brief paper analysis of undercompensation and overcompensation of friction in 1dof mechanical systems this paper investigates the effects of undercompensation and overcompensation of friction in pd controlled 1dof mechanical systems the friction force that is acting on the mechanical system and the friction compensation term in the feedback loop are described by a class of discontinuous friction models consisting of static coulomb and viscous friction and including the stribeck effect lyapunov s stability theorem and lasalle s invariance principle are applied to prove that undercompensation of friction leads to steady state errors and the properties of the w limit set of trajectories of a two dimensional autonomous differential inclusion are used to show that overcompensation of friction may induce limit cycling furthermore the analysis also indicates that the limit cycling effect can be eliminated by tuning the pd controller gains

a geometric optimization approach to detecting and intercepting dynamic targets using a mobile sensor network a methodology is developed to deploy a mobile sensor network for the purpose of detecting and capturing mobile targets in the plane the sensing pursuit problem considered in this paper is analogous to the marco polo game in which a pursuer marco must capture multiple mobile targets that are sensed intermittently and with very limited information the competing objectives exhibited by this problem arise in a number of surveillance and monitoring applications in this paper the mobile sensor network consists of a set of robotic sensors that must track and capture mobile targets based on the information obtained through cooperative detections when these detections form a satisfactory target track a mobile sensor is switched to pursuit mode and deployed to capture the target in minimum time since the sensors are installed on robotic platforms and have limited range the geometry of the platforms and of the sensors fields of view play a key role in obstacle avoidance and target detection a new cell decomposition approach is presented to determine the probability of detection and the cost of operating the sensors from the geometric properties of the network and its workspace the correctness and complexity of the algorithm are analyzed proving that the termination time is a function of the network parameters and of the number of required detections

robust l2 gain control for nonlinear systems with projection dynamics and input constraints an example from traffic control we formulate the l 2 gain control problem for a general nonlinear state space system with projection dynamics in the state evolution and hard constraints on the set of admissible inputs we develop specific results for an example motivated by a traffic signal control problem a state feedback control with the desired properties is found in terms of the solution of an associated hamilton jacobi isaacs equation the storage function or value function of the associated game and the critical point of the associated hamiltonian function discontinuities in the resulting control as a function of the state and due to the boundary projection in the system dynamics lead to hybrid features of the closed loop system specifically jumps of the system description between two or more continuous time models trajectories for the closed loop dynamics must be interpreted as a differential set inclusion in the sense of filippov construction of the storage function is via a generalized stable invariant manifold for the flow of a discontinuous hamiltonian vector field which again must be interpreted in the sense of filippov for the traffic control model example the storage function is constructed explicitly the control resulting from this analysis for the traffic control example is a mathematically idealized averaged control which is not immediately implementable implementation issues for traffic problems will be discussed elsewhere

on the existence of caratheodory solutions in mechanical systems with friction it is shown that the differential equation with discontinuous right hand side which describes the dynamic behavior of a mechanical system with friction has a caratheodory solution this result supports theoretically the prior work on the control of mechanical systems with friction which assumes the existence of caratheodory solutions without proof

nonsmooth lyapunov pairs for infinite dimensional first order differential inclusions the main objective of this paper is to provide new explicit criteria to characterize weak lower semicontinuous lyapunov pairs or functions associated to first order differential inclusions in hilbert spaces these inclusions are governed by a lipschitzian perturbation of a maximally monotone operator the dual criteria we give are expressed by means of the proximal and basic subdifferentials of the nominal functions while primal conditions are described in terms of the contingent directional derivative we also propose a unifying review of many other criteria given in the literature our approach is based on advanced tools of variational analysis and generalized differentiation

nonsmooth lyapunov pairs for differential inclusions governed by operators with nonempty interior domain the general theory of lyapunov stability of first order differential inclusions in hilbert spaces has been studied by the authors in the previous paper adly et al in nonlinear anal 75 3 985 1008 2012 this new contribution focuses on the case when the interior of the domain of the maximally monotone operator governing the given differential inclusion is nonempty this includes in a natural way the finite dimensional case the current setting leads to simplified more explicit criteria and permits some flexibility in the choice of the generalized subdifferentials some consequences of the viability of closed sets are given our analysis makes use of standard tools from convex and variational analysis

