Asymmetric Constraints Research Articles

Adaptive neural network state constrained fault-tolerant control for a class of pure-feedback systems with actuator faults

In this paper, an adaptive neural network (NN) constrained fault-tolerant control (FTC) method is proposed for a class of nonlinear pure feedback systems with actuator faults and state constraints. By designing a fault-tolerant compensation controller and a new asymmetric time-varying tangent Barrier Lyapunov function (ATVTBLF), the problem of time-varying asymmetric state constraints caused by actuator failure is solved. The actuator takes into account both loss of effectiveness and bias fault. Different from the existing asymmetric BLF, the new BLF solves the problem of asymmetry under tangent constraints and expands the application range of the asymmetric constraint. NN is used to approximate the unknown items generated in the process of designing fault-tolerant controllers. Based on the Lyapunov stability analysis, it is proved that all signals in the closed-loop system are semi-globally uniformly ultimately bounded (SGUUB), and all states do not violate the bounds. Finally, the simulation example verifies the effectiveness of the proposed method.

Anti-saturation adaptive fault-tolerant control with fixed-time prescribed performance for UAV under AOA asymmetric constraint

This paper presents an anti-saturation adaptive fault-tolerant control scheme with fixed-time prescribed performance for the longitudinal model of fixed wing UAV under actuator faults, control input saturation, angle of attack (AOA) asymmetric constraint and uncertainties. First, by introducing equivalent error transformation technique, the error transformed models of the altitude and airspeed tracking subsystems are strictly constructed. Second, asymmetric saturation function, auxiliary system and barrier Lyapunov function (BLF) are incorporated to guarantee AOA maintain in the asymmetric constraint. Then, neural network approximation structures are combined with adaptive robust terms to handle the lumped disturbances. Furthermore, Nussbaum-type gain technique is adopted to deal with the unknown time-varying parameter arising from input saturation and actuator faults. According to the stability analysis, the altitude and airspeed tracking errors evolve strictly inside the fixed-time performance envelops, while the AOA remains in asymmetric constraint and all signals in closed-loop system are uniformly ultimately bounded. Finally, numerical simulation is presented to verify the effectiveness and superiority of proposed control scheme.

Asymptotic stabilization of nonlinear systems with convex-polytope input constraints by continuous input

In this paper, we propose an asymptotic stabilization controller for a nonlinear system with a convex-polytope input constraint. Moreover, we show that the controller has inverse optimality in the domain of attraction. The controller input is continuous in the set in which the asymptotic stabilization is guaranteed. We consider the asymmetric constraint for zero-input, and this bias is adjusted by using a non-uniform scaling on each vertex point in the neighborhood of the origin. Therefore, the input cost of the inverse optimal performance functional is approximated by a quadratic function near the origin.

Optimal event‐triggered control for C‐T system with asymmetric constraints based on dual heuristic dynamic programing structure

AbstractIn this article, a method that applies event‐triggered (ET) mechanism control to continuous‐time (C‐T) nonlinear systems with asymmetric constraints based on dual heuristic dynamic programing (DHP) structure is proposed. At first, we derive ET mechanism from traditional time‐triggered and give the Hamilton–Jacobi–Isaacs (HJI) equation. Second, we give the triggering condition and prove the stability of system under ET mechanism. Then, two neural networks (NNs) are introduced, one of which is the critic network, which is designed to approximate the partial derivatives of value function with respect to inputs, and approximate disturbance policy. The other is the action network, which is used to acquire the estimation optimal control policy. Furthermore, we choose a suitable Lyapunov candidate function to prove that the system and NNs weight estimation errors are uniformly ultimately bounded (UUB). Besides, it is important that we prove that Zeno phenomenon can be avoided. Finally, simulation results are shown that the proposed method is feasible.

Power Spectra of Constrained Codes With Level-Based Signaling: Overcoming Finite-Length Challenges

