Design of a Functional H Filter for Linear Singular Systems With an Additional Unknown Input, Bounded Disturbance, and Variable Time Delay

Designing delay-dependent functional observers for LTI systems with multiple known time-varying state delays and unknown time-varying input delays is studied. The input delays are arbitrary, but the state delays should be upper-bounded. In addition, two scenarios of slow-varying and fast-varying state delays are investigated. The results of the paper can also be considered as one of the first contributions considering unknown-input functional observer design for linear systems with multiple time-varying state delays. Based on the Lyapunov Krasovskii approach, delay-dependent sufficient conditions of the exponential stability of the observer in each scenario are established in terms of linear matrix inequalities. Because of using effective techniques, such as the descriptor transformation and an advanced weighted integral inequality, the proposed stability criteria can result in larger stability regions compared with the other papers that study functional observers for time-varying delay systems. Furthermore, to help with the design procedure, a genetic algorithm-based scheme is proposed to adjust a weighting matrix in the established linear matrix inequalities. Two numerical examples illustrate the design procedure and demonstrate the efficacy of the proposed observer in each scenario. Copyright © 2016 John Wiley & Sons, Ltd.

In this paper we propose a new method of a time design observer for a bilinear system with unknown input and constant time delays in both state and control vectors. This approach is based on the stability of Lyapunov Krasovskii stability theory and the matrix inequality resolution approach (LMI). It provides an estimation of a functional state vector. The proposed method is tested on a given numerical example and proves its effectiveness.

In this paper, the adaptive control problem is addressed for active vehicle suspension systems with the unknown nonlinearity as well as the unknown time-varying input delay. A dynamic gain control frame is proposed to suppress vehicle vibration and maintain the required suspension performance. Firstly, a dynamic gain extended state observer (ESO) is constructed to obtain the unknown velocity information and nonlinearity for the implementation of the control scheme. Moreover, a robust control method with a dynamic gain control term and a time delay compensation term is designed to mitigate the effect of unknown input time delay and uncertainty on system stability. By resorting to the Lyapunov-Krasovkii stability theory, the ultimate uniform boundedness of all signals in the closed-loop vehicle active suspension system is guaranteed. Finally, an example is presented as an illustration of the effectiveness of the proposed method.

Robust backstepping control of uncertain nonlinear systems with unknown time-varying input delay

For an individual affected by a neuromuscular condition (NC), functional electrical stimulation (FES)-induced cycling provides a means of functional restoration and therapeutic exercise. Although FES-cycling has been shown to have numerous benefits, there are challenges to implementing closed-loop FES control for coordinated motion. For example, there exists a potentially destabilizing input delay between the application (or removal) of stimulation and the resulting muscle force. Moreover, switching between multiple actuators (such as FES or motor control) can also be destabilizing. This brief develops delay-dependent switching conditions and a robust control method to account for an unknown time-varying input delay of a switched system. A Lyapunov-like analysis is performed to yield semiglobal exponential cadence tracking to an ultimate bound. Experiments were performed on six able-bodied participants and four participants with NCs to validate the developed controller. The proposed controller resulted in an average cadence error of 0.01 ± 2.00 revolutions per minute (RPM) for the able-bodied participants and 0.01 ± 2.72 RPM for participants with NCs.

Functional electrical stimulation (FES) is commonly used to facilitate cycling tasks for people with lower-limb movement disorders. In this work, FES and motor controllers are designed to track a desired power and cadence, respectively, and a Lyapunov-based switched systems analysis is performed to guarantee uniformly ultimately bounded power tracking and global exponential cadence tracking for a switched, delayed, nonlinear, and uncertain FES-cycling system. A unique challenge in this problem is that there is an unknown time-varying input delay to produce force, and a different unknown time-varying residual input delay where force is still produced after stimulation is removed. These delays impact the dwell-time conditions that dictate stimulation timing, and if not properly accounted for can lead to undesired effects such as antagonistic muscles exerting force at the same time or potential instabilities. The proposed controllers were validated by experimental analysis of four participants with neurological conditions (NCs) and five able-bodied participants, and yielded average power and cadence tracking errors of 0.01 ± 0.09 W and −0.05 ± 0.65 revolutions per minute (RPM), respectively, for the able-bodied participants and 0.01 ± 1.11 W and −0.07 ± 1.17 RPM, respectively, for the participants with NCs.