convergence of neural networks for programming problems via a nonsmooth lojasiewicz inequality this paper considers a class of neural networks nns for solving linear programming lp problems convex quadratic programming qp problems and nonconvex qp problems where an indefinite quadratic objective function is subject to a set of affine constraints the nns are characterized by constraint neurons modeled by ideal diodes with vertical segments in their characteristic which enable to implement an exact penalty method a new method is exploited to address convergence of trajectories which is based on a nonsmooth lstrokojasiewicz inequality for the generalized gradient vector field describing the nn dynamics the method permits to prove that each forward trajectory of the nn has finite length and as a consequence it converges toward a singleton furthermore by means of a quantitative evaluation of the lstrokojasiewicz exponent at the equilibrium points the following results on convergence rate of trajectories are established 1 for nonconvex qp problems each trajectory is either exponentially convergent or convergent in finite time toward a singleton belonging to the set of constrained critical points 2 for convex qp problems the same result as in 1 holds moreover the singleton belongs to the set of global minimizers and 3 for lp problems each trajectory converges in finite time to a singleton belonging to the set of global minimizers these results which improve previous results obtained via the lyapunov approach are true independently of the nature of the set of equilibrium points and in particular they hold even when the nn possesses infinitely many nonisolated equilibrium points

adaptive coordinated tracking of multi agent systems with quantized information abstract in this paper we study the adaptive coordinated tracking problem for continuous time first order integrator systems with quantized information under switching undirected and fixed directed communication graphs respectively the combined effect of quantized relative information error and quantized absolute information error on the tracking result is investigated both the logarithmic quantizers and uniform quantizers are considered it is shown that when logarithmic quantizers are used exact coordinated tracking can still be achieved by properly choosing the design parameters in the controller while when uniform quantizers are used practical coordinated tracking can be achieved with tracking error bounds proportional to the quantizer parameter simulation examples are provided to illustrate the results

invertible linear maps on borel subalgebras preserving zero lie products abstract let g be a simple lie algebra of rank l over an algebraically closed field of characteristic zero b a borel subalgebra of g an invertible linear map on b is said preserving zero lie products in both directions if for x y b x y 0 if and only if x y 0 in this paper it is shown that an invertible linear map on b preserving zero lie products in both directions if and only if it is a composition of an inner automorphism a graph automorphism a scalar multiplication map and a diagonal automorphism which extends the main result in 8 from a linear solvable lie algebra to far more general cases

a class of zero product determined lie algebras abstract let l be a lie algebra over a field f we say that l is zero product determined if for every f linear space v and every bilinear map l l v the following condition holds if x y 0 whenever x y 0 then there exists a linear map f from l l to v such that x y f x y for all x y l this article shows that every parabolic subalgebra p of a finite dimensional simple lie algebra defined over an algebraically closed field is always zero product determined applying this result we present a method different from that of wang et al 2010 9 to determine zero product derivations of p and we obtain a definitive solution for the problem of describing two sided commutativity preserving maps on p

extended invariance principle for nonautonomous switched systems stability analysis is developed for nonlinear nonautonomous switched systems trajectories of which admit generally speaking a nonunique continuation on the right for these systems krasovskii lasalle s invariance principle is extended in such a manner to remain true even in the nonautonomous case in addition to a nonsmooth lyapunov function with negative semidefinite time derivatives along the system trajectories the extended invariance principle involves a coupled indefinite function to guarantee asymptotic stability of the system in question as an illustration of the capabilities of this principle a switched regulator of a fully actuated manipulator with frictional joints is constructed

zero product determined some nest algebras abstract let alg n be a nest algebra associated with the nest n on a real or complex hilbert space h we say that alg n is zero product determined if for every linear space n and every bilinear map alg n alg n v the following holds if a b 0 whenever ab 0 then there exists a linear map t such that a b t ab for all a b alg n if we replace in this definition the ordinary product by the jordan resp lie product then we say that alg n is zero jordan resp lie product determined we show that any finite nest algebra over a complex hilbert space is zero product determined and it is also zero jordan product determined moreover we show that any finite dimensional nest algebra on a real or complex hilbert space is zero lie resp associative jordan product determined in addition we characterize separately strongly operator topology continuous bilinear map from alg n alg n into a topological linear space v with the property that a b 0 whenever ab 0 or a b 0 whenever ab ba 0

brief paper on the algebraic characterization of invariant sets of switched linear systems in this paper a suitable lasalle principle for continuous time linear switched systems is used to characterize invariant sets and their associated switching laws an algorithm to determine algebraically these invariants is proposed the main novelty of our approach is that we require no dwell time conditions on the switching laws by not focusing on restricted control classes we are able to describe the asymptotic properties of the considered switched systems observability analysis of a flying capacitor converter is proposed as an illustration

commuting traces of biadditive mappings commutativity preserving mappings and lie mappings biadditive mappings b r r r where r is a prime ring with certain additional properties satisfying b x x x xb x x for all x r are characterized as an application we determine the structures of commutativity preserving mappings lie isomorphisms and lie derivations of certain prime rings

