Optimal averaging time for improving observer accuracy of stochastic dynamical systems

In the problem of remote estimation by a centralized observer, improvements to the accuracy of observer estimates come at a cost of higher communication bandwidth and energy consumption. In this article we improve observer estimation accuracy by reducing the measurement variance on the sensor node before its transmission to the centralized observer node. The main contribution is to show that measurement variance is a trade-off between dynamical system variance and sensor variance. As a result there is an optimal averaging time that minimizes measurement variance, providing more accurate measurement to the observer. The optimal averaging time is computable by solving a univariate optimization problem

Some Properties of Distances and Best Proximity Points of Cyclic Proximal Contractions in Metric Spaces

This paper presents some results concerning the properties of distances and existence and uniqueness of best proximity points of p-cyclic proximal, weak proximal contractions, and some of their generalizations for the non-self-mapping T:⋃i∈p-Ai→⋃i∈p-Bi  (p≥2), where Ai and Bi, ∀i∈p-={1,2,…,p}, are nonempty subsets of X which satisfy TAi⊆Bi,∀i∈p-, such that (X,d) is a metric space. The boundedness and the convergence of the sequences of distances in the domains and in their respective image sets of the cyclic proximal and weak cyclic proximal non-self-mapping, and of some of their generalizations are investigated. The existence and uniqueness of the best proximity points and the properties of convergence of the iterates to such points are also addressed

P-PI and super twisting sliding mode control schemes comparison for high-precision CNC machining

Multi-axis high precision machining uses linear motors actuators in order to deal with robustness and stability in the broad range of cutting conditions. Currently, Computer Numerical Controls (CNCs) integrate PID type controllers in order to deal with tracking errors and disturbances. Moreover, CNCs introduce feed-forward control loop to cope with model variations. However, to overcome the influences of disturbances and model uncertainties natural control approach is adopted by sliding mode controller (SMC). This paper proposes a super-twisting sliding mode control algorithm to cope with the switching control for keeping the dynamics of the system within the designed requirements. Furthermore, the paper compares the behaviour of P-PI position-velocity control approach and super-twisting SMC. The implementation and evaluation of the algorithms in Matlab shows that super-twisting SMC is able to track the reference signal more accurate and robustness against the estimated processing parameters and disturbances. The main source of instability in sliding mode controller knowing as chattering is minimized when applied the super-twisting control algorithm

Properties of convergence of a class of iterative processes generated by sequences of self-mappings with applications to switched dynamic systems

This article investigates the convergence properties of iterative processes involving sequences of self-mappings of metric or Banach spaces. Such sequences are built from a set of primary self-mappings which are either expansive or non-expansive self-mappings and some of the non-expansive ones can be contractive including the case of strict contractions. The sequences are built subject to switching laws which select each active self-mapping on a certain activation interval in such a way that essential properties of boundedness and convergence of distances and iterated sequences are guaranteed. Applications to the important problem of stability of dynamic switched systems are also given.The authors are very grateful to the Spanish Government for Grant DPI2012-30651 and to the Basque Government and UPV/EHU for Grants IT378-10, SAIOTEK S-PE13UN039 and UFI 2011/07. The authors are also grateful to the referees for their suggestions

New Results on Positive Realness in the Presence of Delayed Dynamics

Positive realness is a very important tool for the achievement of hyperstability and passivity of dynamic systems. This paper is devoted to extend some positive realness results of transfer functions in the presence of point-delayed delayed dynamics. Sufficiency-type conditions which guarantee the positive realness of delayed transfer functions under point delays are given. The value of the direct input-output interconnection gain is seen to be crucial in the performed analysis. The relevance of the results rely in the importance of the hyperstability property of closed-loop systems under non-linear and time-varying controller devices. In fact if the feed-forward controlled plant has a strictly positive real transfer function then the closed-loo system is asymptotically hyperstable , that is, globally asymptotically Lyapunov´s stable for any non-linear time-varying controller which belongs to a hyperstable class defined as that which satisfies a Popov´s type inequality

Generalized Cyclic p-Contractions and p-Contraction Pairs Some Properties of Asymptotic Regularity Best Proximity Points, Fixed Points

