Arbitrary Disturbances Research Articles

Adaptive model-free disturbance rejection for continuum robots

This paper presents two model-free control strategies for the rejection of unknown disturbances in continuum robots. The strategies utilize a neural network-based approximation technique to estimate the uncertain Jacobian matrix using position measurements. The first strategy is designed for periodic disturbances and employs an adaptive model-free controller in conjunction with an adaptive disturbance observer. The second strategy is designed for robustness against arbitrary disturbances and employs time-varying input and update law gains that grow monotonically, resulting in the achievement of asymptotic, exponential, and prescribed-time reference trajectory tracking. The notion of fixed-time stabilization in prescribed time is particularly noteworthy, as it allows for the predefinition of a terminal time, independent of initial conditions and system parameters. A formal stability analysis is presented for each strategy, and the strategies are both tested experimentally with a concentric tube robot subject to unknown disturbances.

New results on the motion of interfaces of multi-layer radial Hele-Shaw flows

We study the dynamical system arising from the linear stability analysis of multi-layer radial Hele-Shaw flows with time-dependent injection rates. An analysis of the system provides conditions under which the disturbances on all interfaces either monotonically decrease or monotonically increase. Additionally, we show that in any multi-layer radial Hele-Shaw flow, if all of the interfaces are circular initially except for one perturbed interface then there exists a time-dependent injection rate such that the circular interfaces remain circular as they propagate and the disturbance on the perturbed interface decays. The motion of the interfaces is also investigated numerically by integrating the dynamical system for the case of constant and time-independent injection rates. This reveals some very interesting dynamics of interfaces in multi-layer flows. It is found that: (i) A disturbance of one interface can be transferred to the other interface(s); (ii) The disturbances on the interfaces can develop either in phase or out of phase from any arbitrary initial disturbance; and (iii) The dynamics of the flow can change dramatically with the addition of more interfaces. With time-dependent injection rate, there are more possibilities. In particular it is shown that an appropriate injection rate can result in a stable configuration, which consists of all perfectly circular interfaces except for one that is perturbed with a monochromatic wave of infinitesimal amplitude. The prescribed injection rate results in the perturbation decaying even if the configuration (i.e., the setup consisting of all but one circular interface and one perturbed circular interface) itself is unstable to disturbances on any one or more of the circular interfaces. However, it may not be without a challenge to realize such a flow in practice.

Effect of static compression on near-field tsunami waves: Three-dimensional solution

An analytical solution of three-dimensional surface wave profiles due to arbitrary spatio-temporal disturbance of a circular ocean bottom in a compressible ocean is obtained by incorporating the influence of the static ocean background compression under the assumptions of linearized water wave theory. Time-domain simulations of the surface profile in three dimensions and the pressure distribution within the water column for a circular uniform rise and tilt are shown. The corresponding animation movies depict the temporal evolution of the surface profile and pressure field inside the water column eloquently, which was not shown in earlier literature. The impact of static compression is also discussed through the simulations. A novel analytical expression of the potential function for a generic tilted motion (rmcos(mθ),m∈Z) of the circular ocean floor is derived. An efficient numerical code is developed to find surface elevation and pressure distribution, implementing the inverse Fourier integral as matrix multiplication. Validation is performed for the specific case of a rising flat ocean floor, showing the oscillations due to acoustic-gravity modes. Initially, a simplified problem of a flat rising ocean bottom is solved using the eigenfunction matching method, which involves finding a particular solution for the nonhomogeneous ocean bottom condition and the solution for its homogeneous counterpart. Solutions are obtained using a newly developed inner product between the depth-dependent functions. Later, a Green function technique is used to incorporate the impact of the arbitrary spatio-temporal motion of the circular portion of the ocean bed. The solution obtained from the eigenfunction matching method is utilized to obtain the analytical form of Green’s function and, eventually, an expression of surface elevation and pressure distribution inside the ocean water column.

Model-free control for autonomous prevention of adverse events in robotics.

