FLBS control can provide a stabilized walking movement even with the existence of large disturbances and uncertainties by implementing smooth chatter-free signals. Stability of the method is proven using the Lyapunov theorem based on the hybrid zero dynamics and Poincaré map. The simulations show the controller performance such as robustness and chatter-free response in the presence of uncertainty and disturbance.

A smooth adaptive sliding-mode-based controller is developed for BTT missiles considering nonlinear couplings and aerodynamic uncertainties, wherein fixed-time stability theory is synthesised into sliding-mode control algorithm, such that control variables follow the desired command within fixed-bounded convergence time. Unlike other terminal sliding-mode-related works, the bound of settling time is independent of initial states, indicating that performance metrics, for instance the convergence rate, can be evaluated in advance. The control input is designed to be intrinsically smooth, based on adaptive estimations, and therefore the problem of singularity and chattering is effectively eliminated. Simulation results demonstrate the satisfactory performance and validate the effectiveness of the designed approach.

We determine the optimal robust strategy of an individual who seeks to maximize the (penalized) probability of reaching a bequest goal when she is uncertain about the drift of the risky asset and her hazard rate of mortality. We assume the individual can invest in a Black–Scholes market. We solve two optimization problems with ambiguity. The first is to maximize the penalized probability of reaching a bequest goal without life insurance in the market. In the second problem, in addition to investing in the financial market, the individual is allowed to purchase term life insurance to help her reach her bequest goal. As the individual becomes more ambiguity averse concerning the drift of the risky asset, she becomes more conservative with her investment strategy. Also, as she becomes more ambiguity averse about her hazard rate of mortality, numerical work indicates she is more likely to buy life insurance when the ambiguity towards the return of the risky asset is not too large.

In this paper, a novel robust model reference adaptive impedance control (RMRAIC) scheme is presented for an active transtibial ankle prosthesis. The controller makes the closed loop dynamics of the prosthesis similar to a reference impedance model and provides asymptotic tracking of the response trajectory of this impedance model. The interactions between human and prosthesis are taken into account by designing a second-order reference impedance model. The proposed controller is robust against parametric uncertainties in the nonlinear dynamic model of the prosthesis. Also, the controller has robustness against bounded uncertainties due to unavailable ground reaction forces and unmeasurable feedbacks of accelerations at the socket place. Moreover, an appropriate Series Elastic Actuator (SEA) mechanism for the prosthetic ankle is included in this work and its effects are discussed. Tracking performance and stability of the closed-loop system are proven via the Lyapunov stability analysis. Using simulations on an overall amputee prosthetic foot system, the effectiveness of the proposed RMRAIC controller is investigated for the task of level ground walking.

This paper addresses the systematic approach to design formation control for kinematic model of unicycle-type nonholonomic mobile robots. These robots are difficult to stabilize and control due to their nonintegrable constraints. The difficulty of control increases when there is a requirement to control a cluster of nonholonomic mobile robots in specific formation. In this paper, the design of the control scheme is presented in a three-step process. First, a robust state-feedback point-to-point stabilization control is designed using sliding mode control. In the second step, the controller is modified so as to address the tracking problem for time-varying reference trajectories. The proposed control scheme is shown to provide the desired robustness properties in the presence of the parameter variation, in the region of interest. Finally, in third step, tracking problem of a single nonholonomic mobile robot extends to formation control for a group of mobile robots in the leader–follower scenario using integral terminal- based sliding mode control augmented with stabilizing control. Starting with the transformation of the mathematical model of robots, the proposed controller ensures that the robots maintain a constant distance between each other to avoid collision. The main problem with the proposed controller is that it requires all states specially velocities. Therefore, the state-feedback control scheme is then extended to output feedback by incorporating a highgain observer. With the help of Lyapunov analysis and appropriate simulations, it is shown that the proposed output-feedback control scheme achieves the required control objectives. Furthermore, the closed loop system trajectories reach to desired equilibrium point in finite time while maintaining the special pattern.

This paper studies how model uncertainty influences economic fluctuation when trend inflation is high. We introduce Hansen and Sargent’s [(2008) Robustness, Princeton University Press] robust control techniques into a New Keynesian model with non-zero trend inflation. We reveal the following three points. First, we find that robust monetary policy responds more aggressively. This aggressiveness increases with trend inflation. Second, as the trend inflation rises, the response of macroeconomic variables is larger under robust policy. Third, stronger robustness tends to lead to indeterminate equilibrium as trend inflation increases. Consequently, the economy might be volatile when trend inflation is high due to robustness from the view of both variance and determinacy. We interpret the results as indicating that the model uncertainty might be the one of the factors causing large macroeconomic fluctuations when trend inflation is high.