distributed leader follower flocking control for multi agent dynamical systems with time varying velocities abstract using tools from algebraic graph theory and nonsmooth analysis in combination with ideas of collective potential functions velocity consensus and navigation feedback a distributed leader follower flocking algorithm for multi agent dynamical systems with time varying velocities is developed where each agent is governed by second order dynamics the distributed leader follower algorithm considers the case in which the group has one virtual leader with time varying velocity for each agent i this algorithm consists of four terms the first term is the self nonlinear dynamics which determines the final time varying velocity the second term is determined by the gradient of the collective potential between agent i and all of its neighbors the third term is the velocity consensus term and the fourth term is the navigation feedback from the leader to avoid an impractical assumption that the informed agents sense all the states of the leader the new designed distributed algorithm is developed by making use of observer based pinning navigation feedback in this case each informed agent only has partial information about the leader yet the velocity of the whole group can still converge to that of the leader and the centroid of those informed agents having the leader s position information follows the trajectory of the leader asymptotically finally simulation results are presented to demonstrate the validity and effectiveness of the theoretical analysis surprisingly it is found that the local minimum of the potential function may not form a commonly believed lattice

finite time connectivity preserving consensus of networked nonlinear agents with unknown lipschitz terms this technical note studies finite time consensus problem for a team of networked nonlinear agents with unknown lipschitz terms under communication constraints where each agent has a limited sensing range because the induced interaction graph is typically state dependent and dynamic we propose a distributed nonlinear consensus algorithm that is capable of preserving the initial interaction patterns by using tools from nonsmooth analysis sufficient conditions are obtained such that finite time consensus can be reached an upper bound of the convergence time is derived via a two step analysis the validity of the theoretical result is shown by one simulation example

tracking control for hybrid systems with state triggered jumps this paper addresses the tracking problem in which the controller should stabilize time varying reference trajectories of hybrid systems despite the fact that discrete events or jumps in hybrid systems can often not be controlled directly as e g is the case in impacting mechanical systems the controller should still stabilize the desired trajectory a major complication in the analysis of this hybrid tracking problem is that in general the jump times of the plant do not coincide with those of the reference trajectory consequently the conventional euclidean tracking error does not converge to zero even if trajectories converge to the reference trajectory in between jumps and the jump times converge to those of the reference trajectory hence standard control approaches can not be applied we propose a novel definition of the tracking error that overcomes this problem and formulate lyapunov based conditions for the global asymptotic stability of the hybrid reference trajectory using these conditions we design hysteresis based controllers that solve the hybrid tracking problem for two exemplary systems including the well known bouncing ball problem

extension of order preserving maps on a cone we examine the problem of extending in a natural way order preserving maps that are defined on the interior of a closed cone k 1 taking values in another closed cone k 2 to the whole of k 1 we give conditions in considerable generality for cones in both finite and infinite dimensional spaces under which a natural extension exists and is continuous we also give weaker conditions under which the extension is upper semi continuous maps f defined on the interior of the non negative cone k in r n which are both homogeneous of degree 1 and order preserving are non expanding in the thompson metric and hence continuous as a corollary of our main results we deduce that all such maps have a homogeneous order preserving continuous extension to the whole cone it follows that such an extension must have at least one eigenvector in k 0 in the case where the cycle time chi f of the original map does not exist such eigenvectors must lie in partial k 0 we conclude with some discussions and applications to operator valued means we also extend our results to an intermediate situation which arises in some important application areas particularly in the construction of diffusions on certain fractals via maps defined on the interior of cones of dirichlet forms

finite time stabilisation of cyclic formations using bearing only measurements this paper studies decentralised formation control of multiple vehicles in the plane when each vehicle can only measure the local bearings of their neighbours by using bearing only sensors since the inter vehicle distance cannot be measured the target formation involves no distance constraints more specifically the target formation considered in this paper is an angle constrained cyclic formation where each vehicle has exactly two neighbours and the angle at each vehicle subtended by its two neighbours is pre specified to stabilise the target formation we propose a discontinuous control law that only requires the sign information of the angle errors due to the discontinuity of the proposed control law the stability of the closed loop system is analysed by employing a locally lipschitz lyapunov function and nonsmooth analysis tools we prove that the target formation is locally finite time stable with collision avoidance guaranteed

generalized derivations on unital algebras determined by action on zero products abstract let a be a unital algebra having a nontrivial idempotent and let m be a unitary a bimodule we consider linear maps f g a m satisfying f x y x g y 0 whenever x y a are such that x y 0 for example when a is zero product determined algebra e g algebra generated by idempotents f and g are generalized derivations f x f 1 x d x and g x x g 1 d x for all x a where d a m is a derivation if a is not generated by idempotents then there exist also nonstandard solutions for maps f and g in the case of a being a triangular algebra under some condition on bimodule m the characterization of maps f and g is given we also consider conditions on algebra a making it a zero product determined algebra

existence of carathe spl acute odory solutions in nonlinear systems with discontinuous switching feedback controllers in this note we consider the existence of a carathe spl acute odory solution in a single input single output nonlinear system with a discontinuous switching feedback controller the main contribution is to show that if the nonlinear system can be transformed into a global normal form then we can specify the value of the discontinuous switching feedback controller on the switching hypersurface so that the closed loop system has a carathe spl acute odory solution

