robust control of cascaded and individually feedback linearizable nonlinear systems abstract feedback linearization technique is applied to design robust controllers for a class of nonlinear uncertain systems every system in the class is a series connection of finite number of nonlinear subsystems which are individually feedback linearizable and have significant but matched nonlinear functional uncertainties the key difference between this work and existing robust results is that the matching conditions and the existence of feedback linearization transformation are only required individually for each subsystem a constructive robust control design procedure is proposed for the unique control in the overall system the procedure is conceptually simple and contains three steps first perform input output feedback linearization for all individual subsystems second design fictitious robust controllers for inputs of each subsystem as if the subsystem had an independent control finally a mapping is developed which maps the individual fictitious controls recursively into the unique control of the overall system since neither the matching conditions nor feedback linearization are required for the overall system this becomes the broadest class of nonlinear uncertain or known systems for which a robust regular tracking control can be constructed using feedback linearization method global stability of the overall system is always guaranteed

on brown s and newton s methods with convexity hypotheses in the context of the monotone newton theorem mnt it has been conjectured that discretised brown iterations converge at least as fast as discretised newton iterations because such is the case for analytic iterations with easily verified hypotheses it is proved here that brown analytic iterations converge strictly faster than newton ones as a consequence the same result holds for discretised iterations with conveniently small incremental steps however in the general context of the mnt it may happen that newton s discretised method converges faster than brown s but this situation can be remedied in many cases by conveniently shifting the initial value so that those hypotheses ensuring the reverse are satisfied thus a fairly effective solution is given to the problem stated initially

brief paper output feedback variable structure control design with an h2 performance bound constraint in this paper we give an lmi based method for designing an output feedback variable structure control vsc system with an h 2 constraint the uncertain system model under consideration may have nonmatching disturbance input signals nonmatching disturbance input signal reduction is performed via h 2 norm minimization in terms of a constrained riccati inequality we give a sufficient condition for the existence of a linear sliding surface and a compensator guaranteeing an h 2 constraint and we show that the control parameters can be characterized by using the solution to the given inequality condition we also give a simple lmi based design algorithm of an output feedback vsc law guaranteeing an h 2 constraint finally by using a design example we show that our method can supplement the existing results

nonlinear decoupling via feedback a differential geometric approach the paper deals with the nonlinear decoupling and noninteracting control problems a complete solution to those problems is made possible via a suitable nonlinear generalization of several powerful geometric concepts already introduced in studying linear multivariable control systems the paper also includes algorithms concerned with the actual construction of the appropriate control laws

global stabilization of nonlinear systems with a class of unmatched uncertainties abstract global and asymptotic stabilization of uncertain dynamical systems which violate the matching conditions is investigated a class of unmatched uncertainties called equivalently matched uncertainties is defined a robust controller is proposed to stabilize the uncertain system asymptotically in the large provided that the nominal system is uniformly asymptotically stable and that the unmatched uncertainties are equivalently matched the required information about uncertain dynamics in the system is merely that the uncertainties are bounded in euclidean norm by known functions of the system state

continuous feedback guaranteeing uniform ultimate boundedness for uncertain linear delay systems an application to river pollution control we employ the stability result of thowsen on a class of linear delay systems containing uncertain elements and subject to uncertain inputs to manage a simple one reach model of a river system with time delay and subject to uncertain but bounded input as well as parameter disturbances two important indices of water quality namely biochemical oxygen demand bod and dissolved oxygen do are used as state variables while controls in the form of effluent discharge rate of bod and in stream aeration rate of do are employed to steer the system to a calculable neighborhood of a desired steady state and then maintain it there

global stabilization with almost disturbance decoupling of a class of uncertain non linear systems in this paper we study the global stabilization of a class of non linear uncertain systems while decoupling the output from external disturbances to any specified degree of accuracy the class of non linear systems considered could be viewed as a generalization of uniform rank multivariable linear systems which have the property that all their infinite zeros are of the same order although the plants considered are non linear the compensator developed here is linear our compensator which achieves global exponential stability and almost disturbance decoupling of the output requires only output feedback rather than full state feedback model uncertainty is dealt with either by restricting the uncertain elements to particular subspaces satisfying the so called matching conditions and or by treating a family of plants for which a single controller simultaneously globally exponentially stabilizes all the plants in while achieving almost disturbance decoupling of the output

improving jacobi and gauss seidel iterations abstract when convergent jacobi or gauss seidel iterations can be applied to solve systems of linear equations a natural question is how convergence rates are affected if the original system is modified by performing some gaussian elimination we prove that if the initial iteration matrix is nonnegative then such elimination improves convergence our results extend those contained in 4

disturbance observer based robust mixed h2 h fuzzy tracking control for hypersonic vehicles this paper introduces a disturbance observer do based mixed h2 h robust fuzzy tracking control design for the longitudinal dynamics of a generic hypersonic vehicle hv with modeled and unmodeled disturbances a takagisugeno ts fuzzy model is firstly employed to approximate the nonlinear dynamics of hv subsequently based on the fuzzy model a do is constructed to estimate the modeled disturbance next by integrating the hv dynamics the tracking error integral and the disturbance estimation error dynamics an augmented system is established for the control design then a do based mixed h2 h robust fuzzy control design is developed to ensure the asymptotic stability as well as the mixed h2 h control performance of the augmented system the proposed control scheme includes a fuzzy tracking controller with state feedback plus the tracking error integral a robust nonlinear compensator for eliminating the matched part of the compound disturbance consisting of the unmodeled disturbance and fuzzy modeling error and a do based compensator for the modeled disturbance cancellation the outcome of the do based mixed h2 h robust fuzzy control problem is formulated in terms of linear matrix inequalities lmis furthermore by utilizing the existing lmi optimization technique a suboptimal controller is obtained in the sense of minimizing an upper bound of h2 performance finally simulation results on an hv demonstrate the effectiveness of the proposed design method

