Error Constraints Research Articles

Singularity-Free Fixed-Time Fuzzy Control for Robotic Systems With User-Defined Performance

In this article, the singularity-free adaptive fuzzy fixed-time control problem is studied for an uncertain n-link robotic system with the position tracking error constraint. The controlled robotic system can be described as a multiple-input-multiple-output system.To implement the user-defined performance, an improved error conversion mechanism based on performance functions is presented such that the converted error is limited to an interval greater than zero, and an appropriate barrier Lyapunov function (BLF) is constructed to avoid the breach of position tracking error constraint. The fuzzy approximator is utilized to estimate the unknown functions. The significance and challenges of this article are to establish a new error conversion mechanism and design corresponding BLF that can be integrated into fixed-time control design to present a singularity-free adaptive fuzzy fixed-time control scheme. Benefits of the proposed adaptive fixed-time controller in comparison to the current approaches are that it cannot cause the singularity issue appearing in backstepping-based fixed-time control design and ensures quick transient response. Combining with Lyapunov stability theory, the boundedness of the closed-loop signals is ensured, and the position tracking error can be constrained in the user-defined performance boundaries. Finally, simulation results demonstrate the feasibility of the proposed control strategy.

Distributed fault-tolerant consensus tracking control for multiple Lagrangian systems with preset error bound constraints

Actuator faults often occur in physical systems, which seriously affect the transient performance and control accuracy of the system. For the finite-time consensus tracking problem of multiple Lagrangian systems with actuator faults and preset error constraints, a novel distributed fault-tolerant controller is proposed in this paper. The proposed controller is developed based on the barrier Lyapunov function method and the adding a power integrator technique, which can not only guarantee the steady-state performance of the system but also its transient performance. Due to its strong sensitivity to the variation of system errors, the proposed controller can quickly eliminate the system initial errors and the error perturbations caused by actuator faults. That is, the controller can guarantee that the consensus error converges to zero in a finite time and is always constrained within the preset error bound. Finally, the effectiveness of the developed controller is verified by simulation of a multi-manipulator system.

Comparing the performance and composition of tracking error constrained and unconstrained portfolios

Active portfolios subject to tracking error constraints are bound by an ellipse in absolute risk-return space, known as the constant tracking error frontier, where the absolute risk is the standard deviation of portfolio returns. Portfolios within this space are presented: Jorion’s (2003) portfolio, which lies on the frontier and has the same risk as the benchmark, and the maximum Sharpe ratio portfolio (also on the frontier and referred to as the constant tracking error constrained market portfolio in this paper). Using historical data from an emerging market (South Africa), the performance and composition of these portfolios are explored and compared with the traditional market portfolio (the maximum Sharpe portfolio on the efficient frontier). The results illustrate how these portfolios perform during bull and bear markets and provide an indication of the positions in assets and the amount of rebalancing required to maintain these portfolios: (i) Contrary to theory, the returns and Sharpe ratio of the traditional market portfolio are substantially worse than the constrained portfolios for extended periods of time; (ii) The constrained portfolios perform similarly and require less rebalancing; (iii) There is evidence for statistically significant correlations between the compositions of the traditional market portfolio and the constrained portfolios, and further research is recommended. This work may be used to install optimal risk-adjusted active investment strategies net of transaction costs.

Non-Proportionality Indices and Error Constraint in Modal Analysis of Viscously Damped Linear Structures

Use of modal procedures in systems with non-proportional damping (such as structures with added viscous damping systems) results in response errors, shown in this study to depend on dissimilar and often conflicting conditions for different variables and stories; thus, it is not possible to propose simple rules based on structural or damping properties to limit the error in a global way. However, four existing indices (originally proposed to measure damping non-proportionality) present a positive correlation with the extreme errors in modal procedures for all variables and stories. Thus, limiting the index value is a sufficient condition to keep the error in all variables within a given threshold. For practical application, limit values for these indices are tabulated as a function of error and can be used as an acceptance criterion for the validity of modal procedures.