nonpathological lyapunov functions and discontinuous caratheodory systems differential equations with discontinuous right hand side and solutions intended in caratheodory sense are considered for these equations sufficient conditions which guarantee both lyapunov stability and asymptotic stability in terms of nonsmooth lyapunov functions are given an invariance principle is also proven

perron frobenius theorem for nonnegative multilinear forms and extensions we prove an analog of perron frobenius theorem for multilinear forms with nonnegative coefficients and more generally for polynomial maps with nonnegative coefficients we determine the geometric convergence rate of the power algorithm to the unique normalized eigenvector

consensus tracking for second order nonlinear multi agent systems with switching topologies and a time varying reference state abstractin this study the authors consider the consensus tracking problem for second order nonlinear multi agent systems with switching topologies and a time varying reference state the dynamics of each agent consists of nonlinear inherent dynamics in order to reach consensus tracking a class of nonsmooth control protocols is proposed which only depends on the agent s own information and its neighbours information with the aid of algebraic graph theory matrix theory and lyapunov theory some corresponding sufficient conditions guaranteeing consensus tracking under the proposed control protocols are derived finally the numerical simulations are given to illustrate the effectiveness of the developed theoretical results

on bilinear maps on matrices with applications to commutativity preservers abstract let m n be the algebra of all n n matrices over a commutative unital ring c and let l be a c module various characterizations of bilinear maps m n m n l with the property that x y 0 whenever x any y commute are given as the main application of this result we obtain the definitive solution of the problem of describing not necessarily bijective commutativity preserving linear maps from m n into m n for the case where c is an arbitrary field moreover this description is valid in every finite dimensional central simple algebra

an invariance principle for nonlinear discrete autonomous dynamical systems this note proposes an extension of lasalle s invariance principle for nonlinear discrete autonomous dynamical systems the invariance principle is extended to allow the first difference of the auxiliar scalar function usually a lyapunov function to be positive in some bounded regions moreover a uniform version is proposed to deal with nonlinear discrete dynamical systems that vary with parameters both extensions have the original invariance principle as a particular case as a consequence a larger class of systems can be treated with this new theory the extensions are very useful to obtain attractor estimates as well as their corresponding stability regions the uniform version in particular is useful to obtain estimates that are uniform regarding parameters

modular adaptive control of uncertain euler lagrange systems with additive disturbances a novel adaptive nonlinear control design is developed which achieves modularity between the controller and the adaptive update law modularity between the controller update law design provides flexibility in the selection of different update laws that could potentially be easier to implement or used to obtain faster parameter convergence and or better tracking performance for a general class of linear in the parameters lp uncertain euler lagrange systems subject to additive bounded non lp disturbances the developed controller uses a model based feedforward adaptive term in conjunction with the recently developed robust integral of the sign of the error rise feedback term modularity in the adaptive feedforward term is made possible by considering a generic form of the adaptive update law and its corresponding parameter estimate this generic form of the update law is used to develop a new closed loop error system and stability analysis that does not depend on nonlinear damping to yield the modular adaptive control result

estimation of spatially distributed processes using mobile spatially distributed sensor network the problem of estimating a spatially distributed process described by a partial differential equation pde whose observations are contaminated by a zero mean gaussian noise is considered in this work the basic premise of this work is that a set of mobile sensors achieve better estimation performance than a set of immobile sensors to enhance the performance of the state estimator a network of sensors that are capable of moving within the spatial domain is utilized specifically such an estimation process is achieved by using a set of spatially distributed mobile sensors the objective is to provide mobile sensor control policies that aim to improve the state estimate the metric for such an estimate improvement is taken to be the expected state estimation error using different spatial norms two guidance policies are proposed the current approach capitalizes on the efficient filter gain design in order to avoid intense computational requirements resulting from the solution to filter riccati equations simulation studies implementing and comparing the two proposed control policies are provided

rise based adaptive control of a control affine uncertain nonlinear system with unknown state delays a continuous robust adaptive control method is designed for a class of uncertain nonlinear systems with unknown constant time delays in the states specifically a robust adaptive control method and a delay free gradient based desired compensation adaptation law dcal are utilized to compensate for unknown time delays linearly parameterizable uncertainties and additive bounded disturbances for a general nonlinear system despite these disturbances a lyapunov krasovskii based analysis is used to conclude that the system output asymptotically tracks a desired time varying bounded trajectory

