on vanishing stability regions in nonlinear systems with high gain feedback when local stabilization of nonlinear systems is achieved by linear feedback the resulting stability region may vanish as the feedback gains increase this is demonstrated by examples in which neglected nonlinearities create an unstable limit cycle around an asymptotically stable equilibrium as the feedback gains tend to infinity the unstable limit cycle shrinks to the equilibrium if a feedback linearization design is applied the same instability mechanism may occur when the nonlinearities are not precisely known

high gain feedback in non linear control systems abstract high gain state and output feedback are investigated for non linear control systems with a single additive input by using singular perturbation techniques classical approximation results tihonov like theorems in singular perturbation theory are extended to non linear control systems by defining a composite additive control strategy a control dependent fast equilibrium manifold and non linear change of coordinates those tools and an appropriate change of coordinates show that high gain state feedback and variable structure control systems can be equivalently used for approximate non linearity compensation in feedback linearizable systems next the effect of high gain output feedback is shown to be related to the strong invertibility property and the relative order of invertibility for strongly invertible systems the slow reduced subsystem coincides with the dynamics of the inverse system when zero input is applied and with the unobservable dynamics when a certain input output feedback linear

correspondence comments on robust stabilization of mimo nonlinear time varying mismatched uncertain systems the main false conclusion wang soh chai automatica 33 1997 2197 was pointed out by a simple counterexample

quantum 2 spheres and big q jacobi polynomials orthogonal bases for the algebras of functions of podles quantum 2 spheres are explicitly determined in terms of bigq jacobi polynomials this gives a group theoretic interpretation of the symmetric bigq jacobi polynomials and the symmetricq hahn polynomials

slow peaking and low gain designs for global stabilization of nonlinear systems this paper presents an analysis of the slow peaking phenomenon a pitfall of low gain designs that imposes basic limitations to large regions of attraction in nonlinear control systems the phenomenon is best understood on a chain of integrators perturbed by a vector field up x u that satisfies p x 0 0 peaking may cause a loss of global controllability unless severe growth restrictions are imposed on p x u these growth restrictions are expressed as a higher order condition with respect to a particular weighted dilation related to the peaking exponents of the nominal system when this higher order condition is satisfied an explicit control law is derived that achieves global asymptotic stability of x 0 this stabilization result is extended to more general cascade nonlinear systems in which the perturbation p x spl upsi spl upsi spl upsi spl xi u sup t contains the state spl xi and the control u of a stabilizable subsystem spl xi spl dot a spl xi u as an illustration a control law is derived that achieves global stabilization of the frictionless ball and beam model

control design for large scale lur e systems with arbitrary information structure constraints abstract in this paper an lmi based approach is proposed for the design of static output feedback for multi nonlinear lur e postnikov systems the resulting control laws ensure absolute stability and at the same time maximize the size of the nonlinear sectors the proposed method is computationally efficient and can accommodate feedback laws with arbitrary information structure constraints the effectiveness of this approach is demonstrated on a large scale example with 100 state variables

controllability observability of expanded composite systems abstract the relation between original and expanded systems within the inclusion principle from the point of view of controllability observability of both subsystems and composite systems is studied it is proved that complementary matrices always exist ensuring that the subsystems and the overall expanded system are simultaneously controllable observable two practically important large classes of complementary matrices are identified to offer results computationally attractive first the existence of complementary matrices ensuring controllability observability of decoupled subsystems is proved then using this result the same property is proved for the composite expanded system

dual inclusion principle for overlapping interconnected systems restriction and aggregation are two dual inclusion conditions which are revealed in the research field of inclusion principle for state space descriptions of overlapping interconnected systems an input state output dual inclusion principle is proposed for linear time invariant systems and their dual systems with the focus on restriction and aggregation in duality for direct contraction of control laws and state observers in these two special inclusion cases dual relationships of restriction and aggregation inclusion conditions are formulated between an original system and its dual system overlapping decentralized controller design problems are considered within the framework of the dual inclusion principle it is shown that if dual inclusion is satisfied in the same type of expansions restriction or aggregation for both original system and its dual system direct contraction can be applied to designed control laws or state observers from the expansion to the original space while dual informatio