Portfolio performance under tracking error and benchmark volatility constraints

Purpose Using a portfolio comprising liquid global stocks and bonds, this study aims to limit absolute risk to that of a standardised benchmark and determine whether this has a significant impact on expected return in both high volatility period (HV) and low volatility period (LV). Design/methodology/approach Using a traditional benchmark comprising 40% equity and 60% bonds, a constant tracking error (TE) frontier was constructed and implemented. Portfolio performance for different TE constraints and different economic periods (expansion and contraction) was explored. Findings Results indicate that during HV, replicating benchmark portfolio risk produces portfolios that outperform both the maximum return (MR) portfolio and the benchmark. MR portfolios outperform those with the same risk as that of the benchmark in LV. The MR portfolio weights assets to obtain the highest return on the TE frontier. During HV, the benchmark replicated risk portfolio obtained a higher absolute risk value than that of the MR portfolio because of an inefficient benchmark. In HV, the benchmark replicated risk portfolio favoured intermediate maturity treasury bills. Originality/value There is a dearth of literature exploring the performance of active portfolios subject to TE constraints. This work addresses this gap and demonstrates, for the first time, the relative portfolio performance of several standard portfolio choices on the frontier.

Finite-Time Adaptive Fuzzy Prescribed Performance Control for High-Order Stochastic Nonlinear Systems

In this article, the high-order nonlinear system is commonly studied in an underactuated weakly coupled mechanical system, the control design is difficult from the tractional control design for nonlinear systems. Thus, we study the finite-time fuzzy adaptive error constraint control problem for stochastic high-order nonlinear nonstrict feedback systems. Fuzzy logic systems are utilized to identify the unknown nonlinear dynamics, a new error transfer variable is used to achieve the prescribed performance. Based on adding a power integrator technique and adaptive backstepping recursive control, a novel adaptive fuzzy finite-time prescribed performance control scheme is developed. By utilizing stochastically finite-time stable theory, the proposed control method can guarantee that the high-order system is semi-global finite-time stable in probability. Finally, both numerical and practical simulations are provided to verify the feasibility and effectiveness of the developed control method.

Data-driven sliding mode control of shape memory alloy actuators with prescribed performance

This paper proposes a data-driven sliding mode control (SMC) method with tracking error constraint for a shape memory alloy (SMA) actuated system. More specifically, a new SMC method with prescribed performance is investigated by adopting the equivalent dynamic linearization technique and a novel transformed error algorithm to guarantee that the tracking error can converge into a preassigned region. Meanwhile, the proposed control method can effectively ensure the convergence rate and the steady-state error within a prescribed bound, merely depending on the input/output data without implicit or explicit information of the systems, which is more valuable for the practical application. The presented control method has been implemented on an SMA actuated system successfully and experimental results have shown that the proposed control is easily applicable and highly precise. In addition, the tracking error of the SMA actuated system can be constrained in a preassigned domain by the proposed control method.

AxBMs: Approximate Radix-8 Booth Multipliers for High-Performance FPGA-Based Accelerators

The focus of existing designs on approximate radix-8 Booth multipliers has been on ASIC-based platforms. These multipliers are based on an approximation as defined for ASIC-based systems, so they cannot achieve comparable performance gains when used for FPGA-based hardware accelerators. This is due to the inherited architectural differences between FPGAs and ASICs. This brief bridges this gap by proposing high-performance approximate radix-8 Booth multipliers whose designs target FPGA-based systems. Hence, two approximate radix-8 Booth multipliers (referred to as AxBM1 and AxBM2) are proposed. Approximation is implemented such that the 6-input lookup table (LUT) and the associated carry chains of the FPGAs are fully utilized. AxBM2 exhibits 49% improvement in delay compared to the previous best FPGA-targeted design (Booth-Approx). AxBM2 has the advantage of complementing errors; this feature has been combined with truncation to achieve up to 60% in energy savings. Moreover, the resolution of the previous state-of-the-art error-energy Pareto front is improved, such that better energy gains can be achieved for a given error constraint. As a case study, the proposed multipliers are applied to the application of Sobel edge detection, AxBM2 detected 98.45% edges with energy savings of 26.41%.