Introduction: Preventive control is a critical feature in autonomous technology to ensure safe system operations. One application where safety is most important is robot-assisted needle interventions. During incisions into a tissue, adverse events such as mechanical buckling of the needle shaft and tissue displacements can occur on encounter with stiff membranes causing potential damage to the organ. Methods: To prevent these events before they occur, we propose a new control subroutine that autonomously chooses a) a reactive mechanism to stop the insertion procedure when a needle buckling or a severe tissue displacement event is predicted and b) an adaptive mechanism to continue the insertion procedure through needle steering control when a mild tissue displacement is detected. The subroutine is developed using a model-free control technique due to the nonlinearities of the unknown needle-tissue dynamics. First, an improved version of the model-free adaptive control (IMFAC) is developed by computing a fast time-varying partial pseudo derivative analytically from the dynamic linearization equation to enhance output convergence and robustness against external disturbances. Results and Discussion: Comparing IMFAC and MFAC algorithms on simulated nonlinear systems in MATLAB, IMFAC shows 20% faster output convergence against arbitrary disturbances. Next, IMFAC is integrated with event prediction algorithms from prior work to prevent adverse events during needle insertions in real time. Needle insertions in gelatin tissues with known environments show successful prevention of needle buckling and tissue displacement events. Needle insertions in biological tissues with unknown environments are performed using live fluoroscopic imaging as ground truth to verify timely prevention of adverse events. Finally, statistical ANOVA analysis on all insertion data shows the robustness of the prevention algorithm to various needles and tissue environments. Overall, the success rate of preventing adverse events in needle insertions through adaptive and reactive control was 95%, which is important toward achieving safety in robotic needle interventions.

Youla Parameterization-Based Fractional Repetitive Control of Arbitrary Frequency Disturbance Rejections for Line-of-Sight Stabilization

Youla Parameterization-Based Fractional Repetitive Control of Arbitrary Frequency Disturbance Rejections for Line-of-Sight Stabilization

Tuning-free filtering for stochastic systems with unmodeled measurement dynamics

This paper applies variational Bayesian to the stochastic system filtering problem for arbitrary measurement disturbances. Considering the system’s robustness when confronted with disturbances, we model its dynamics with a random walk model. Afterward, by assuming an inverse-Gamma distribution, the newly introduced covariance is estimated under a variational Bayesian (VB) framework. The proposed filter improves robustness against additive disturbance and degrades automatically into a Kalman filter when without disturbance. Moreover, this filter avoids the labor-intensive process of tuning parameters. A numerical simulation and an on-site vehicle navigation experiment are given to illustrate the effectiveness of the proposed filter.

Prescribed‐time adaptive bipartite time‐varying formation tracking for multiple Lagrangian systems with arbitrary disturbance

SummaryThis article focuses on the problem of bipartite time‐varying formation tracking for multiple Lagrangian systems with prescribed‐time adaptive sliding mode under the signed digraph. First, for each Lagrangian system, the local prescribed‐time disturbance estimator is proposed to estimate arbitrary disturbances in the prescribed time with the condition of bounded disturbances. Then the distributed prescribed‐time observers are designed to observe the position and velocity of the leader, and the consensus problem is transformed into bipartite formation tracking via introducing above observers. Based on designing two types of observers and disturbance estimators, a new prescribed‐time adaptive sliding mode controller is designed to ensure the tracking errors of the sliding mode surface converge to origin in a prescribed time. Ultimately, the feasibility of the provided results is further demonstrated through numerical simulation.

