Optimal design of imperfect,anisotropic, ring-stiffened cylinders under combined loads

Development of an algorithm to perform the optimal sizing of buckling resistant, imperfect, anisotropic ringstiffened cylinders subjected to axial compression, torsion, and internal pressure is presented. An axisymmetric, geometrically nonlinear prebuckling equilibrium configuration is assumed and both stress and stability constraints are considered. The enforcement of stability constraints is treated in a way that does not require any eigenvalue analysis. Case studies performed using a combination of penalty function and feasible direction optimization methods indicate that the presence of the axisymmetric initial imperfection in the cylinder wall can significantly affect the optimal designs. Weight savings associated with the addition of two rings to the unstiffened cylinder and/or the addition of internal pressure is substantial when torsion makes up a significant fraction of the combined load state.     

On interconnected systems,passivity and some generalisations

A sufficient condition for the stability of large-scale interconnections of N linear time-variant systems is presented. Such a condition represents important extensions to passivity criteria and ensures stability by means of the existence of a positive definite (full-block) matrix P which is a common solution to Lyapunov equations involving a diagonal stacking of the N systems and the interconnection structure matrix. An experimental methodology for the verification of the sufficient condition also is proposed, based on evolutionary computation techniques. Applications of the new stability results are provided through illustrative examples, which are developed using particle swarm optimisation and genetic algorithms.     

Stability, dynamics of convergence and tuning of observer-based kinetics estimators

This work discusses issues concerning stability, tuning and dynamics of convergence of observer-based kinetics estimators. The analysis focuses on both continuous and discrete time formulations of the estimation algorithms. Concerning the former, it is shown that, with proper tuning, stability can be guaranteed, while simultaneously imposing a desired quasi-time invariant second order time response for the convergence of estimates to true values. Concerning the latter, an algorithm is presented, based on a forward Euler discretisation, whose error system is shown to be linear time-invariant. Furthermore, stability conditions were derived, which define the stable domain for the discretisation period as function of the tuning parameters. The theory is illustrated with a case-study of Baker's yeast fermentation. Results clearly confirm the theoretical developments. In particular, results concerning the stability domain for the Euler-based discrete formulation of the estimator are shown to have relevant practical implications.     

SHeRo: Scalable hexapod robot for maintenance,repair, and operations

Improper maintenance, repair, and operations of societal centric structures can lead to catastrophic failures that drastically affect global economy, the environment, and everyday life. Due to the remote, cramped and highly irregular environmental nature of these structures, routine manual procedures and operations can be rather tedious, dangerous, and hazardous for humans. Automating maintenance, repair, and operations removes human workers from having to crawl within highly cluttered and constrained spaces, breathing in stale air mixed with fumes from welding or particulate from repair work, and provides higher reliability and consistency in the repair work. This paper introduces SHeRo, a scalable hexapod robot designed for maintenance, repair, and operations within remote, inaccessible, irregular, and hazardous environments. The scalability of the design enhances traditional hexapod robot designs by incorporating two prismatic joints into each leg. A detailed discussion on the design and realization of SHeRo is provided. An analysis on the stability and workspace of SHeRo is presented and a dynamic criterion is developed to integrate the concepts of robot stability and constant orientation workspace into a stable workspace. The analytical solution of the lateral stable workspace of SHeRo is derived along with a metric for comparing stable workspace between different robot configurations. A simulated demonstration and two physical experimental demonstrations are presented showing the advantage of introducing scalability into the hexapod robot design along with the workspace enhancement and flexibility of the scalable hexapod robot.     

The advanced-step NMPC controller: Optimality, stability and robustness

Widespread application of dynamic optimization with fast optimization solvers leads to increased consideration of first-principles models for nonlinear model predictive control (NMPC). However, significant barriers to this optimization-based control strategy are feedback delays and consequent loss of performance and stability due to on-line computation. To overcome these barriers, recently proposed NMPC controllers based on nonlinear programming (NLP) sensitivity have reduced on-line computational costs and can lead to significantly improved performance. In this study, we extend this concept through a simple reformulation of the NMPC problem and propose the advanced-step NMPC controller. The main result of this extension is that the proposed controller enjoys the same nominal stability properties of the conventional NMPC controller without computational delay. In addition, we establish further robustness properties in a straightforward manner through input-to-state stability concepts. A case study example is presented to demonstrate the concepts.     

Globally asymptotic stability of a class of neutral-type neural networks with delays.