Prescribed performance output feedback synchronisation control of bilateral teleoperation system with actuator nonlinearities

This work investigates output feedback synchronisation control of uncertain bilateral teleoperation system with synchronisation error constraints, time-varying delay, actuator backlash-like hysteresis and unknown control direction. The constrained system is transformed into unconstrained one via the output error transformation. A Prescribed-Performance Function (PPF) is proposed to ensure that all the outputs with predefined transient and steady states' performances converge to a predefined set. In addition, a radial basis function neural network (RBFNN) is utilised to estimate the uncertain dynamics. Moreover, a Nussbaum-type function is introduced to tackle the loss of control direction due to the actuator backlash-like hysteresis. By Lyapunov stability analysis, all the closed-loop signals are guaranteed to converge to a small neighbourhood of the origin. Finally, simulation results are provided to demonstrate the effectiveness of the proposed method.

Global smoothing for five-axis linear paths based on an adaptive NURBS interpolation algorithm

The five-axis tool path generated by CAM software usually consists of a series of linear paths. The tangent direction at the corner of the adjacent line segment will suddenly change, and the curvature is also discontinuous, which will cause vibration and shock during the machining process. Thus, a global corner smoothing algorithm based on cubic NURBS interpolation is proposed to smooth the linear paths in this paper, so as to achieve G2 continuous for five-axis linear paths. The algorithm proposed does not require matrix operations to solve the control points, and it can also reduce the number of control points while satisfying the interpolation error. The algorithm is then used to generate smooth NURBS path for ceramic core burrs and blockage repair. The simulation and experiment show that the algorithm proposed can satisfy the error constraints, reduce the vibration of the motion axis, and improve the surface quality of laser cutting.

Decentralized optimal tracking control for large‐scale nonlinear systems with tracking error constraints

SummaryIn this article, a decentralized optimal tracking control strategy is proposed for a class of nonlinear systems with tracking error constraints by utilizing adaptive dynamic programming (ADP). It should be noted that ADP technology cannot be directly used to solve decentralized optimal tracking problem of large‐scale interconnected nonlinear system with nonzero equilibrium points, since that an infinite domain performance index function may result in an unsolvable solution. In addition, by introducing a smooth function, the constrained tracking error is transformed into an unconstrained one. Then, the error dynamics and a new infinite domain performance index function are designed, such that ADP technology can be used. Following the designed performance index function, the tracking error can be ensured within a small neighborhood of zero. Finally, the feasibility and the effectiveness of the proposed decentralized optimal control scheme are verified through two simulation examples.

Low-Cost Active Anomaly Detection with Switching Latency

Consider the problem of detecting anomalies among multiple stochastic processes. Each anomaly incurs a cost per unit time until it is identified. Due to the resource constraints, the decision-maker can select one process to probe and obtain a noisy observation. Each observation and switching across processes accompany a certain time delay. Our objective is to find a sequential inference strategy that minimizes the expected cumulative cost incurred by all the anomalies during the entire detection procedure under the error constraints. We develop a deterministic policy to solve the problem within the framework of the active hypothesis testing model. We prove that the proposed algorithm is asymptotic optimal in terms of minimizing the expected cumulative costs when the ratio of the single-switching delay to the single-observation delay is much smaller than the declaration threshold and is order-optimal when the ratio is comparable to the threshold. Not only is the proposed policy optimal in the asymptotic regime, but numerical simulations also demonstrate its excellent performance in the finite regime.