decentralized estimation and control with overlapping information sets the objective of this note is to present a solution to the decentralized estimation and control problem for linear discrete time varying systems composed of overlapping subsystems the solution is based on the expansion contraction framework of the inclusion principle it is shown how decentralized estimation and control laws can be independently computed for the expanded system and then contracted for implementation in the original system to satisfy the overlapping information structure constraint

overlapping decompositions expansions contractions and stability of hybrid systems inclusion and extension principles are defined and studied for hybrid systems the controller design problem for hybrid systems is then considered within the framework of the extension principle it is shown that if the extension principle is used then any controller designed in the expanded spaces is contractible to the original spaces for implementation the stability of hybrid systems is also considered a number of definitions of stability for hybrid systems are given and it is shown that if a system which includes another system is stable then the included system is also stable furthermore it is shown that if a controller designed for the expanded system achieves stability then the contracted controller also achieves stability for the original system decentralized controller design with overlapping decompositions is also discussed within the framework of extension an example is provided to illustrate the proposed approach

generalized selection of complementary matrices in the inclusion principle this paper presents a strategy for choosing complementary matrices in the framework of the inclusion principle with state lq optimal control of lti systems it is based on translating the basic restrictions given by the inclusion principle into explicit block structures for these matrices the degree of freedom given by these structures is illustrated by means of an example of overlapping decentralized control design

stabilization in probability of nonlinear stochastic systems with guaranteed region of attraction and target set we deal with nonlinear dynamical systems consisting of a linear nominal part perturbed by model uncertainties nonlinearities and both additive and multiplicative random noise modeled as a wiener process in particular we study the problem of finding suitable measurement feedback control laws such that the resulting closed loop system is stable in some probabilistic sense to this aim we introduce a new notion of stabilization in probability which is the natural counterpart of the classical concept of regional stabilization for deterministic nonlinear dynamical systems and stands as an intermediate notion between local and global stabilization in probability this notion requires that given a target set a trajectory starting from some compact region of the state space containing the target remains forever inside some larger compact set eventually enters any given neighborhood of the target in finite time and remains thereinafter all these events being guaranteed with some probability we give a lyapunov based sufficient condition for achieving stability in probability and a separation result which splits the control design into a state feedback problem and a filtering problem finally we point out constructive procedures for solving the state feedback and filtering problem with arbitrarily large region of attraction and arbitrarily small target for a wide class of nonlinear systems which at least include feedback linearizable systems the generality of the result is promising for applications to other classes of stochastic nonlinear systems in the deterministic case our results recover classical stabilization results for nonlinear systems

contractibility of dynamic lti controllers using complementary matrices a generalized structure of complementary matrices involved in the input state output inclusion principle for linear time invariant systems including contractibility conditions for static state feedback controllers is well known in this note it is shown how to further extend this structure when considering contractibility of dynamic controllers necessary and sufficient conditions for contractibility are proved in terms of both unstructured and block structured complementary matrices for general expansion contraction transformation matrices explicit sufficient conditions for blocks of complementary matrices ensuring contractibility are proved for general expansion contraction transformation matrices moreover these conditions are further specialized for a particular class of transformation matrices

decentralized estimation and control with overlapping input state and output decomposition abstract the extension principle which was introduced recently is generalized to the case of input state and output expansion estimator and controller design problems are considered within the framework of the extension principle decentralized estimator and controller design with overlapping decompositions is also discussed within the same framework it is shown that if the extension principle is used then any estimator or controller designed in the expanded spaces is contractible to the original spaces for implementation furthermore it is shown that if an estimator designed for the expanded system achieves good estimation and or asymptotic estimation then the contracted estimator also achieves good estimation and or asymptotic estimation for the original system similarly it is also shown that if a controller designed for the expanded system achieves stability and or good performance then the contracted controller achieves stability and or good performance for the original system