In various practical systems, certain data patterns are prone to errors if written or transmitted. In magnetic recording and communication over transmission lines, data patterns causing consecutive transitions that are not sufficiently separated are prone to errors. In Flash memory with two levels per cell, data patterns causing high–low–high charge levels on adjacent cells are prone to errors. Constrained codes are used to eliminate error-prone patterns, and they can also achieve other goals. Recently, we introduced efficient binary symmetric lexicographically-ordered constrained (LOCO) codes and asymmetric LOCO (A-LOCO) codes to increase density in magnetic recording systems and lifetime in Flash systems by eliminating the relevant detrimental patterns. Due to their application, LOCO and A-LOCO codes are associated with level-based signaling. Studying the power spectrum of a random signal with certain properties is principal for any storage or transmission system. It reveals important properties such as the average signal power at DC, the bandwidth of the signal, and whether there are discrete power components at certain frequencies. In this paper, we first modify a framework from the literature in order to introduce a method to derive the power spectrum of a sequence of constrained data associated with level-based signaling. We apply our method to infinitely long sequences satisfying symmetric and asymmetric constraints. Next, we show how to generalize the method such that it works for a stream of finite-length codewords as well, thus demonstrating how to overcome the associated finite-length challenges. We use the generalized method to devise closed forms for the spectra of finite-length LOCO and A-LOCO codes from their transition diagrams. Our LOCO and A-LOCO spectral derivations can be performed for any code length and can be extended to other constrained codes. We plot these power spectra, and discuss various important spectral properties for both LOCO and A-LOCO codes. We also briefly discuss an alternative method for deriving the power spectrum and introduce an idea towards reaching the spectra of self-clocked codes.

Intelligent optimal tracking with asymmetric constraints of a nonlinear wastewater treatment system

AbstractThe wastewater treatment is an effective method for alleviating the shortage of water resources. In this article, a data‐driven iterative adaptive tracking control approach is developed to improve the control performance of the dissolved oxygen concentration and the nitrate nitrogen concentration in the nonlinear wastewater treatment plant. First, the model network is established to obtain the steady control and evaluate the new system state. Then, a nonquadratic performance functional is provided to handle asymmetric control constraints. Moreover, the new costate function and the tracking control policy are derived by using the dual heuristic dynamic programming algorithm. In the present control scheme, two neural networks are constructed to approximate the costate function and the tracking control law. Finally, the feasibility of the proposed algorithm is confirmed by applying the designed strategy to the wastewater treatment plant.

Adaptive neural output-feedback control for a class of output-constrained switched stochastic nonlinear systems

In this paper, a neural network-based adaptive output-feedback control problem is investigated for a class of output-constrained switched stochastic nonlinear systems. By introducing nonlinear mapping, the asymmetric and symmetric output constrained stochastic nonlinear system is transformed into a new system without any constraint. It is the first time that a switching system is used to convert symmetric and asymmetric output constraints in the same system. An adaptive neural output-feedback controller is developed based on the backstepping technique. A state observer is designed to estimate the unmeasurable system state signals. An adaptive controller is designed to ensure that the output tracking error converges to a small region of the origin. The control scheme ensures that all signals in the closed-loop systems are semi-global uniformly ultimately bounded. Results of simulation cases are presented to prove the effectiveness of the theoretical analysis.

Symmetric and Asymmetric Multiple Impulsive Constraints Without Friction and Their Characterization

We present two meaningful and effective non-ideal constitutive characterizations for a multiple impulsive constraints {mathcal {S}} comprising a finite number of non-ideal frictionless constraints of codimension 1, described in the geometric setup given by the space–time bundle {mathcal {M}} of a mechanical system in contact/impact with {mathcal {S}}. Thanks to the geometric structures associated to the elements of {mathcal {S}}, we introduce a symmetric characterization, that does not distinguish the elements forming {mathcal {S}} as regards mechanical behavior, and an asymmetric one that makes this distinction. Both the characterizations provide a generalization of the characterization of ideal multiple constraints presented in Pasquero (Q Appl Math 76(3):547–576, 2018). The iterative nature of these characterizations allows the introduction of two algorithms determining the right velocity of the system in case of single or multiple contact/impact with symmetric or asymmetric constraints {mathcal {S}}, once the elements forming {mathcal {S}} and the left velocity of the system are known. We show the effectiveness of the two possible choices with explicit implementations of these algorithms in two significant examples: a simplified Newton’s cradle system for the symmetric characterization and a disk in multiple contact/impact with two walls of a corner for the asymmetric one.

Prescribed-time formation control of surface vessels with asymmetric constraints on LOS range and bearing angles

This paper investigates a prescribed-time formation control problem for a group of underactuated surface vessels (USVs) with asymmetric constraints on the line-of-sight range and bearing angle tracking errors. To cope with the time-varying constraints, we present a control method based on asymmetric barrier Lyapunov functions. A scaling function is introduced in the control law with which the settling time can be prescribed in advance as needed. The controllers are developed under the backstepping method framework, with the environmental disturbance being estimated by a novel prescribed-time observer, to ensure the global prescribed-time convergence of the USV formation. We prove that under the proposed control method, despite the interference of environmental disturbance, the formation tracking errors can converge to zero in the prescribed time without violating the constraints on the tracking errors. Simulation results further illustrate the effectiveness of the method proposed in this paper.