Event-Triggered Adaptive Fault-Tolerant Control for Nonaffine Uncertain Systems With Output Tracking Errors Constraints

This article studies the event-triggered adaptive fuzzy output feedback fault-tolerant control problem for nonaffine uncertain systems with output tracking errors constraints and actuator faults. First, the mean value theorem and input compensation method are used to decouple the control input signal, and an adaptive state observer is established to estimate unknown state. Then, in the presence of disturbances and actuator faults, an improved event-triggered adaptive fault-tolerant control strategy is designed to adjust control input signals, which effectively reduce the computing burden in communication, and the input-to-state stability assumption is not required. Furthermore, it is proved by Lyapunov stability analyses that the proposed control method guarantees output tracking errors can converge to the prescribed performance bounds and all signals are uniformly ultimately bounded. Finally, the validity of the control algorithm is verified through the simulation results.

Research on Human Motion Monitoring Method Based on Multi-Joint Constraint Filter Model

In recent years, with the increasing application of human motion monitoring technology in virtual reality, medical health, human-computer interaction, and other fields, higher requirements have been put forward for measurement accuracy. Aiming at the problem of large accumulative measurement error and multi-joint constraint in the traditional inertial measurement system, a multi-joint constrained filter model human motion monitoring method based on data fusion is proposed. Firstly, an accelerometer and magnetometer are used to construct the initial attitude angle calculation model of the human body at rest. Secondly, combined with gyroscope, accelerometer and magnetometer, the attitude optimal estimation model based on Extended Kalman Filter (EKF) algorithm for human body motion was established. Then, a global coordinate system of human multi-joints is established, and the joint constraint is introduced into the attitude optimal estimation model by using the estimation projection method, and the multi-joint constraint filtering model of human motion monitoring is constructed. Finally, a multi-inertial measurement unit (MIMU) human motion monitoring system was built, and the simulation and experimental analysis were carried out. The experimental results show that the maximum angular measurement error is about 1° after filtering with the motion monitoring method proposed in this paper. Compared with the existing algorithm, the accuracy of the three angle measurements is improved by 38.2%, 39.3% and 67.4%, respectively. Based on this, the human motion monitoring system designed can effectively monitor human motion.

Fixed-Time Adaptive Fuzzy Control for Uncertain Nonstrict-Feedback Systems With Time-Varying Constraints and Input Saturations

This article investigates the adaptive fuzzy tracking control design for uncertain nonstrict-feedback nonlinear systems with time-varying constraints and asymmetric input saturations. It is known that time-varying output constraint, time-varying error constraints, and input saturations are commonly seen issues in many practical engineering systems due to inherent physical limitations and performance requirements. To deal with these problems and improve the convergence rate of the control system, a novel fixed-time convergent adaptive fuzzy control scheme is proposed for the considered uncertain nonlinear systems via the time-varying barrier Lyapunov function (BLF) technique. First, to deal with the unknown nonlinearities and uncertainties in the system dynamic model, fuzzy logic systems are utilized to approximate the unknown functions of the considered model. Then, the problem of asymmetric input amplitude and rate saturations is handled by constructing a unified smooth characterizing function and an innovative auxiliary design signal system. Subsequently, considering physical limitations and performance requirements, a novel time-varying BLF-based adaptive fuzzy backstepping control scheme is designed for the uncertain nonstrict-feedback nonlinear systems to realize superior tracking performances and keep the states staying in predefined time-varying compact regions during operations. Further, rigorous theoretical analyses have been conducted to show that the proposed control scheme achieves fixed-time convergence of all signals in the closed-loop control system. Finally, representative simulation results verify the effectiveness of the proposed control scheme.

