Nonconstrained System Research Articles

Distributed Adaptive Fuzzy Containment Control for State-Constrained Multiagent Systems With Uncertain Leaders

This article investigates the containment control for state-constrained multiagent systems. Existing results assume that the dynamic of the multiple leaders is known as prior knowledge. First, a distributed adaptive observer is used to estimate the leader's unknown parameters. The local reference signal and its high-order derivatives are generated by an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$n$</tex-math></inline-formula> th-order filter, which will be employed in the backstepping design procedures. Second, a log-type nonlinear state-dependent barrier function is established to cope with the time-varying asymmetric full-state constraints. The constrained system is equivalently transformed into a nonconstrained one. Finally, a distributed adaptive fuzzy containment control scheme is developed for the nonconstrained system. Only one adaptive law is required in each distributed controller, and no feasibility conditions and partial-derivative terms are involved in the virtual and actual controllers. In addition, the time derivatives of the candidate Lyapunov functions are guaranteed to be negative semidefinite by introducing a series of reduced-order smooth functions. It is proved that the containment error converges to a user-predefined interval, and all the signals in the closed-loop system are bounded. The time-varying asymmetric full-state constraints imposed on the followers are not violated. Two illustrative examples demonstrate the effectiveness of the suggested approach.

Reinforcement learning based adaptive optimal control for constrained nonlinear system via a novel state-dependent transformation

Existing schemes for state-constrained systems either impose feasibility conditions or ignore the optimality. In this article, an adaptive optimal control scheme for the strict-feedback nonlinear system is proposed, which benefits from two design steps. Firstly, a novel nonlinear state-dependent function (NSDF) is formulated to equivalently transform the system into a non-constrained one to deal with state constraints without the requirements on feasibility conditions. Secondly, an adaptive optimal control scheme is designed for the non-constrained system, in which reinforcement learning (RL) is utilized to yield the optimal controller in each designing procedure. Updating rules of the actor and critic neural network are driven by the modified adaptive laws, used to approximate the optimal virtual and actual controllers. It is proved that all the signals in the closed-loop system are bounded and the output tracking error converges to an adjustable neighborhood of the origin not affected by the proposed NSDF. Two simulation examples are presented illustrating the effectiveness of the proposed scheme.

Prescribed Performance Guidance Law with Multiple Constraints

In the terminal guidance phase of intercepting aerial target, a guidance law, satisfying impact angle constraint, acceleration constraint, and second-order dynamic characteristic of interceptor autopilot, is designed based on the prescribed performance control and dynamic surface control method. Firstly, a two-dimensional plane interception model considering the dynamic characteristics of autopilot and input constraints is established. Furthermore, for the nonconstrained system, based on the dynamic surface control, the prescribed performance reaching law is used to ensure that the line-of-sight angle and the line-of-sight angle rate can converge to the prescribed range in finite time. At the same time, an adaptive law is used to estimate the uncertainty caused by target maneuver and autopilot. Then, aiming at the acceleration constraint, an auxiliary system is established to convert the restricted system into a nonrestricted system. The finite-time convergence of the terminal line-of-sight tracking error, the line-of-sight rate, and the uniform ultimate boundedness of the system are rigorously proved by Lyapunov stability theory. Finally, the simulation results show that the proposed guidance law can make the interceptor have better interception performance when attacking targets with different maneuvering forms.

Fixed-time constrained acceleration reconstruction scheme for robotic exoskeleton via neural networks

Accurate acceleration acquisition is a critical issue in the robotic exoskeleton system, but it is difficult to directly obtain the acceleration via the existing sensing systems. The existing algorithm-based acceleration acquisition methods put more attention on finite-time convergence and disturbance suppression but ignore the error constraint and initial state irrelevant techniques. To this end, a novel radical bias function neural network (RBFNN) based fixed-time reconstruction scheme with error constraints is designed to realize high-performance acceleration estimation. In this scheme, a novel exponential-type barrier Lyapunov function is proposed to handle the error constraints. It also provides a unified and concise Lyapunov stability-proof template for constrained and non-constrained systems. Moreover, a fractional power sliding mode control law is designed to realize fixed-time convergence, where the convergence time is irrelevant to initial states or external disturbance, and depends only on the chosen parameters. To further enhance observer robustness, an RBFNN with the adaptive weight matrix is proposed to approximate and attenuate the completely unknown disturbances. Numerical simulation and human subject experimental results validate the unique properties and practical robustness.

Maximizing ORC performance with optimal match of working fluid with system design

This article compares constrained system design to non-constrained system design for the basic Organic Rankine Cycle (ORC). The 12 working fluids studied include eight dry-type, three isentropic, and one wet-type fluids. The ORC model was developed using Aspen HYSYS® and validated with data obtained from the literature. The constrained design compared the performance of working fluids for a fixed heat exchanger and turbine configuration. A non-constrained design was studied by altering the design specifications for the heat exchangers and turbine to match the working fluid. An energy and exergy analysis was performed using first and second law efficiency. The exergy analysis was also used to study exergy destruction across the ORC components. Cost analysis was performed by comparing the levelized cost of electricity (LCOE) for each working fluid in both designs.It was observed that non-constrained design favored working fluids with higher critical temperatures. Switching from constrained to non-constrained design lowered the LCOE for higher critical temperature working fluids such as R601, R601a, R123, R245ca, R245fa, R600, and R236ea. R245ca, R601, and R236ea show 11%, 10%, and 9% decrease in LCOE, respectively. No significant change in efficiency is observed for lower critical temperature working fluids such as R236fa and R134a. Also, no increase in net power was observed for lower critical temperature working fluids, suggesting that modifying design does not affect the performance of ORC. LCOE increased for R600a, R152a, and R227ea and remained unchanged for R236fa and R134a.