Robust neural network‐based tracking control for unmanned surface vessels under deferred asymmetric constraints

AbstractIn this article, the constraints on unmanned surface vessels are imposed after a certain time after the system operation. Based on the shift function, this article proposes an asymmetric barrier Lyapunov function and achieves the control scheme with deferred and asymmetric full‐state constraints. In addition, radial basis function neural network and an antiwindup compensator are adopted for the problems of uncertainties and input saturation. The simulation results demonstrate the feasibility of the proposed control strategies.

The effect of total knee geometries on kinematics: An experimental study using a crouching machine.

Obtaining anatomic knee kinematics after a total knee is likely to improve outcomes. We used a crouching machine to compare the kinematics of standard condylar designs with guided motion designs. The standard condylars included femoral sagittal radii with constant radius, J-curve and G-curve; the tibial surfaces were of low and high constraint. The guided motion designs were a medial pivot and a design with asymmetric condylar shapes and guiding surfaces. The machine had a flexion range from 0° to 125°, applied quadriceps and hamstring loading, and simulated the collateral soft tissues. The kinematics of all standard condylar knees were similar, showing only small anterior-posterior displacements and internal-external rotations. The two asymmetric designs showed posterior displacements during flexion, but less axial rotations than anatomic knees. The quadriceps forces throughout flexion were very similar between all designs, reflecting similar lever arms. It was concluded that standard condylar designs, even with variations in sagittal radii, are unlikely to reproduce anatomic kinematics. On the other hand, designs with asymmetric constraint between medial and lateral sides, and other guiding features, are likely to be the way forward. The mechanical testing method could be further improved by superimposing shear forces and torques during the flexion-extension motion, to include more stressful in vivo functional conditions.

Adaptive Finite-Time Tracking Control of Nonholonomic Multirobot Formation Systems With Limited Field-of-View Sensors.

This article studies the vision-based tracking control problem for a nonholonomic multirobot formation system with uncertain dynamic models and visibility constraints. A fixed onboard vision sensor that provides the relative distance and bearing angle is subject to limited range and angle of view due to limited sensing capability. The constraint resulting from collision avoidance is also taken into account for safe operations of the formation system. Furthermore, the preselected specifications on transient and steady-state performance are provided by considering the time-varying and asymmetric constraint requirements on formation tracking errors for each robot. To address the constraint problems, we incorporate a novel barrier Lyapunov function into controller design and analysis. Based on the recursive adaptive backstepping procedure and neural-network approximation, we develop a vision-based formation tracking control protocol such that formation tracking errors can converge into a small neighborhood of the origin in finite time while meeting the requirements of visibility and performance constraints. The proposed protocol is decentralized in the sense that the control action on each robot only depends on the local relative information, without the need for explicit network communication. Moreover, the control protocol could extend to an unconstrained multirobot system. Both simulation and experimental results show the effectiveness of the control protocol.

Asymmetric Constraint Fourier Ptychography Microscopy

Fourier ptychography microscopy (FPM) is a phase retrieval technique, which can simultaneously realize a large field of view and high spatial resolution. Most of the related improved works of FPM focus on system construction and algorithm improvement. Several parameters such as adjacent sub-spectrum overlap ratio and recovery sequence affect the performance of the FPM framework too. In this letter, we propose an asymmetric constraint Fourier ptychography microscopy (ACFPM) framework. We demonstrate the feasibility and efficiency of the proposed framework through simulations and actual experiments. Results indicate that introducing asymmetry in the Fourier domain without considerable influence on sub-spectrum overlap ratio can evidently improve the reconstruction quality of high-resolution image.

New design of anti-windup and dynamic output feedback control for TCP/AQM system with asymmetrical input constraints

In this paper two important problems, i.e. Denial of Service (DoS) attack and saturated input, are considered for the TCP/AQM system. The first problem is modelled in a quantitative manner over the system dynamics. Then, Linear Matrix Inequality (LMI) condition for synthesising a Dynamic Output Feedback (DOF) controller with guaranteed cost approach is proposed. The second problem is inherently asymmetric, and a generalised sector condition is derived to obtain stability conditions based on quadratic Lyapunov functions. Sufficient conditions in terms of LMIs for designing the anti-windup compensator are then derived. By solving these LMIs, the controller matrices along with the less bound of the cost function and an appropriate anti-windup compensator are obtained. Through Network Simulator 3 (NS3) the efficiency of the theory is illustrated.