This paper studies a general p-contractive condition of a self-mapping T on X, where (X ,d) is either a metric space or a dislocated metric space, which combines the contribution to the upper-bound of d(Tx , Ty), where x and y are arbitrary elements in X of a weighted combination of the distances d(x,y) , d(x,Tx),d(y,Ty),d(x,Ty),d(y,Tx), |d(x,Tx)−d(y,Ty)| and |d(x,Ty)−d(y,Tx)|. The asymptotic regularity of the self-mapping T on X and the convergence of Cauchy sequences to a unique fixed point are also discussed if (X,d) is complete. Subsequently, (T, S) generalized cyclic p-contraction pairs are discussed on a pair of non-empty, in general, disjoint subsets of X. The proposed contraction involves a combination of several distances associated with the (T, S)-pair. Some properties demonstrated are: (a) the asymptotic convergence of the relevant sequences to best proximity points of both sets is proved; (b) the best proximity points are unique if the involved subsets are closed and convex, the metric is norm induced, or the metric space is a uniformly convex Banach space. It can be pointed out that both metric and a metric-like (or dislocated metric) possess the symmetry property since their respective distance values for any given pair of elements of the corresponding space are identical after exchanging the roles of both elements.This research was funded by Basq ue Government, Grant number IT1555-22

Stage-dependent structured discrete time models for mosquito population evolution with survivability : solution properties, equilibrium points, oscillations, and population feedback controls

This paper relied on the investigation of the properties of the stage-structured model of coupled larvae and adult mosquito populations' evolution when parameterized, in general, by time-varying (or stage-dependent) sequences. In particular, the investigated properties were the non-negativity of the solution under non-negative initial conditions, the boundedness of the sequence solutions under any finite non-negative initial conditions, the equilibrium points, and the convergence conditions to them in the event that the parameterizing sequences converge to finite limits. Some further properties that were investigated relied on deriving the oscillation conditions of the solutions under certain conditions of the parameterizations. The use of feedback controls to decrease the foreseen numbers of alive mosquitoes in future evolution stages is also proposed. The proposed control actions are exerted on the birth rate and/or the maximum progression rate sequences. Some illustrative examples are also given

Hierarchical Optimization-Based Model Predictive Control for a Class of Discrete Fuzzy Large-Scale Systems Considering Time-Varying Delays and Disturbances

Altres ajuts: Acord transformatiu CRUE-CSICIn this manuscript, model predictive control for class of discrete fuzzy large-scale systems subjected to bounded time-varying delay and disturbances is studied. The considered method is Razumikhin for time-varying delay large-scale systems, in which it includes a Lyapunov function associated with the original non-augmented state space of system dynamics in comparison with the Krasovskii method. As a rule, the Razumikhin method has a perfect potential to avoid the inherent complexity of the Krasovskii method especially in the presence of large delays and disturbances. The considered large-scale system in this manuscript is decomposed into several subsystems, each of which is represented by a fuzzy Takagi-Sugeno (TS) model and the interconnection between any two subsystems is considered. Because the main section of the model predictive control is optimization, the hierarchical scheme is performed for the optimization problem. Furthermore, persistent disturbances are considered that robust positive invariance and input-to-state stability under such circumstances are studied. The linear matrix inequalities (LMIs) method is performed for our computations. So the closed-loop large-scale system is asymptotically stable. Ultimately, by two examples, the effectiveness of the proposed method is illustrated, and a comparison with other papers is made by remarks

On Some Properties of a Class of Eventually Locally Mixed Cyclic/Acyclic Multivalued Self-Mappings with Application Examples

In this paper, a multivalued self-mapping is defined on the union of a finite number of subsets p(≥2) of a metric space which is, in general, of a mixed cyclic and acyclic nature in the sense that it can perform some iterations within each of the subsets before executing a switching action to its right adjacent one when generating orbits. The self-mapping can have combinations of locally contractive, non-contractive/non-expansive and locally expansive properties for some of the switching between different pairs of adjacent subsets. The properties of the asymptotic boundedness of the distances associated with the elements of the orbits are achieved under certain conditions of the global dominance of the contractivity of groups of consecutive iterations of the self-mapping, with each of those groups being of non-necessarily fixed size. If the metric space is a uniformly convex Banach one and the subsets are closed and convex, then some particular results on the convergence of the sequences of iterates to the best proximity points of the adjacent subsets are obtained in the absence of eventual local expansivity for switches between all the pairs of adjacent subsets. An application of the stabilization of a discrete dynamic system subject to impulsive effects in its dynamics due to finite discontinuity jumps in its state is also discussed.Basque Government, Grant IT1555-22