almost disturbance decoupling for single input single output nonlinear systems the almost disturbance decoupling problem for nonlinear single input single output systems is addressed by using singular perturbation methods and high gain feedback sufficient conditions and the explicit high gain nonlinear state feedback in solvable cases are given they generalize both previous almost results for linear systems and exact ones for nonlinear systems the necessity of the conditions is discussed in particular an example is given where the main structural condition is not satisfied and the high gain control designed on the basis of linear approximations fails to achieve almost disturbance decoupling for the original system

reduction and non linear controllability of symmetric distributed systems this paper considers the reduction problem for distributed control systems in particular we consider controllability of systems containing multiple instances of diffeomorphic components where the overall system dynamics is invariant with respect to a discrete group action a subclass of such systems are systems with a set of identical components where the overall system dynamics are invariant with respect to physically interchanging these components the main result is a proposition which shows that for an equivalence class of symmetric systems of this type controllability of the entire class of systems can be determined by analysing the member of the equivalence class with the smallest state space the reduction methods developed are illustrated by considering the controllability of a team of mobile robots and a platoon of underwater vehicles

on the q analogues of some transformations of nearly poised hypergeometric series a number of transformation formulas for very well poised basic hypergeometric series have been obtained which in the limit q 1 approach the known transformation formulas for nearly poised ordinary hypergeometric series

on a generalization of the rogers generating function abstract we derive a generalization of the rogers generating function for the continuous q ultraspherical rogers polynomials whose coefficient is a 1 2 from that expansion we derive corresponding specialization and limit transition expansions for the continuous q hermite continuous q legendre laguerre and chebyshev polynomials of the first kind using a generalized expansion of the rogers generating function in terms of the askey wilson polynomials by ismail simeonov whose coefficient is a 7 8 we derive corresponding generalized expansions for the wilson continuous q jacobi and jacobi polynomials by comparing the coefficients of the askey wilson expansion to our continuous q ultraspherical rogers expansion we derive a new quadratic transformation for basic hypergeometric functions which relates an 7 8 to a 1 2 we also obtain several definite integral representations which correspond to the above mentioned expansions through the use of orthogonality

a unifying framework for the semiglobal stabilization of nonlinear uncertain systems via measurement feedback we study the problem of semiglobally stabilizing an uncertain nonlinear system consisting of a linear nominal system perturbed by either nonlinearities or model uncertainties our approach relies on well known h sub spl infin linear control tools and allows one to recover and improve in the unifying framework of a semiglobal separation result existing results on the semiglobal stabilization via output feedback in particular we discuss the case of uncorrupted outputs input and output nonlinearities or model uncertainties which may include for example practical situations such as backlash hysteresis and saturations the key feature of our design procedure is given by the choice of two continuous functions the first one is instrumental in constructing a stabilizing controller the second one arises in the candidate lyapunov function for the closed loop system relying on our main theorem we give general tools for achieving large regions of attraction via bounded measurement feedback for a wide class of nonlinear uncertain interconnected systems

compact matrix pseudogroups the compact matrix pseudogroup is a non commutative compact space endowed with a group structure the precise definition is given and a number of examples is presented among them we have compact group of matrices duals of discrete groups and twisted deformed su n groups the representation theory is developed it turns out that the tensor product of representations depends essentially on their order the existence and the uniqueness of the haar measure is proved and the orthonormality relations for matrix elements of irreducible representations are derived the form of these relations differs from that in the group case this is due to the fact that the haar measure on pseudogroups is not central in general the corresponding modular properties are discussed the haar measures on the twistedsu 2 group and on the finite matrix pseudogroup are found

stochastic link activation for distributed filtering under sensor power constraint we consider the problem of link activation for distributed estimation with power constraint to satisfy the requirement of power consumption we propose a stochastic link activation scheme where each sensor equipped with a distributed estimator sends data to its neighboring sensors according to different probabilities first we design the optimal estimator gain of each sensor to minimize the state estimation error covariance then we find an upper bound of the expected state estimation error covariance and provide a sufficient condition to guarantee the stability of the proposed estimator finally we formulate the link activation problem as an optimization problem and convert it to a convex optimization