continuous uniform finite time stabilization of planar controllable systems continuous homogeneous controllers are utilized in a full state feedback setting for the uniform finite time stabilization of a perturbed double integrator in the presence of uniformly decaying piecewise continuous disturbances semiglobal strong mathcal c 1 lyapunov functions are identified to establish uniform asymptotic stability of the closed loop planar system uniform finite time stability is then proved by extending the homogeneity principle of discontinuous systems to the continuous case with uniformly decaying piecewise continuous nonhomogeneous disturbances a finite upper bound on the settling time is also computed the results extend the existing literature on homogeneity and finite time stability by both presenting uniform finite time stabilization and dealing with a broader class of nonhomogeneous disturbances for planar controllable systems while also proposing a new class of homogeneous continuous controllers

generalized derivations of lie algebras abstract suppose l is a finite dimensional lie algebra with multiplication l l l let l denote the set of triples f f f with f f f hom l l such that f i l i l f f we consider the lie algebra gender l f hom l l f f f f f l well researched subalgebras of gender l include the derivation algebra der l f hom l l f f f l and the centroid c l f hom l l f 0 f l we now study the subalgebra qder l f hom l l f f f f l and the subspace qc l f hom l l f f 0 l in characteristic 2 gender l qder l qc l and we are concerned with the inclusions der l qder l and c l qc l qder l if z l 0 then c l qc l qder l and under reasonable conditions on lie algebras with toral cartan subalgebras we show qder l der l c l if l is a parabolic subalgebra of a simple lie algebra of rank 1 in characteristic 0 then we even have gender l ad l i l in general qc l is not closed under composition or lie bracket however if z l 0 then qc l is a commutative associative algebra and we describe conditions that force qc l c l or equivalently gender l qder l we show that in characteristic 0 gender l preserves the radical of l thus generalizing the classical result for der l we also discuss some applications of the main results to the study of functions f hom l l such that f or f i l defines a lie multiplication

matrix theoretic conditions for the realizability of sliding manifolds systems of the type s ksgn s s rm where sgn is the vector sign function usually determine the realizability of sliding modes in control systems with high frequency gain k a new condition on k is established for the global stability of this system using a nonsmooth liapunov function this condition is used to establish necessary and sufficient stability conditions for second order systems

on convergence for piecewise affine models of gene regulatory networks via a lyapunov approach in this paper we analyse convergence and stability properties for piecewise affine models of gene regulatory networks by means of piecewise quadratic lyapunov functions in the first part we present the piecewise affine model of a gene regulatory network then after proving a result on the existence of a minimal attractive and positively invariant box we describe a linear matrix inequalitie framework to construct a lyapunov function for the system in the second part of the work after a characterization of the system solutions when considering also isolated zeno behavior of the trajectories a monotonicity property of the so found lyapunov function is formally proved together with a result on the convergence of the trajectories in the sense of measure finally we present two examples showing the applicability and utility of the main theoretical results previously explained

on the rendezvous problem for multiple nonholonomic agents in this note a decentralized feedback control strategy that drives a system of multiple nonholonomic unicycles to a rendezvous point in terms of both position and orientation is introduced the proposed nonholonomic control law is discontinuous and time invariant and using tools from nonsmooth lyapunov theory and graph theory the stability of the overall system is examined similarly to the linear case the convergence of the multi agent system relies on the connectivity of the communication graph that represents the inter agent communication topology the control law is first defined in order to guarantee connectivity maintenance for an initially connected communication graph moreover the cases of static and dynamic communication topologies are treated as corollaries of the proposed framework

quantization effects on synchronized motion of teams of mobile agents with second order dynamics abstract for a team of mobile agents governed by second order dynamics this paper studies how different quantizers affect the performances of consensus type schemes to achieve synchronized collective motion it is shown that when different types of quantizers are used for the exchange of relative position and velocity information between neighboring agents different collective behaviors appear under the chosen logarithmic quantizers and with symmetric neighbor relationships we prove that the agents velocities and positions get synchronized asymptotically we show that under the chosen symmetric uniform quantizers and with symmetric neighbor relationships the agents velocities converge to the same value asymptotically while the differences of their positions converge to a bounded set we also show that when the uniform quantizers are not symmetric the agents velocities may grow unboundedly through simulations we present richer undesirable system behaviors when different logarithmic and uniform quantizers are used such different quantization effects underscore the necessity for a careful selection of quantization strategies especially for multi agent systems with higher order agent dynamics

using fuzzy logic to design separation function in flocking algorithms flocking algorithms essentially consist of three components alignment cohesion and separation to track a desired trajectory the flock center should move along the desired trajectory and thus the fourth component navigation is necessary the alignment cohesion and navigation components are well implemented through consensus protocols and tracking controls while the separation component is designed through heuristic based approaches this paper proposes a fuzzy logic solution to the separation component the ts rules and gaussian membership functions are used in fuzzy logic for fixed network flocking a standard stability proof by using lasalle s invariance principle is provided for dynamic network flocking a filipov solution definition is given for nonsmooth dynamics then a lasalle s invariance principle for nonsmooth dynamics is used to prove the stability a group of mobile robots with double integrator dynamics is simulated for the flocking algorithms in a 2 d environment