Several stability conditions for a class of systems with retarded-type delays are presented in the literature. However, no results have yet been presented for neural networks with neutral-type delays. Accordingly, this correspondence investigates the globally asymptotic stability of a class of neutral-type neural networks with delays. This class of systems includes Hopfield neural networks, cellular neural networks, and Cohen-Grossberg neural networks. Based on the Lyapunov stability method, two delay-independent sufficient stability conditions are derived. These stability conditions are easily checked and can be derived from the connection matrix and the network parameters without the requirement for any assumptions regarding the symmetry of the interconnections. Two illustrative examples are presented to demonstrate the validity of the proposed stability criteria.     

Globally asymptotical stability of discrete-time analog neuralnetworks

Some globally asymptotical stability criteria for the equilibrium states of a general class of discrete-time dynamic neural networks with continuous states are presented using a diagonal Lyapunov function approach. The neural networks are assumed to have the asymmetrical weight matrices throughout the paper. The resulting criteria are described by the diagonal stability of some matrices associated with the network parameters. Some novel stability conditions represented by either the existence of the positive diagonal solutions of the Lyapunov equations or some inequalities are given. Using the equivalence between the diagonal stability and the Schur stability for a nonnegative matrix, some simplified global stability conditions are also presented. Finally, some examples are provided for demonstrating the effectiveness of the global stability conditions presented.     

Development of Revolute-Joint Element with Rotation Limits, Locking, Resistive Moment and Damping

. The revolute-joint is an important component of a mechanical system. Thus, the motion simulation of multibodies connected with revolute-joints is of common interest. A simple revolute-joint can be easily represented in a numerical way, whereby the bending moment at the particular joint equals zero. Formulation becomes complicated when involving bending limits, the resistive moment and the damping effect. Furthermore, several bodies connected with revolute-joints form a complex system. This has been particularly useful for simulating a multibody system. A novel revolute-joint model is proposed in this paper. Several possible methods are suggested to handle bending limits. The incor-poration of the resistive moment and damping effects are also presented. The numerical stability of the revolute element is discussed, and a stability criterion suggested. The revolute-joint element is incorporated into an explicit finite difference code developed by the authors. Numerical examples are shown for different methods and conditions.     

On the convergence,consistency and stability of a one-step method for numerical integration of ordinary differential equation

This paper present a comprehensive review of the celebrated work of Fatunla (1976). An extension of the work to include among other things, its convergence, stability and the consistency is also presented.     

On stability, -gain and control for switched systems

This paper addresses the issues of stability, L₂-gain analysis and H_∞ control for switched systems via multiple Lyapunov function methods. A concept of general Lyapunov-like functions is presented. A necessary and sufficient condition for stability of switched systems is given in terms of multiple generalized Lyapunov-like functions, which enables derivation of improved stability tests, an L₂-gain characterization and a design method for stabilizing switching laws. A solution to the H_∞ control problem for switched systems is also provided.     

Exponentially incremental (Q,S, R)-dissipativity and incremental stability for switched time-varying nonlinear systems

Exponentially incremental (Q,S,R)-dissipativityand incremental stability for switched time-varying nonlinear systems are studied whose subsystems are not required to be exponentially incrementally (Q,S,R)-dissipative. The sufficient conditions for switched time-varying nonlinear systems to be exponentially incrementally (Q,S,R)-dissipative are presented by the design of state-dependent switching laws. Incremental stability for switched time-varying nonlinear systems are derived based on exponentially incremental (Q,S,R)-dissipativity. Exponentially incremental (Q,S,R)-dissipativity is shown to be preserved under feedback interconnection by the design of a composite state-dependent switching law. Two simulation examples are provided to show the effectiveness of the proposed approaches.     

Oscillation,stability, and boundedness of second-order differential systems with random impulses

The model of second-order linear differential systems with random impulses is brought forward in this paper. Then, necessary and sufficient conditions for oscillation in mean, p-moment stability and p-moment boundedness are obtained by several theorems that compare solutions of this system with the corresponding nonimpulsive differential system. At last, an example is presented to show the application of obtained results.     