brief paper controllability and observability of expanded systems with overlapping decompositions the expanded system concept of siljak and his coworkers enables the design of robust overlapping controllers and observers for large scale systems to be carried out in a purely decentralised way in this paper we study the stability and detectability properties of expanded systems and show that it is only in certain special cases that these properties are preserved when the system is expanded these special cases define the classes of systems where the expanded system concept can be used for controller or observer design

an inclusion principle for dynamic systems the purpose of this paper is to present a detailed study of the inclusion concept in dynamic systems which is a suitable mathematical framework for comparing systems with different dimensions the framework offers immediate results in reduced order modeling and the overlapping decentralized control of complex systems the presentation which is limited to linear constant systems relies on both the matrix algebra computations and the geometric elements structure to provide a balanced view of the issues involved in the concept of inclusion the framework is quite broad and has been used to consider nonlinear and time varying systems as well as systems with hereditary and stochastic effects

achieving nonvanishing stability regions with high gain cheap control using h techniques the second order case abstract this paper demonstrates how to use an asymptotically h optimal controller to stabilize a second order system subject to unknown disturbances such that the stability region does not vanish as the feedback gains increase the high gain feedback arises when one attempts to achieve the lowest achievable limit of the disturbance attenuation under the h design this type of gain increase can cause the stability region to vanish if the disturbance contains nonlinear terms the analysis using lyapunov techniques derives a sufficient condition on the design parameters to prevent the stability region from vanishing in addition to describing exact solutions for six different cases the paper provides simulations to illustrate the results

interconnection based performance analysis for a class of decentralized controllers this paper is concerned with decentralized controller design for large scale interconnected systems of pseudo hierarchical structure given such a system one can use existing techniques to design a decentralized controller for the reference hierarchical model obtained by eliminating certain weak interconnections of the original system although this indirect controller design is appealing as far as the computational complexity is concerned it does not necessarily result in satisfactory performance for the original pseudo hierarchical system an lq cost function is defined in order to evaluate the performance discrepancy between the pseudo hierarchical system and its reference hierarchical model under the designed decentralized controller a discrete lyapunov equation is then solved to compute this performance index however due to the large scale nature of the system this equation cannot be handled efficiently in many real world systems thus attaining an upper bound on this cost function can be more desirable than finding its exact value in practice for this purpose a novel technique is proposed which only requires solving a simple lmi optimization problem with three variables the problem is then reduced to a scalar optimization problem for which an explicit solution is provided it is also shown that when the original model is exactly hierarchical then the upper bounds obtained from the lmi and scalar optimization problems will both be equal to zero

inclusion principle for descriptor systems the purpose of this paper is to propose an expansion contraction framework for linear constant descriptor systems within the inclusion principle for dynamic systems our primary objective is to provide an explicit characterization of the expansion process whereby a given descriptor system is expanded into the larger space where all its solutions are reproducible by the expanded descriptor system if appropriate initial conditions are selected when a control law is formulated in the expanded space the proposed characterizations provide contractibility conditions for implementation of the control law in the original system a full freedom is provided for selecting appropriate matrices in the proposed expansion contraction control scheme in particular the derived theoretical framework serves as a flexible environment for expansion contraction control design of descriptor systems under overlapping information structure constraints

contractibility of overlapping decentralized control abstract the purpose of this paper is to generalize the concept of contractibility of decentralized control laws in the inclusion principle after a system with overlapping subsystems is expanded into a larger space and decentralized control laws are formulated for the disjoint subsystems the laws need to be contracted for implementation in the original space we propose broader definitions of restriction and aggregation in the framework of inclusion which provide more flexibility in the contraction phase of the expansion contraction process in particular we discuss contractibility conditions for dynamic output controllers including state observers which have been of special interest in applications