Delayed finite-dimensional observer-based control of 1-D parabolic PDEs

This note studies the LQ and LQG problems for linear time invariant systems with a single time-varying input delay and instantaneous (memoryless) state feedback. We extend the memoryless state feedback solution proposed in [1] in two directions. We prove that in the deterministic case a memoryless state feedback can be in general optimal only up to a certain delay, for which we provide a sufficient, and sometimes strict, bound. Moreover, we show that this memoryless control is optimal also in the case of time-varying delays and that the quadratic cost functional has the same value as in the case without delay. For time varying delays the control law requires that the relationship between time points in which the input is generated and applied is known and invertible even if the delay function needs not to be differentiable or even continuous. Finally, we prove that the cost functional is bounded also in the stochastic case for the same delay interval as in the deterministic case, but with a larger cost than the delay-less LQG solution.

Teleoperation system performance suffers from the delays in communication lines. These delays are usually variable time delays. The customary wave variable technique used for constant time delays cannot provide satisfactory results to stabilize the system under variable delays. Another problem is observed in the position tracking performance of the limited-workspace teleoperation systems. Although wave variable technique is proven to track position demands successfully under constant time delays given that there is no communication failure, position tracking performance also degrades under variable delays. In this paper, a new controller is proposed to stabilize the system and enhance position tracking performance under variable time delays. This proposed controller is then applied to an identical master-slave teleoperation configuration which qualifies as a limited-workspace teleoperation system.

Signal correlator with programmable variable time delay based on optical coherent transients

Motorized functional electrical stimulation (FES) cycling has been demonstrated to have numerous health benefits for individuals suffering from neurological disorders. FES-cycling is usually designed to track the desired trajectories in real time. However, there are input delays between the exertion of the stimulation and the corresponding muscle contraction that potentially destabilize the system and undermine training efforts. Meanwhile, muscle fatigue gives rise to a time-varying input delay and decreased force. Moreover, switching between FES and motor control can be chattering and destabilizing owing to the high frequency. This article constructs Lyapunov-Krasovskii functionals to analyze the stability and robustness of the nonlinear cycling system with time-varying input delay. A new average dwell time condition is then provided to ensure the input-to-state stability of the considered systems. Finally, numerical simulations are illustrated to verify the effectiveness of the developed controller.

In this paper, the problem of stability and tracking performance of FRVF (Forbidden Region Virtual Fixture) for bilateral nonlinear teleoperation systems is studied in presence of varying time delay. It is proved that PD-like controllers can stabilize the teleoperation systems with FRVF in slave side and variable time delay in communication channels. It is also proved by proposed Lyapunov-Krasovskii's function that the mentioned problem of stability and tracking performance of FRVF is satisfied. Finally, the proficiency of this approach is demonstrated by simulating the method on a pair of 6-DOF (Degree of Freedom) PHANToM Omni robots with nonlinear dynamics. Keywords— Virtual fixture; variable delay; delayed teleoperation system; nonlinear teleoperation.

Stabilization and robustness analysis for time-varying systems with time-varying delays using a sequential subpredictors approach

Adaptive control is essential and effective for reliable quadrotor operations in the presence of uncertain modeling parameters and unknown time-delayed inputs. This paper presents an original radial basis function neural network-based adaptive fractional-order backstepping controller (RBF-ADFOBC). The nonlinearity of the time-delayed inputs is eliminated by introducing an augmented state variable via Pade’s approximation method. For each subsystem in the quadrotor dynamics, a companioned second-order compensation system is developed. The candidate Lyapunov functions are then properly designed by incorporating the control errors, parameter uncertainties and estimation errors of the neural networks’ weight vectors. It is shown that the semi-globally uniformly ultimately boundedness of all the state variables and the estimation error of uncertain parameters can be guaranteed. In addition, the trajectory-tracking error of the state variables can be driven to an adjustable small neighborhood of origin by properly setting the selectable parameters. Numerical simulations reveal that the tracking performance of the proposed controller can be improved continuously as the fractional order increases to a specific positive value, and the controller with a negative order may demonstrate higher robustness to the modeling uncertainties. Favorably, the comparison to the other two previous controllers further reveals the superior tracking accuracy and robustness of the proposed RBF-ADFOBC controller.

In the present work, a control method is developed to yield lower limb tracking with neuromuscular electrical stimulation (NMES), despite an unknown time-varying input delay intrinsic to NMES, uncertain nonlinear dynamics, and additive bounded disturbances. A novel filtered tracking error signal is designed to obtain a delay-free control expression in the closed-loop error system. Furthermore, the filtered tracking error signal removes the requirement of exact knowledge of the input delay in the control design. The control development is based on an approach that uses Lyapunov-Krasovskii functionals in a Lyapunov-based stability analysis to prove ultimately bounded tracking error signals. Experimental results are provided to demonstrate the performance of the developed controller.