existence of solutions to a class of nonlinear convergent chattering free sliding mode control systems sliding mode control is a nonlinear control technique which is robust against some classes of uncertainties and disturbances however this control produces chattering which can cause instability due to unmodeled dynamics and can also cause damage to actuators or the plant there are essentially two ways to counter the chattering phenomenon one way is to use higher order sliding mode and the other way is to add a boundary layer around the switching surface and use continuous control inside the boundary the problem with the first method is that the derivative of a certain state variable is not available for measurement and therefore methods have to be used to observe that variable in the second method it is important that the trajectories inside the boundary layer do not try to come outside the boundary after entering the boundary layer control laws producing chattering free sliding mode using a boundary layer have been proposed and the existence of solutions to the system using these control laws are presented

the perron frobenius theorem for homogeneous monotone functions if a is a nonnegative matrix whose associated directed graph is strongly connected the perron frobenius theorem asserts that a has an eigenvector in the positive cone r n we associate a directed graph to any homogeneous monotone function f r n r n and show that if the graph is strongly connected then f has a nonlinear eigenvector in r n several results in the literature emerge as corollaries our methods show that the perron frobenius theorem is really about the boundedness of invariant subsets in the hilbert projective metric they lead to further existence results and open problems

control of contact problem in constrained euler lagrange systems stabilization of an euler lagrange system onto a constraint surface when the system makes contact with a nonzero impact velocity is an important problem in systems interacting with external environments potential applications include robotic surface following and surface finishing operations in manufacturing industry in the paper the constrained dynamic equations are modeled as a set of nonsmooth differential equations depending on whether the system lies on the constraint surface or the system repeatedly makes and loses contact with the constraint surface the focus is on the initial condition problem i e the system hits the constraint with a nonzero impact velocity a new discontinuous control scheme is proposed that ensures stable regulation of the system onto the constraint surface

asymptotic tracking of uncertain systems with continuous control using adaptive bounding this paper presents a robust adaptive control design method for a class of multiple input multiple output uncertain nonlinear systems in the presence of parametric and nonparametric uncertainties and bounded disturbances using the approximation properties of the unknown continuous nonlinearities and the adaptive bounding technique the developed controller achieves asymptotic convergence of the tracking error to zero while ensuring boundedness of parameter estimation errors the algorithm does not assume the knowledge of any bound on the unknown quantities in designing the controller it is based on an integral technique involving the filtered tracking error and produces a continuous control theoretical developments are illustrated via simulation results

maximizing visibility in nonconvex polygons nonsmooth analysis and gradient algorithm design this paper presents a motion control algorithm for a planar mobile observer such as a mobile robot equipped with an omnidirectional camera we propose a nonsmooth gradient algorithm for the problem of maximizing the area of the region visible to the observer in a non self intersecting nonconvex polygon first we show that the visible area is almost everywhere a locally lipschitz function of the observer location second we provide a novel version of the lasalle invariance principle for discontinuous vector fields and lyapunov functions with a finite number of discontinuities finally we establish the asymptotic convergence properties of the nonsmooth gradient algorithm and illustrate numerically its performance

global stabilization of rigid formations in the plane this paper considers the problem of distributed control of rigid formation shapes in the plane for multi agent systems a constructive perturbation method is proposed and combined with the conventional gradient control law the proposed control law stabilizes the desired rigid formation in a global sense for all initial conditions except the case when a pair of communicating agents happen to have the same initial location it also avoids collisions between any two communicating agents during the motion simulation results are provided to illustrate the effectiveness of the control algorithm

further results on the use of nussbaum gains in adaptive neural network control in this note the use of nussbaum gains for adaptive neural network nn control is examined extending previous approaches that have been successfully applied to prove the forward completeness property boundedness up to finite time we address the boundedness for all time up to infinity problem an example is constructed showing that this is not possible in general with the existing theoretical tools to achieve boundedness for all time a novel hysteresis based deadzone scheme with resetting is introduced for the associated update laws in this way a unique piecewise continuously differentiable solution is obtained while the error converges in finite time within some arbitrarily small region of the origin using the proposed modification an adaptive nn tracking controller is designed for a class of multiple input multiple output nonlinear systems

lower semicontinuous solutions of hamilton jacobi bellman equations the value function of mayer s problem arising in optimal control is investigated and lower semicontinuous solutions of the associated hamilton jacobi bellman equation are defined in three equivalent ways under quite weak assumptions about the control system the value function is the unique solution moreover it is stable with respect to perturbations of the control system and the cost it coincides with the viscosity solution whenever it is continuous