quadratic transformation formulas for basic hypergeometric series starting with some of the known transformation formulas for well poised 2 1 and very well poised 8 7 basic hypergeometric series we obtain q analogues of 36 quadratic transformation formulas given in 2 11 of higher transcendental functions vol 1 edited by erdelyi et al we also derive some new quadratic transformation formulas that give rise to identities connecting very well poised but unbalanced 10 9 series in base q with very well poised and balanced 12 11 series in base q 2 a rogers ramanujan type identity is also found as a limiting case

automatic generation of hypergeometric identities by the beta integral method in this article hypergeometric identities or transformations for p 1fp series and for kampe de feriet series of unit arguments are derived systematically from known transformations of hypergeometric series and products of hypergeometric series respectively using the beta integral method in an automated manner based on the mathematica package hyp as a result we obtain some known and some identities which seem to not have been recorded before in literature

uniform semiglobal practical asymptotic stability for non autonomous cascaded systems and applications it is due to the modularity they provide that results for cascaded systems have proved their utility in numerous control applications as well as in the development of general control techniques based on adding integrators nevertheless the standing assumptions in most of the present literature on cascaded systems is that when decoupled the subsystems constituting the cascade are uniformly globally asymptotically stable ugas hence existing results fail in the more general case when the subsystems are uniformly semiglobally practically asymptotically stable uspas this situation is often encountered in control practice e g in control of physical systems with external perturbations measurement noise unmodelled dynamics etc after giving a rigorous framework for the analysis of such stability properties this paper generalizes previous results for cascades by establishing that under a uniform boundedness condition on its solutions the cascade of two uspas systems remains uspas an analogous result is derived for uniformly semiglobally asymptotically stable usas systems in cascade furthermore we show the utility of our results in the pid control of mechanical systems affected by unknown non dissipative forces and considering the dynamics of the dc motors

model abstraction and inclusion principle a comparison this paper discusses connections between the inclusion principle and model abstraction in large scale hierarchical control systems it also provides conditions for implementation of controllability and observability in linear continuous time dynamic systems satisfying either aggregation or restriction conditions as well as for observability implementation in linear continuous time dynamic systems satisfying conditions for abstraction

hierarchically consistent control systems large scale control systems typically possess a hierarchical architecture in order to manage complexity higher levels of the hierarchy utilize coarser models of the system resulting from aggregating the detailed lower level models in this layered control paradigm the notion of hierarchical consistency is important as it ensures the implementation of high level objectives by the lower level system in this paper we define a notion of modeling hierarchy for continuous control systems and obtain characterizations for hierarchically consistent linear systems with respect to controllability objectives as an interesting byproduct we obtain a hierarchical controllability criterion for linear systems from which we recover the best of the known controllability algorithms from numerical linear algebra

linear feedback stabilization of nonlinear systems with an uncontrollable critical mode abstract linear feedback stabilization of nonlinear systems is studied for systems whose linearization at an equilibrium point possesses a simple critical mode that is uncontrollable the results complement previous work on the synthesis of nonlinear stabilizing control laws the present work addresses continuous time systems for which the linearization has either a simple zero eigenvalue or a pair of simple pure imaginary eigenvalues both the stability analysis and stabilizing control design employ results on stability of bifurcations of parameterized systems

on the assignability of infinite root loci in almost disturbance decoupling in this paper we investigate in detail the almost disturbance decoupling problem with state feedback an alternative proof of the sufficiency part of the original result by willoms 1981 on this problem requiring the construction of a sequence of feedback matrices is given it is shown that one can achieve almost disturbance decoupling by letting some of the closed loop eigenvalues run to infinity according to a spatial arrangement determined by the infinite zero structure the proofs of our results use the fact that almost controllability subspaces can be approximated by controlled invariant subspaces our results on the closed loop eigenstructure are stated in terms of such approximating sequences we also prove a generalization of a theorem by wonham 1979 used in the context of minimal order observer design

linearization and input output decoupling for general nonlinear systems necessary and sufficient conditions are obtained for the linearization and input decoupling by state feedback of general nonlinear systems it is shown how these conditions can be derived from the already known conditions for affine nonlinear systems thereby also elucidating the existing theory for affine systems