Neural‐network‐based event‐triggered adaptive security path following control of autonomous ground vehicles subject to abnormal actuator signal

AbstractThe malicious physical attacks from both sensor and actuator sides make real threats to the security and safety of autonomous ground vehicles (AGVs). This paper focuses on the problem of neural‐network‐based event‐triggered adaptive security control (ET‐ASC) scheme for path following of AGVs subject to arbitrary abnormal actuator signal. First, we assume that an arbitrary abnormal signal is caused by arbitrary malicious attacks or disturbances from actuators. Then, radial basis function neural network (RBF‐NN) is used to reconstruct such abnormal actuator signal. Second, modelling issues on security path following control of AGVs with Sigmoid‐like ETC scheme are shown when the AGV is suffering from abnormal actuator signal. In what follows, an ET‐ASC scheme is developed to mitigate the adverse effects of abnormal actuator signal with the reconstructed abnormal signal based on a novel Sigmoid‐like event‐triggered communication scheme. By using the proposed RBF‐NN‐based ET‐ASC scheme, control performance can be guaranteed under arbitrary malicious actuator signal rather than such attacks following a specific probability distribution. Final, some simulation experiments are provided to verify the effectiveness of proposed ET‐ASC scheme.

Effect of static compression on tsunami waves: Two-dimensional solution

This study provides an analytical solution for the surface wave profile resulting from an arbitrary temporal ocean bottom disturbance in a compressible ocean. The solution also considers the impact of static compression of the ocean background. The problem is formulated in two dimensions and solved using the Fourier transformation and eigenfunction matching method, which requires a new inner product and determining a particular solution to account for the non-homogeneous boundary condition. To verify the solution's validity, it is compared with the corresponding Green's function formulation, which employs the movement of the ocean floor as a source. The Green's function technique can handle the ocean floor's arbitrary spatial movement, which is demonstrated through two specific profiles. Additionally, the shallow water limit is derived to provide further validation. A time-domain simulation of the surface profile is presented, comparing the case with and without static compression. The effect of static compression is found to be small but non-negligible for typical ocean depths.

Boundedness of the Optimal State Estimator Rejecting Unknown Inputs

The Kitanidis filter is a natural extension of the Kalman filter to systems subject to arbitrary unknown inputs or disturbances. Though the optimality of the Kitanidis filter was founded for general time varying systems more than 30 years ago, its boundedness and stability analysis is still limited to time invariant systems, up to the authors' knowledge. In the framework of general time varying systems, this paper establishes upper and lower bounds of the error covariance of the Kitanidis filter, as well as upper bounds of all the auxiliary variables involved in the filter. By preventing data overflow, upper bounds are crucial for all recursive algorithms in real time applications. The upper and lower bounds of the error covariance will also serve as the basis of the Kitanidis filter stability analysis, like in the case of time varying system Kalman filter.

Tan-Type BLF-Based Attitude Tracking Control Design for Rigid Spacecraft with Arbitrary Disturbances

This study deals with the problem of disturbances in observer-based attitude tracking control for spacecraft in the presence of inertia-matrix uncertainty and arbitrary disturbance. Following the backstepping control, a tan-type barrier Lyapunov function (BLF)-based attitude tracking control method with prescribed settling time and performance is systematically developed. The proposed control framework possesses three advantages over the existing attitude controllers. Firstly, the singularity problem associated with the use of fractional power in fixed-time control is effectively resolved without employing any command filter or piece-wise continuous function. Secondly, inspired by the concept of the tan-type BLF approach, any desired performance for the attitude tracking error is satisfied. Lastly, the total disturbance, including the system’s uncertainty, external disturbances, and time-derivative of the virtual control, is precisely reconstructed during a predefined time, even if the initial estimation error tends to infinity. Moreover, this time is determined as a tunable gain in the observer. The numerical simulations confirm the superior performance of the proposed control strategy in comparison with the existing pertinent works.

Sparse Filtering Under Norm-Bounded Exogenous Disturbances Using Observers

The paper considers the sparse filtering problem under arbitrary norm-bounded exogenous disturbances. We propose a simple and universal observer-based approach to its solution, based on the LMI technique and the method of invariant ellipsoids; it allows the use of a reduced number of system outputs. From a technical point of view of application, we reduce the original problem to semi-definite programming, which is easily solved numerically. The proposed simple approach is easy to implement and can be equally extended to systems in continuous and discrete time.