This paper presents a robust tracking controller for electrically driven robots, without the need for velocity measurements of joint variables. Many observers require the system dynamics or nominal models, while a model-free observer is presented in this paper. The novelty of this paper is presenting a new observer–controller structure based on function approximation techniques and Stone–Weierstrass theorem using differential equations. In fact, it is assumed that the lumped uncertainty can be modeled by linear differential equations. Then, using Stone–Weierstrass theorem, it is verified that these differential equations are universal approximators. The advantage of proposed approach in comparison with previous related works is simplicity and reducing the dimensions of regressor matrices without the need for any information of the systems’ dynamic. Simulation results on a 6-degrees of freedom robot manipulator driven by geared permanent magnet DC motors indicate the satisfactory performance of the proposed method in overcoming uncertainties and reducing the tracking error. To evaluate the performance of proposed controller in practical implementations, experimental results on an SCARA manipulator are presented.

The problem of robust adaptive control of a robotic manipulator subjected to uncertain dynamics and joint space constraints is addressed in this paper. Command filters are used to overcome the time derivatives of virtual control, thus reducing the need for desired trajectory differentiations. A barrier Lyapunov function is used to deal with the joint space constraints. A robust adaptive support vector regression architecture is used to reduce filtering errors, approximation errors and handle dynamic uncertainties. The stability analysis of the closed-loop system using the Lyapunov theory permits to highlight adaptation laws and to prove that all signals of the closed-loop system are bounded. Simulations show the effectiveness of the proposed control strategy.

This study derives a robust adaptive control of electrically driven robot manipulators using a support vector regression (SVR)-based command filtered adaptive backstepping approach. The robot system is supposed to be subject to model uncertainties, neglected dynamics, and external disturbances. The command filtered backstepping algorithm is extended to the case of the robot manipulators. A robust term is added to the common adaptive SVR algorithm, to mitigate the effects of the SVR approximation error in the path tracking performance. The stability analysis of the closed loop system using the Lyapunov theory permits to highlight adaptation laws and to prove that all the signals in the closed loop system are bounded. Simulations show the effectiveness of the proposed control strategy.

This paper considers applications where a human agent is navigating a semi-autonomous mobile robot in an environment with obstacles. The human input to the robot can be based on a desired navigation objective, which may not be known to the robot. Additionally, the semi-autonomous robot can be programmed to ensure obstacle avoidance as it navigates the environment. A shared control architecture can be used to appropriately fuse the human and the autonomy inputs to obtain a net control input that drives the robot. In this paper, an adaptive, near-continuous control allocation function is included in the shared controller, which continuously varies the control effort exerted by the human and the autonomy based on the position of the robot relative to obstacles. The developed control allocation function facilitates the human to freely navigate the robot when away from obstacles, and it causes the autonomy control input to progressively dominate as the robot approaches obstacles. A harmonic potential field-based non-linear sliding mode controller is developed to obtain the autonomy control input for obstacle avoidance. In addition, a robust feed-forward term is included in the autonomy control input to maintain stability in the presence of adverse human inputs, which can be critical in applications such as to prevent collision or roll-over of smart wheelchairs due to erroneous human inputs. Lyapunov-based stability analysis is presented to guarantee finite-time stability of the developed shared controller, i.e., the autonomy guarantees obstacle avoidance as the human navigates the robot. Experimental results are provided to validate the performance of the developed shared controller.

This paper presents a high-order sliding mode approach to design variable structure controllers for nonlinear multivariable cross-coupling systems whereby a change in either control input affects the control loops of all the subsystems dynamics. A hybrid-sliding mode control (hybrid-SMC) scheme is constructed combining a new equivalent control algorithm with a high-order discontinuous control algorithm to benefit from the advantages of both control strategies. The hybrid-SMC scheme uses weighting coefficients to weight and combine controllers. The equivalent control algorithm uses a relative degree concept through dynamic constraints imposed on the sliding variables to overcome the limitations of the conventional approaches and to provide an optimum tracking performance. A scale-laboratory helicopter model is used to sum up the main features and demonstrate the effectiveness of the developed control scheme. The proposed hybrid-SMC strategy is compared to existing sliding mode-based control approaches in terms of tracking performance, stability and control efforts. The obtained results demonstrate the validity and efficiency of the proposed hybrid-SMC scheme.