non standard analysis and representation of reality the aim of this paper is to show that the representation with the help of non standard analysis of a real phenomenon presenting different observation scales allows an important simplification of language indeed it is convenient to have available the concept of infinitely small and infinitely large quantities in dealing with the macroscopic effects of microscopic phenomena this is illustrated on two examples the representation of two time scales systems and the representation of noise

contractible controller design and optimal control with state and input inclusion abstract a new inclusion concept which involves both state and input expansion is introduced it is shown that with the approach undertaken here any control law designed in the expanded spaces is always contractible to the original spaces the inclusion of the cost functions is also discussed and necessary and sufficient conditions are derived it is shown that unlike the case when the two input spaces are identical the inclusion conditions must in general depend on the control laws however certain sufficient conditions which do not involve final control laws can be found if the inclusion is taken with respect to the optimal control finally controller design with overlapping decompositions is discussed within the framework of the new inclusion concept and optimal control

robust exponential stabilization for large scale uncertain impulsive systems with coupling time delays abstract in this paper we aim to study robust exponential stabilization for a large scale uncertain impulsive system with coupling time delays furthermore we also provide an estimation of the rate of convergence of exponential stabilization by utilizing the lyapunov method and razumikhin technique we shall design the feedback hybrid controllers in terms of linear matrix inequalities under which the robust exponential stability is achieved for a closed loop large scale uncertain impulsive system with coupling time delays moreover we shall also use the results obtained to design impulsive controllers for a large scale uncertain continuous system under which the closed loop continuous system achieves robust and exponential stability to illustrate our results one example is solved

robust overlapping guaranteed cost control of uncertain state delay discrete time systems this note presents a new extension of the inclusion principle to cope with the problem of designing robust overlapping controllers for state delayed discrete time systems with norm bounded uncertainties using the concept of guaranteed cost control expansion contraction relations for systems and contractibility conditions for output guaranteed cost memoryless controllers are proved including conditions on the equality of guaranteed performance bounds the controllers are designed in the expanded space using a linear matrix inequality lmi delay independent procedure specifically adapted to this class of problems the designed controllers are then contracted and implemented into the original system the results are specialized for the overlapping decentralized control design the method enables an effective construction of block tridiagonal controllers a numerical illustrative example is supplied

on the linear equivalents of nonlinear systems this paper studies feedback equivalence of nonlinear systems an equivalence relation is established for the systems x f x u a complete characterization of the class of nonlinear systems which are equivalent to controllable linear systems is obtained

semi global robust output regulation of minimum phase nonlinear systems based on high gain nonlinear internal model we consider the assumption of existence of the general nonlinear internal model that is introduced in the design of robust output regulators for a class of minimum phase nonlinear systems with rth degree r 2 the robust output regulation problem can be converted into a robust stabilisation problem of an augmented system consisting of the given plant and a high gain nonlinear internal model perfectly reproducing the bounded including not only periodic but also nonperiodic exogenous signal from a nonlinear system which satisfies some general immersion assumption the state feedback controller is designed to guarantee the asymptotic convergence of system errors to zero manifold furthermore the proposed scheme makes use of output feedback dynamic controller that only processes information from the regulated output error by using high gain observer to robustly estimate the derivatives of the regulated output error the stabilisation analysis of the resulting closed loop systems leads to regional as wel

characterization of stability region for general autonomous nonlinear dynamical systems the existing characterization of stability regions was developed under the assumption that limit sets on the stability boundary are exclusively composed of hyperbolic equilibrium points and closed orbits the characterizations derived in this technical note are a generalization of existing results in the theory of stability regions a characterization of the stability boundary of general autonomous nonlinear dynamical systems is developed under the assumption that limit sets on the stability boundary are composed of a countable number of disjoint and indecomposable components which can be equilibrium points closed orbits quasi periodic solutions and even chaotic invariant sets