Reconstruction of the patella with an autogenous iliac graft: clinical and radiologic results in thirteen patients.

Extension lag, quadriceps weakness and subluxation of the extensor apparatus are known complications of patellectomy. In the case of total knee joint replacement with a nonconstrained system an instability may be encountered. Reconstruction of the patella allows restoration of the moment arm to improve quadriceps leverage. The goal of our study was to analyse the clinical and radiological results after reconstruction of the patella with an autogenous iliac graft. 13 previously patellectomized patients had reconstruction of the patella with an autogenous iliac graft and were retrospectively studied by clinical and radiographic examination. For evaluation we used the scores of Feller and the Knee Society. Also, all complications were recorded. After an average follow-up of 40.1 months, nine patients had full strength of the quadriceps, while six had an improved function of the extensor apparatus. The mean Feller score was 21.8 and the Knee Society score was 67.3 for knee and 57.5 for function. Six complications occurred including three infections, two problems with the replaced patella and one fracture of the anterior superior iliac spine. Reconstruction of the patella with an autogenous iliac graft enables the strength of the extensor apparatus with restoration of the knee joint.

On the singularities of a constrained (incompressible-like) tensegrity-cytoskeleton model under equitriaxial loading

Singularity theory is applied for the study of the characteristic three-dimensional tensegrity-cytoskeleton model after adopting an incompressibility constraint. The model comprises six elastic bars interconnected with 24 elastic string members. Previous studies have already been performed on non-constrained systems; however, the present one allows for general non-symmetric equilibrium configurations. Critical conditions for branching of the equilibrium are derived and post-critical behaviour is discussed. Classification of the simple and compound singularities of the total potential energy function is effected. The theory is implemented into the cusp catastrophe for the case of one-dimensional branching of the buckling-allowed tensegrity model, and an elliptic umbilic singularity for compound branching of a rigid-bar model. It is pointed out that singularity studies with constraints demand a quite different mathematical approach than those without constraints.

Total ankle replacement. Review and critical analysis of the current status

Therapy resistant ankle pain and the disadvantages of ankle arthrodesis lead to the development of numerous ankle joint prostheses. When considering all ankle joint endoprosthetic developments since 1970, two different kinds of prosthesis can be distinguished. (i) Two component prostheses which can be further classified as constrained, semiconstrained and nonconstrained and (ii) three component prostheses with a free gliding core (multiaxial systems). After encouraging short term results in the 1970s and early 1980s, disappointing long term results led to disuse of most of the previously developed prostheses. The two most frequent complications were aseptic loosening and wound healing. Aseptic loosening can result from large bone resection (tibial 8–16 mm and talar ca 7 mm) which lead to a fixation of soft cancellous bone which is not able to resist the forces acting on the anchoring systems. Besides bone resection, the geometry of an ankle joint replacement also plays an important part in aseptic loosening. This is clearly shown by the results from constrained design where the highest loosening rates occur in ankle joint prosthesis. The nonconstrained systems and multiaxial systems with free gliding core both showed lower loosening rates, but because of an unphysiologically large range of motion they are associated with stability problems. Constrained designs neglect the anatomical and biomechanical characteristics of the ankle joint leading to an unphysiological unidimensional range of motion as, regarding the anatomy and biomechanics of the ankle joint, it is evident that the ankle joint is not a real hinge joint. The curvatures of the talus and the tibial surfaces show varying radii. The radii of the talus are described as counter-rotating spiral radii and the tibial as a unform radius. These anatomical characteristics allow axial vertical rotation in the ankle joint as well as extension and flexion. In future, the incorporation of more anatomical characteristics should be taken into account when designing a new ankle joint replacement, in particular the counter-rotating spiral radii of the talus. As well as incorporating anatomical curvatures into the design of an ankle joint system it is also necessary to reduce the bone resections to achieve lower loosening rates and thus better results.

OBTAINING DYNAMICAL GROUPS AND QUANTUM DEGREES OF FREEDOM BY USING NOETHER’S THEOREM: THE PLANAR LANDAU SYSTEM

The noncompact quantum dynamical group SU(2, 1) and the associated su(2, 1) spectrum-generating algebra of the nonrelativistic planar Landau system are constructively obtained from the classical theory, by considering time-dependent Noether symmetry transformations and along the lines of a procedure recently proposed by Castaños, Frank and López-Peña. For this nonconstrained system in the circular gauge, we have found an explicitly time-dependent Hermitian invariant operator, which is crucial for the correct identification of the number of quantum degrees of freedom.