finite time distributed consensus via binary control protocols this paper investigates the finite time distributed consensus problem for multi agent systems using a binary consensus protocol and the pinning control scheme compared with other consensus algorithms which need the complete state or output information of neighbors the proposed algorithm only requires sign information of the relative state measurements that is the differences between a node s state and that of its neighbors this corresponds to only requiring a single bit quantization error relative to each neighbor this signum protocol is realistic in terms of observed behavior in animal groups where relative motion is determined not by full time signal measurements but by coarse estimates of relative heading differences between neighbors the signum protocol does not require explicit measurement of time signals from neighbors and hence has the potential to significantly reduce the requirements for both computation and sensing analysis of discontinuous dynamical systems is used including the filippov solutions and set valued lie derivative based on the second order information on the evolution of lyapunov functions the conditions that guarantee the finite time consensus for the systems are identified numerical examples are given to illustrate the theoretical results

a novel actor critic identifier architecture for approximate optimal control of uncertain nonlinear systems an online adaptive reinforcement learning based solution is developed for the infinite horizon optimal control problem for continuous time uncertain nonlinear systems a novel actor critic identifier aci is proposed to approximate the hamilton jacobi bellman equation using three neural network nn structures actor and critic nns approximate the optimal control and the optimal value function respectively and a robust dynamic neural network identifier asymptotically approximates the uncertain system dynamics an advantage of using the aci architecture is that learning by the actor critic and identifier is continuous and simultaneous without requiring knowledge of system drift dynamics convergence of the algorithm is analyzed using lyapunov based adaptive control methods a persistence of excitation condition is required to guarantee exponential convergence to a bounded region in the neighborhood of the optimal control and uniformly ultimately bounded uub stability of the closed loop system simulation results demonstrate the performance of the actor critic identifier method for approximate optimal control

input to state stability and interconnections of discontinuous dynamical systems in this paper we will extend the input to state stability iss framework to continuous time discontinuous dynamical systems dds adopting piecewise smooth iss lyapunov functions the main motivation for investigating piecewise smooth iss lyapunov functions is the success of piecewise smooth lyapunov functions in the stability analysis of hybrid systems this paper proposes an extension of the well known filippov s solution concept that is appropriate for open systems so as to allow interconnections of dds it is proven that the existence of a piecewise smooth iss lyapunov function for a dds implies iss in addition a small gain iss interconnection theorem is derived for two dds that both admit a piecewise smooth iss lyapunov function this result is constructive in the sense that an explicit iss lyapunov function for the interconnected system is given it is shown how these results can be applied to construct piecewise quadratic iss lyapunov functions for piecewise linear systems including sliding motions via linear matrix inequalities

stability and dynamics of a harmonically excited elastic perfectly plastic oscillator this paper deals with the stability and the dynamics of a harmonically excited elastic perfectly plastic oscillator the hysteretical system is written as a non smooth forced autonomous system it is shown that the dimension of the phase space can be reduced using adapted variables free vibrations of such a system are then considered for the damped system the extended direct method of liapounov is applied to this non smooth mechanical system and the asymptotic stability of the origin is proven in the new phase space the forced vibration of such an oscillator is treated by numerical approach by using the time locating techniques the stability of the limit cycles is analytically investigated with a perturbation approach the boundary between elastoplastic shakedown and alternating plasticity is given in closed form it is shown that this boundary corresponds to a bifurcation boundary for the undamped system period doubling bifurcation finally the equivalent damping of this hysteretic system is characterized from dynamical properties

upper and lower bounds for the iterates of order preserving homogeneous maps on cones abstract we define upper bound and lower bounds for order preserving homogeneous of degree one maps on a proper closed cone in r n in terms of the cone spectral radius we also define weak upper bounds for these maps for a proper closed cone c r n we prove that any order preserving homogeneous of degree one map f int c int c has a lower bound if c is polyhedral we prove that the map f has a weak upper bound we give examples of weak upper bounds for certain order preserving homogeneous of degree one maps defined on the interior of r n

viable control for uncertain nonlinear dynamical systems described by differential inclusions in this paper we will study the viable control problem for a class of uncertain nonlinear dynamical systems described by a differential inclusion the goal is to construct a feedback control such that all trajectories of the system are viable in a map moreover for any initial states no viable in the map under the feedback control all solutions of the system are steered to the map with an exponential convergence rate and viable in the map after a finite time t in this case an estimate of the time t of all trajectories attaining the map is given in the nanomedicine system an example inspired from cerebral embolism and cerebral thrombosis problems illustrates the use of our main results

zero product determined matrix algebras abstract let a be an algebra over a commutative unital ring c we say that a is zero product determined if for every c module x and every bilinear map a a x the following holds if x y 0 whenever xy 0 then there exists a linear operator t such that x y t xy for all x y a if we replace in this definition the ordinary product by the lie resp jordan product then we say that a is zero lie resp jordan product determined we show that the matrix algebra m n b n 2 where b is any unital algebra is always zero product determined and under some technical restrictions it is also zero jordan product determined the bulk of the paper is devoted to the problem whether m n b is zero lie product determined we show that this does not hold true for all unital algebras b however if b is zero lie product determined then so is m n b