guaranteed roll off in a class of high gain feedback design problems a number of synthesis problems associated with almost disturbance decoupling by state or measurement feedback is considered starting from a mathematical definition of the notion of high frequency roll off known results on the solvability of these problems are generalized to the situation in which we require their solvability together with a certain guaranteed roll off between disturbance and control the conditions are formulated in terms of the solvability and approximate solvability of certain matrix equations in rational functions

a canonical form for the inclusion principle of dynamic systems the inclusion principle provides a mathematical framework for comparing behavior of dynamic systems having different dimensions our main objective is to derive a canonical form for larger systems expansions that are obtained by expanding smaller systems contractions the form offers full freedom in selecting appropriate matrices for the expansion contraction process we will broaden the form to include feedback and propose an explicit characterization of contractible control laws subject to overlapping information structure constraints

nonlinear norm observability and simulation of control systems abstract the bi simulation relation has recently been attracting growing interest in the study of nonlinear control systems in the hope that through such a relation the behaviors and properties of a nonlinear system can be inferred from those of another system which is easier to handle in this paper we consider the propagation of the property of nonlinear norm observability through a simulation relation given two control systems that are related by a graph simulation relation we derive conditions under which the norm observability of the simulating system implies the norm observability of the simulated system the obtained results are given in terms of set valued functions several examples are included to illustrate various applications of our results

bisimilar linear systems the notion of bisimulation in theoretical computer science is one of the main complexity reduction methods for the analysis and synthesis of labeled transition systems bisimulations are special quotients of the state space that preserve many important properties expressible in temporal logics and in particular reachability in this paper the framework of bisimilar transition systems is applied to various transition systems that are generated by linear control systems given a discrete time or continuous time linear system and a finite observation map we characterize linear quotient maps that result in quotient transition systems that are bisimilar to the original system interestingly the characterizations for discrete time systems are more restrictive than for continuous time systems due to the existence of an atomic time step we show that computing the coarsest bisimulation which results in maximum complexity reduction corresponds to computing the maximal controlled or reachability invariant subspace inside the kernel of the observations map these results establish strong connections between complexity reduction concepts in control theory and computer science

sequential design of multi overlapping controllers for longitudinal multi overlapping systems in this paper a strategy to design multi overlapping controllers for systems with longitudinal multi overlapping structure is presented the design process uses the inclusion principle to carry out a multi step expansion that allows the decentralized design of a sequence of expanded local controllers these expanded local controllers are subsequently contracted to produce a multi overlapping controller that can be implemented in the original system to illustrate the proposed methodology the response of a four story building under a seismic excitation is considered

preservation of controllability observability in expanded systems the result contributed by the article is that controllability observability of an original continuous time lti dynamic system can always be simultaneously preserved in expanded systems within the inclusion principle when using block structured complementary matrices this new structure offers more degrees of freedom for the selection of specific complementary matrices than well known used cases such as aggregations and restrictions which enable such preservation only in certain special cases a complete unrestricted transmission of these qualitative properties from the original controllable observable system to its expansion is a basic requirement on the expansion contraction process mainly when controllers observers are designed in expanded systems to be consequently contracted for implementation in initially given systems an original system composed of two overlapped subsystems is adopted as a general prototype ease a numerical example is supplied

decentralized control and overlapping decomposition of mechanical systems part 1 system decomposition this paper improves a new inclusion concept called txtension to mechanical systems described by matrix second order equations recent work on specialization of the inclusion principle has been generalized to the expansion and contraction of input state and output spaces but without the possibility of constructing completely general contractible controllers in this paper necessary and sufficient conditions for extensions and contractible feedback controllers are proved they enable the construction of general contractible controllers without any constraint on the structure of controllers for mechanical systems

a new approach to control design with overlapping information structure constraints in this paper a new strategy is proposed for decentralized state feedback design with overlapping information structure constraints the method combines linear matrix inequalities and the inclusion principle in a way that eliminates controllability problems that are inherent to standard decentralized control design in the expanded space this approach can be extended to include an important class of uncertain nonlinearities and its validity is demonstrated through applications to strings of moving vehicles