Neuro-learning-based adaptive control for state-constrained strict-feedback systems with unknown control direction

A neural networks (NNs)-based learning policy is proposed for strict-feedback nonlinear systems with asymmetric full-state constraints and unknown gain directions. A state-constrained function is introduced such that the proposed adaptive control policy works for systems with constraints or without constraints in a unified structure. Furthermore, the unified state-constrained function can also deal with symmetric and asymmetric constraints without changing adaptive structures, which also avoids discontinuous actions. With Nussbaum gain technique and NNs-based approximation technique, the proposed control method can also effectively deal with the unknown signs of control gains, and matched and mismatched uncertainties are also solved by NN approximation technique. According to the Lyapunov theory, the tracking errors can be proved to be semi-globally uniformly ultimately bounded (SGUUB). Finally the effectiveness of the proposed scheme is validated by numerical simulations.

Command filtered adaptive neural tracking control of uncertain nonlinear time-delay systems with asymmetric time-varying full state constraints and actuator saturation

This article investigates the command filtered adaptive neural tracking control for uncertain nonlinear time-delay systems subject to asymmetric time-varying full state constraints and actuator saturation. To stabilize such a class of systems, the radial basis function neural networks and the backstepping technique are used to structure an adaptive controller. The command filter is utilized to overcome the complexity explosion problem in backstepping. By employing the Lyapunov–Krasovskii functionals, the effect of time-delay is eliminated. The asymmetric time-varying barrier Lyapunov functions are designed to ensure full state constraint satisfaction. Moreover, the hyperbolic tangent function and an instrumental variable are introduced to deal with actuator saturation. All signals in the closed-loop system are proved to be bounded and the tracking error converges to a small neighborhood of the origin. Finally, two examples are provided to illustrate the effectiveness of the proposed method.

Fixed-time stabilisation for switched stochastic nonlinear systems with asymmetric output constraints

In this paper, the fixed-time stabilisation problem is investigated for switched stochastic nonlinear systems with asymmetric output constraints. A novel universal barrier Lyapunov function is proposed to not only handle systems with asymmetric output constraints but also work for systems with symmetric constraints or without constraints, without reshaping the controller framework. On the basis of the stochastic fixed-time stability theorem and adding a power integrator strategy, an elaborate control method is established to ensure that the system state fixed-time converges to zero almost surely without the knowledge of initial conditions. Meanwhile, the system output is always retained in the preset asymmetric region in probability. A practical example is utilised to verify the validity of the proposed theory.

A unified control approach to finite-time stabilization of SOSM dynamics subject to an output constraint

This paper investigates a control design problem for the second-order sliding mode (SOSM) dynamics with mismatched uncertainty subject to the output constraint by means of the adding a power integrator technique. Firstly, a SOSM dynamics with mismatched uncertainty is constructed by retaining some information in the mismatched channel so as to reduce the uncertainty in the control channel, thereby relaxing the control requirement. Secondly, a barrier Lyapunov function (BLF) is designed in consideration of the output constraint to prevent the considered system from escaping from the output constraint. Moreover, the output constraint can be either symmetric or asymmetric. Thirdly, by embedding the above BLF into the adding a power integrator technique, a SOSM controller can be eventually constructed for the SOSM dynamics with the mismatched uncertainty to solve the output constraint problem. The finite-time stability analysis is proved by Lyapunov theory. The simulation results considering the symmetric constraint as well as the asymmetric constraint are provided to demonstrate the validity of the proposed control method.

Chemo-mechanical response of composite electrode systems with multiple binder connections

In Li-ion batteries, the feature of inter-particle connection of a non-active binder can affect lithium diffusion inside the particle and stress development due to the diffusion–stress coupling effect, leading to change in the failure mechanisms of the electrode. In this study, to investigate the effect of binder connection feature on mechanical response, a series of simulations is carried out by changing the particle radius for three cases of single, double, and triple binder connections. The effects of C-rates, lithium flux at the particle–binder interface, level of mechanical constraint, and binder content on the stress development in the particle, binder, and interface domains are explored. We find that two effects of binder confinement and concentration gradients compete in the stress development. For small particles, the binder confinement effect is dominant; while for large particles, the concentration gradients effect is dominant. In addition, the single binder model shows a different stress trend, compared to the multiple binder models, due to asymmetric constraint from the binder. The insights obtained from this study help in the design of composite electrode materials for enhanced battery performance by optimizing parameters.

Second-Order Sliding Mode Control Design Subject to an Asymmetric Output Constraint

In this brief, a novel second-order sliding mode (SOSM) control method is developed to solve the asymmetric output constraint problem by using a power integrator and barrier Lyapunov function (BLF). The new BLF is first constructed based on the asymmetric constraint condition. A novel SOSM algorithm is then constructed for the nonlinear systems with an asymmetric output constraint. Under the proposed SOSM algorithm, the output of the resulting closed-loop system will never escape from the asymmetric constraint. Finally, a pendulum system is adopted to verify the validity of the theoretical results.