Prescribed Time Attitude Tracking Control of Spacecraft With Arbitrary Disturbance

The problem of developing a controller for spacecraft to accomplish attitude maneuvers within a prescribed time, independently of the initial states, is addressed. A fixed-time disturbance observer-based control is established and proved to drive the error state to zero, in a prescribed time, in the presence of modeling and external uncertainties. The key advantages of the proposed control are that the gains are explicitly determined by the prescribed maneuvering time only and that it is also robust to instantaneous disturbances. The control approach enables an efficient design process for attitude control applications with time constraints. Simulation results are presented for the attitude control of a rigid spacecraft to verify the benefits of this control scheme.

Zero-assignment and complex coefficient gain design of generalized proportional-integral observer for robust fault detection

Aiming at early detection of faults in dynamic systems subject to external periodic disturbances, this paper proposes a new generalized proportional-integral observer (GPIO) fault detection scheme with zero-pole joint optimization and novel complex coefficient gain (CCG) of residual evaluation. The focus of the proposed scheme is to reduce the adverse impacts caused by the semi-stationary periodic disturbance whose spectrum is uneven, with most energy being at some dominant frequencies. The proposed GPIO with a complex coefficient gain is designed in a two-stage procedure. In the first stage of zero assignment and pole optimization, the additional zeros introduced by the GPIO’s integration action are allocated to near the disturbance frequency. The gain of the transfer function matrix relating from the disturbances to the fault indicator signals is minimized by pole optimization. In the second stage of designing complex coefficient gain in residual evaluation, the unique feature of rank-deficient caused by the additional zeros assigned in stage one is further exploited to cancel the disturbances in the fault indicator signals (which is also referred to as the fault detection residual in this article). It is proved that, for an arbitrary periodic disturbance with a specific spectrum, the remnant components of the disturbance in the indicator signals generated by the GPIO can cancel each other by a complex gain vector, which can be determined by the zero eigenvalue’s left eigenvector of the rank-deficient of the disturbance transfer function matrix. The sufficient conditions for the convergence of the proposed fault detection filter are also given. Numerical examples illustrate the proposed method’s better performance in detecting minor faults.

Resolvent-based tools for optimal estimation and control via the Wiener–Hopf formalism

The application of control tools to complex flows frequently requires approximations, such as reduced-order models and/or simplified forcing assumptions, where these may be considered low rank or defined in terms of simplified statistics (e.g. white noise). In this work we propose a resolvent-based control methodology with causality imposed via a Wiener–Hopf formalism. Linear optimal causal estimation and control laws are obtained directly from full-rank, globally stable systems with arbitrary disturbance statistics, circumventing many drawbacks of alternative methods. We use efficient, matrix-free methods to construct the matrix Wiener–Hopf problem, and we implement a tailored method to solve the problem numerically. The approach naturally handles forcing terms with space–time colour; it allows inexpensive parametric investigation of sensor/actuator placement in scenarios where disturbances/targets are low rank; it is directly applicable to complex flows disturbed by high-rank forcing; it has lower cost in comparison to standard methods; it can be used in scenarios where an adjoint solver is not available; or it can be based exclusively on experimental data. The method is particularly well suited for the control of amplifier flows, for which optimal control approaches are typically robust. Validation of the approach is performed using the linearized Ginzburg–Landau equation. Flow over a backward-facing step perturbed by high-rank forcing is then considered. Sensor and actuator placement are investigated for this case, and we show that while the flow response downstream of the step is dominated by the Kelvin–Helmholtz mechanism, it has a complex, high-rank receptivity to incoming upstream perturbations, requiring multiple sensors for control.