Observers for Lipschitz nonlinear systems

This paper presents some fundamental insights into observer design for the class of Lipschitz nonlinear systems. The stability of the nonlinear observer for such systems is not determined purely by the eigenvalues of the linear stability matrix. The correct necessary and sufficient conditions on the stability matrix that ensure asymptotic stability of the observer are presented. These conditions are then reformulated to obtain a sufficient condition for stability in terms of the eigenvalues and the eigenvectors of the linear stability matrix. The eigenvalues have to be located sufficiently far out into the left half-plane, and the eigenvectors also have to be sufficiently well-conditioned for ensuring asymptotic stability. Based on these results, a systematic computational algorithm is then presented for obtaining the observer gain matrix so as to achieve the objective of asymptotic stability     

切换状态反馈控制系统的稳定性分析

研究了一类切换控制系统的稳定性分析问题,切换控制器由多个线性状态反馈控制器组成。运用Lyapunov方法得出了稳定性的时域判据,通过求解一个线性矩阵不等式的方法分析切换控制系统的稳定性,利用KYP引理得到了等价的频域判据;并且研究了一类含有参数不确定性的切换控制系统的鲁棒稳定性分析问题,给出了稳定性时域判据和频域判据。稳定性分析的主要结果是基于公共二次Lyapunov函数的,适用于切换系统任意切换的情形,该方法在工程实例中的应用表明了其有效性。     

Finite‐time stability and stabilization of semi‐Markovian jump systems with time delay

Semi‐Markovian jump systems are more general than Markovian jump systems in modeling practical systems. On the other hand, the finite‐time stochastic stability is also more effective than stochastic stability in practical systems. This paper focuses on the finite‐time stochastic stability, exponential stochastic stability, and stabilization of semi‐Markovian jump systems with time‐varying delay. First, a new stability condition is presented to guarantee the finite‐time stochastic stability of the system by using a new Lyapunov‐Krasovskii functional combined with Wirtinger‐based integral inequality. Second, the stability criterion is further proved to guarantee the exponential stochastic stability of the system. Moreover, a controller design method is also presented according to the stability criterion. Finally, an example is provided to illustrate that the proposed stability condition is less conservative than other existing results. Additionally, we use the proposed method to design a controller for a load frequency control system to illustrate the effectiveness of the method in a practical system of the proposed method.     

Modeling of global and local stability in optimization of truss-like structures using frame elements

An approach to take into account global and local stability in the design optimization of truss-like structures is presented. It is based on the use of frame elements and a single global stability constraint. A detailed discussion on key aspects of the proposed approach is presented, together with numerical examples. The proposed approach ensures global stability and does not require the use of Euler formula, avoiding several difficulties encountered in truss optimization. Besides, the examples illustrate that global stability is an important aspect to be taken into account in most practical cases.     

Least order,stable solution of the exact model matching problem

The set of all solutions of the minimal design problem (MDP) is presented in parametric form. This result is obtained by first deriving a parametric representation of all minimal bases of a particular vector space. From this the set of all solutions of the MDP are obtained. Then conditions are placed on the parameters, which conditions define the set of stable solutions of the MDP.Solutions to the nonminimal model matching problem are also presented in parametric form, and it is shown how in principle solutions of successively higher degree can be searched for a stable solution, should the MDP have no stable solution, so that a solution to the model matching problem can be found which has the lowest order consistent with a stability constraint.     

A new unconditionally stable condition based on singular perturbation analysis

Decentralised configuration with integral control action is the most commonly used control strategy in engineering practice. For decentralised integral control, a desired design target is to achieve closed-loop unconditional stability. Campo and Morari presented steady-state conditions, which can be applied to analyse unconditional stability for most multivariable processes. However, they also showed some processes for which the unconditional stability cannot be determined by only investigating the steady-state gain matrices of the processes. This paper presented an easy to use criterion to determine unconditional stability by using singular perturbation analysis and eigen-value sensitivity analysis. Based on the proposed criterion, the unconditional stability of all the examples presented by Campo and Morari can be easily determined. In the meantime, we proved a conjecture proposed by Campo and Morari (a necessary and sufficient condition for Integral Controllability) for up to all Three-Input and Three-Output systems. For higher dimensional systems, we proposed a new conjecture to simplify the verification of Campo and Morari’s conjecture.     

Growth conditions for exponential stability of time-varying perturbed systems

In this paper, we derive some sufficient conditions for practical uniform exponential stability of time-varying perturbed systems based on Lyapunov techniques, whose dynamics are in general unbounded in time, in the sense that the solutions are uniform stable and converge to a small neighbourhood of the origin. Under quite general assumptions, we first present a new converse stability theorem for a large class of time-varying systems, which will be used to prove certain stability properties of nonlinear systems with perturbation. Therefore, a new Lyapunov function is presented that guarantees practical uniform exponential stability of perturbed systems. Furthermore, some illustrative examples are presented.