robust output feedback control of nonlinear stochastic systems using neural networks we present an adaptive output feedback controller for a class of uncertain stochastic nonlinear systems the plant dynamics is represented as a nominal linear system plus nonlinearities in turn these nonlinearities are decomposed into a part obtained as the best approximation given by neural networks plus a remaining part which is treated as uncertainties modeling approximation errors and neglected dynamics the weights of the neural network are tuned adaptively by a lyapunov design the proposed controller is obtained through robust optimal design and combines together parameter projection control saturation and high gain observers high performances are obtained in terms of large errors tolerance as shown through simulations

on stabilization of nonlinear systems with enlarged domain of attraction this paper presents a systematic procedure to design a control law that guarantees asymptotic stability of an equilibrium with an enlarged domain of attraction for a class of nonlinear systems to this end we use a natural extension of well known linear time invariant transformation methods to write the system in controller canonical form with a forcing term the control law is implemented in two steps first we calculate a nonlinear state feedback that cancels the nonlinear terms of the unforced system so that for the resulting system a suitable lyapunov function candidate is available then we add a linear state feedback that stabilizes the equilibrium and maximizes its domain of attraction interestingly enough the latter maximization problem reduces to a classical linear time invariant h minimization problem an example is given to illustrate the procedure

proportional integral controllers for minimum phase nonaffine in control systems we show that stabilizing tracking proportional integral pi controllers can be constructed for minimum phase nonaffine in control systems the constructed pi controller is an equivalent realization of an approximate dynamic inversion controller this equivalence holds only for the time response when applied to the unperturbed system even when restricted to unperturbed minimum phase linear time invariant systems their closed loop robustness properties differ this shows that in general properties that do not define the equivalence relation for systems controllers are not preserved under such equivalence transformations

lyapunov stability of a class of discrete event systems discrete event systems des are dynamical systems which evolve in time by the occurrence of events at possibly irregular time intervals logical des are a class of discrete time des with equations of motion that are most often nonlinear and discontinuous with respect to event occurrences recently there has been much interest in studying the stability properties of logical des and several definitions for stability and methods for stability analysis have been proposed here the authors introduce a logical des model and define stability in the sense of lyapunov and asymptotic stability for logical des then the authors show that more conventional analysis of stability which employs appropriate lyapunov functions can be used for logical des the authors provide a general characterization of the stability properties of automata theoretic des models petri nets and finite state systems furthermore the lyapunov stability analysis approach is illustrated on a manufacturing system that processes batches of n different types of parts according to a priority scheme to prove properties related to the machine s ability to reorient itself to achieve safe operation and a load balancing problem in computer networks to study the ability of the system to achieve a balanced load to minimize underutilization

stabilization of fixed modes in expansions of lti systems the objective of this note is to propose a method for stabilization of structurally fixed modes in expansions of lti dynamic systems in the scope of overlapping decentralized control design based on the expansion contraction framework enabling successful design for a broader class of problems than considered so far the method is based on a judicious choice of complementary matrices in the expanded space numerical examples are provided to illustrate simplicity and efficiency of the proposed approach

hierarchical trajectory refinement for a class of nonlinear systems trajectory generation for nonlinear control systems is an important and difficult problem in this paper we provide a constructive method for hierarchical trajectory refinement the approach is based on the recent notion of f related control systems given a control affine system satisfying certain assumptions we construct a f related control system of smaller dimension trajectories designed for the smaller abstracted system are guaranteed by construction to be feasible for the original system constructive procedures are provided for refining trajectories from the coarser to the more detailed system

decentralized control using quasi block diagonal dominance of transfer function matrices the purpose of this paper is to present a generalization of the nyquist array method to blockwise decompositions which is based upon a new version of block diagonal dominance an additional flexibility of the proposed method is in partitioning of the system matrices into disjoint as well as overlapping submatrices which increases considerably the class of control systems which can be designed via block diagonal dominance within this framework the controllers for individual subsystems can be designed independently of each other so that their union represents a decentralized controller for the overall system