Research and Verification of Trajectory Tracking Control of a Quadrotor Carrying a Load

This paper assumes that considering the unknown and time-varying nature of different strong and weak wind field disturbances and considering the nonlinear, under-driven, strongly coupled quadrotor carrying, a load is disturbed by the complex and variable wind field and unmodeled parts when flying in the real external environment, which will reduce the control effect of the nonlinear controller and make the vehicle fail to affect the flight effect. In order to ensure that the quadrotor carrying a load can carry supplies in the harsh environment for stable trajectory tracking, a neural network adaptive control algorithm is introduced in the article. The neural network algorithm has the role of online dynamic approximation, the compensation of arbitrary external disturbance and the compensation of external disturbance. Its structure is simple and low computation. In the article, the Lyapunov method is used to design the adaptive weight and estimate the weight of the online neural network, and the stability of the system is proved. Finally, the comparison of three algorithms verified by simulation proves that the above interference problem can be solved effectively by the proposed algorithm.

State-based confidence bounds for data-driven stochastic reachability using Hilbert space embeddings

In this paper, we compute finite sample bounds for data-driven approximations of the solution to stochastic reachability problems. Our approach uses a nonparametric technique known as kernel distribution embeddings, and provides probabilistic assurances of safety for stochastic systems in a model-free manner. By implicitly embedding the stochastic kernel of a Markov control process in a reproducing kernel Hilbert space, we can approximate the safety probabilities for stochastic systems with arbitrary stochastic disturbances as simple matrix operations and inner products. We present finite sample bounds for point-based approximations of the safety probabilities through construction of probabilistic confidence bounds that are state- and input-dependent. One advantage of this approach is that the bounds are responsive to non-uniformly sampled data, meaning that tighter bounds are feasible in regions of the state- and input-space with more observations. We numerically evaluate the approach, and demonstrate its efficacy on a neural network-controlled pendulum system.

Integral state-feedback control of linear time-varying systems: A performance preserving approach

An integral extension of state-feedback controllers for linear time-varying plants is proposed, which preserves performance of the nominal controller in the unperturbed case. Similar to time-invariant state feedback with integral action, the controller achieves complete rejection of disturbances whose effective action on the plant is constant with respect to the control input. Moreover, bounded-input bounded-state stability with respect to arbitrary disturbances is shown. A modification for preventing controller windup as well as tuning guidelines are discussed. The efficacy of the proposed technique is demonstrated in simulation for a two-tank system that is linearized along a time-varying reference trajectory.

An alternative method for windup prevention

Abstract Windup effects can be subdivided into controller windup and plant windup. Controller windup can be prevented by stabilizing the compensator during saturation and plant windup by an additional dynamic element. When using a compensating design, i. e., the zeros and poles of the plant are compensated by the poles and zeros of the controller, plant windup does not occur. The compensating control is parametrized by one parameter allowing nearly arbitrary disturbance attenuation. This type of control is restricted to minimum-phase systems. But it has a number of advantages. It simplifies the SISO and especially the MIMO design of compensators with integral action considerably, it has good robustness properties and it allows a diagonal decoupling of the reference behavior for arbitrary MIMO system. Two examples demonstrate the results achievable.

Lagrangian approximations for stochastic reachability of a target tube

We consider the problem of stochastic reachability of a target tube for a discrete-time, stochastic dynamical system with bounded control authority. We propose grid-free algorithms to compute under- and over-approximations of the stochastic reach set, and a corresponding feedback-based controller associated with a given likelihood. Our approach employs set-theoretic (Lagrangian) techniques for nonlinear systems with affine stochastic disturbances. With available set computation tools, these algorithms can only be implemented on linear systems. We use the law of total probability to partition the potentially unbounded disturbance set, and compute minimal and maximal reach sets via a robust approach. We propose a heuristic to partition the disturbance set using an ellipsoid when the disturbance is Gaussian, and a polyhedron otherwise. For linear dynamics and convex and compact sets, we employ existing tools from support functions and robust linear programming to efficiently approximate the stochastic reach set. We synthesize an admissible controller using the disturbance minimal reach sets by solving a series of linear programs. We demonstrate our approach on systems with linear dynamics (time-invariant and time-varying) and arbitrary disturbances (as well as Gaussian), including trajectory following for a Dubin’s vehicle and space vehicle rendezvous and docking.