finite time convergent gradient flows with applications to network consensus this paper introduces the normalized and signed gradient dynamical systems associated with a differentiable function extending recent results on nonsmooth stability analysis we characterize their asymptotic convergence properties and identify conditions that guarantee finite time convergence we discuss the application of the results to consensus problems in multi agent systems and show how the proposed nonsmooth gradient flows achieve consensus in finite time

stability theorems for delay differential inclusions this technical note addresses stability problems of delay differential inclusions a chain rule is proposed for a wide class of lyapunov krasovskii functionals which are not necessarily invariantly differentiable we also obtain an invariance like theorem where the derivative of the candidate functional is bounded above by a continuous negative semidefinite function several examples are given to show the effectiveness of the results

recurrent neural network for non smooth convex optimization problems with application to the identification of genetic regulatory networks a recurrent neural network is proposed for solving the non smooth convex optimization problem with the convex inequality and linear equality constraints since the objective function and inequality constraints may not be smooth the clarke s generalized gradients of the objective function and inequality constraints are employed to describe the dynamics of the proposed neural network it is proved that the equilibrium point set of the proposed neural network is equivalent to the optimal solution of the original optimization problem by using the lagrangian saddle point theorem under weak conditions the proposed neural network is proved to be stable and the state of the neural network is convergent to one of its equilibrium points compared with the existing neural network models for non smooth optimization problems the proposed neural network can deal with a larger class of constraints and is not based on the penalty method finally the proposed neural network is used to solve the identification problem of genetic regulatory networks which can be transformed into a non smooth convex optimization problem the simulation results show the satisfactory identification accuracy which demonstrates the effectiveness and efficiency of the proposed approach

denjoy wolff theorems hilbert metric nonexpansive maps and reproduction decimation operators let k be a closed cone with nonempty interior in a banach space x suppose that f intk intk is order preserving and homogeneous of degree one let q k 0 be a continuous homogeneous of degree one map such that q x 0 for all x k 0 let t x f x q f x we give conditions on the cone k and the map f which imply that there is a convex subset of k which contains the omega limit set x t for every x intk we show that these conditions are satisfied by reproduction decimation operators we also prove that x t k for a class of operator valued means

consensus with quantized relative state measurements in this paper cooperative control of multi agent systems under limited communication between neighboring agents is investigated in particular quantized values of the relative states are used as the control parameters by taking advantage of tools from nonsmooth analysis explicit convergence results are derived for both uniform and logarithmic quantizers under static and time varying communication topologies compared with our previous work less conservative conditions that ensure global convergence are provided moreover second order dynamical systems under similar constraints are taken into account computer simulations are provided to demonstrate the validity of the derived results

idempotent elements determined matrix algebras abstract let m n r be the algebra of all n n matrices over a unital commutative ring r with 2 invertible v be an r module it is shown in this article that if a symmetric bilinear map from m n r m n r to v satisfies the condition that u u e u whenever u 2 u then there exists a linear map f from m n r to v such that x y f x y x y m n r applying the main result we prove that an invertible linear transformation on m n r preserves idempotent matrices if and only if it is a jordan automorphism and a linear transformation on m n r is a jordan derivation if and only if it is jordan derivable at all idempotent points

fast switches in relay feedback systems relays are common in automatic control systems even linear systems with relay feedback are however far from fully understood new results are given about the behavior of these systems via a state space approach it is proved that there exist multiple fast switches if and only if the sign of the first nonvanishing markov parameter of the linear system is positive fast switches are shown to occur as part of stable limit cycles an analysis is developed for these limit cycles that illustrates how they can be predicted

lyapunov stability theory of nonsmooth systems this paper develops nonsmooth lyapunov stability theory and lasalle s invariance principle for a class of nonsmooth lipschitz continuous lyapunov functions and absolutely continuous state trajectories computable tests based on filipov s differential inclusion and clarke s generalized gradient are derived the primary use of these results is in analyzing the stability of equilibria of differential equations with discontinuous right hand side such as in nonsmooth dynamic systems or variable structure control

simplex methods for nonlinear uncertain sliding mode control we develop a new analysis of the behavior of simplex control methods applied to multiple input multiple output nonlinear control systems under uncertainties according to such sliding mode control methods the control vector is constrained to belong to a finite set of fixed or varying vectors with an appropriate switching logic to guarantee the specified sliding condition bounded uncertainties acting on the nominal system are allowed the proposed sliding control methodology relies on the knowledge of the nominal system only we prove rigorously the convergence of these methods to the sliding manifold in a finite time under explicit quantitative conditions on the system parameters and the available bounds of the uncertainty application to a robotic problem is discussed and a nonlinear example is presented