Fixed-time consensus control for multi-agent systems with prescribed performance under matched and mismatched disturbances

The consensus problem is considered for multi-agent systems with disturbances. Three fixed-time prescribed performance methods are proposed to satisfy the transient performance and steady-state performance of multi-agent systems consensus. If the multi-agent systems are affected by matched disturbances, the consensus tracking errors constraints are guaranteed at first. Next, the consensus tracking errors constraints and their change rates constraints are further considered. Moreover, with the help of a fixed-time observer, the consensus tracking errors constraints result is expended to the case of multi-agent systems affected by mismatched disturbances. The proposed methods can provide the satisfactory system performances, including that consensus tracking errors always evolve within predefined bounds, converge to a small closed region containing zero in fixed time and then converge to zero asymptotically. Simulations are provided to verify the effectiveness of the proposed methods.

CORR Synthesis: When Should the Orthopaedic Surgeon Use Artificial Intelligence, Machine Learning, and Deep Learning?

CORR Synthesis: When Should the Orthopaedic Surgeon Use Artificial Intelligence, Machine Learning, and Deep Learning?

FERMAT: FPGA energy reduction method by approximation theory

Today’s field programmable gate arrays (FPGAs) offer a significant computational power and are commonly used in modern commercial digital designs. However, they generally suffer from a large power consumption, which makes them unfit for battery-operated handheld devices. This paper addresses this problem by bringing the notion of approximate computing into the realm of reconfigurable devices such as LUT-based FPGAs. The proposed approximation is done by altering LUT contents in an exact design. The impact of this kind of approximation on output accuracy as well as design power consumption will be discussed. Once the theoretical foundation is established, we propose a method, called FERMAT (FPGA Energy Reduction Method by Approximation Theory), which takes an exact FPGA design and converts it into an approximated equivalent with a considerably reduced power consumption given a maximum error constraint. The effectiveness of FERMAT is shown by measuring the actual power consumption of an FPGA device performing an image processing application. Experimental results show about 8.5% power saving with an imperceptible loss in image quality.

Fuzzy adaptive backstepping load following control for MHTGRs with power error constraint and output disturbances

This paper proposes a fuzzy adaptive backstepping controller for load following of modular high-temperature gas-cooled reactors (MHTGRs) in the presence of power error constraint and output disturbances. The mathematical model of the MHTGRs is firstly constructed based on the point-reactor kinetics equations with one equivalent delayed neutron group. After that, a fuzzy adaptive backstepping control strategy with the consideration of power error constraint and output disturbances is proposed to improve load following performance. The proposed control scheme enables the power error never to violate constraint limitation by employing the barrier Lyapunov function method. Meanwhile, the fuzzy logic system (FLS) is applied to accurately estimate model unknown lumped term which consists of unmeasured states and output disturbances, and thereby enhancing the disturbances rejection capability and robustness of the proposed control scheme. Stability analysis and the convergence of the power error are guaranteed according to the Lyapunov directly method. In the end, simulations and comparisons with conventional backstepping controller are conducted to verify the improved load following performance of the proposed fuzzy adaptive backstepping control strategy.

Error Analysis of Grouped Multilevel Space-Time Trellis Coding with the Combined Application of Massive MIMO and Cognitive Radio

In today’s scenario, demand for error-correcting codes with minimal error constraints for wireless communications. Multilevel coding scheme with trellis codes as component codes provides flexible data transmission rates, coding gain, diversity gain with improved spectral efficiency and low decoding complexity. This paper investigates the potential improvements by using the Multilevel coding scheme with massive Multiple-Input Multiple-Output in Cognitive Radio Networks with trellis codes as component codes. This paper discussed space-time coding with beamforming and antenna grouping according to the channel state information. Multilevel Space-time coding is based on multi-level Quadrature Amplitude Modulation signaling and beamforming to mitigate the effect of primary users for the enactment of secondary users in Cognitive Radio. The primary users provide channels dynamically to the secondary user for an unknown duration. Our transmission use Quadrature Amplitude Modulation based signals, with an adaptive grouping of antenna which weight according to the optimization, which inherently depends upon the resource allocation of the secondary user. The results show that the proposed coded system achieves Bit error rate/Symbol error rate/Frame error rate and Signal to noise ratio varies according to sources sensing time.