robust tracking in nonlinear systems a nonlinear feedback multivariable controller is used to implement multivariable tracking in a nonlinear system the tracking error is measured by a general function of system state and the input command the controller is robust in the sense that the tracking error is ultimately bounded in the presence of modeling errors free parameters which affect the form of the controller allow flexibility in determining such factors as the size of the ultimate bound the rate of error decay excursion of the control conditions on the class of modeling errors and the level of system gain restrictive assumptions on the structure of the model and the modeling errors are required but they are treated in a transformation framework which allows the generalization of similar conditions which appear in the prior literature these assumptions hold for robotic manipulators this application is investigated at some length and it appears that the resulting control scheme may have advantages over others which have been proposed in the robotics literature

brief lq performance bounds for adaptive output feedback controllers for functionally uncertain nonlinear systems we consider functionally uncertain systems which can be written in an output feedback form where the nonlinearities are functions of the output only the uncertainty is described by a weighted l 2 norm about a nominal system and an approximate adaptive design is given which ensures output practical stability the main result requires knowledge of the weighted l 2 uncertainty level an upper bound on the lq performance of the output transient and the control input is derived where the cost penalises the output transient and the control effort on the time interval where the output lies outside the prescribed neighbourhood of zero to which we achieve convergence

new matching conditions for output regulation of a class of uncertain nonlinear systems some sufficient conditions for the structure of modelling uncertainties for output regulation of uncertain systems are presented it turns out that these conditions include as special cases the ordinary matching conditions for state regulation of uncertain systems and the disturbance decoupling condition the previous restrictions on the structure of modelling uncertainties can be considerably relaxed in the case of output regulation the significance of the result is shown by a simple example

practical stabilization of a class of uncertain nonlinear systems abstract in this paper the problem of robust control of a class of nonlinear systems with internal and input channel uncertainties is addressed the proposed control algorithm reflects the two level structure of the plant and guarantees the system uniform asymptotic stability with respect to an arbitrary neighbourhood of the nominal system stability point

a mimo sliding control with a first order plus integral sliding condition abstract a straight sliding control for nonlinear time varying mimo multiple input multiple output systems is developed in which matrix norm techniques are utilized to tune the controlling parameters the sliding control provides a straight tuning procedure to obtain the desired system response a first order plus integral s dynamics is derived from a first order plus integral sliding condition the integral in the s dynamics guarantees zero steady state value of s and therefore zero steady state error is warranted the equivalent spring constant and the thickness of the boundary layer enable the separate control of the robustness to unmodeled dynamics and the tracking accuracy to reject high frequency unmodeled dynamics the bandwidth of the s dynamics is limited by tuning the equivalent spring constant the thickness of the boundary layer is adjusted within the sliding condition to fine tune the s dynamics and reduce the tracking error

global robust stabilization of nonlinear cascaded systems this paper gives a sufficient condition for a class of nonlinear cascaded systems to be globally stabilizable via state feedback in the presence of uncertainty which does not necessarily satisfy the so called matching condition the authors result is an extension of the former stabilization results which treated systems without uncertainty in the sense that the uncertainty is taken into account

adaptive regulation for a class of uncertain systems with partial knowledge of uncertainty bounds an adaptive regulation method is presented for a class of uncertain systems where the uncertainty bounds are partially known both the state and the parameter error of the closed loop system are shown to be ultimately bounded the proposed method improves on the adaptive control method of m j corless and g leitmann 1981 so that performance degradation and the destabilization of the control system can be effectively presented in practical situations

variable structure robust control of uncertain time delay systems abstract this paper introduces a variable structure output feedback robust control for uncertain time delay systems new types of switching manifolds with integral terms are implemented to consider larger class of linear systems by overcoming both the observability constraints of the reduced order system and the kimura davison condition two types of control laws are introduced by which an estimate of a region of asymptotic stability to the origin and a region of attraction to the switching manifold are defined

globally stable robust tracking of nonlinear systems using variable structure control and with an application to a robotic manipulator the globally stable robust output tracking for a class of nonlinear systems is considered based only on the knowledge of the bounds on the uncertainties a variable structure control vsc law is developed under the structure matching assumption it is shown that the outputs of the closed loop system asymptotically track given output trajectories despite the uncertainties while maintaining the boundedness of all signals inside the loop all signals inside the loop are shown to be bounded for all time to illustrate the efficiency of the controller the approach is applied to the case of a two degree of freedom dof robotic manipulator with variable payload numerical simulation results are also provided

continuous state feedback guaranteeing uniform ultimate boundedness for uncertain dynamic systems we consider a dynamic system containing uncertain elements only the set of possible values of these uncertainties is known based on this information a class of state feedback controls is proposed in order to guarantee uniform ultimate boundedness of every system response within an arbitrarily small neighborhood of the zero state these feedback controls are continuous functions of the state

bounded amplitude performance of switched lpv systems with applications to hybrid systems this paper discusses recent results on multiple linear agent control for systems satisfying a bounded amplitude performance constraint the plant is assumed to be a linear parameter varying lpv system scheduled along a nominal parameter trajectory in this respect the control problem represents a plant operating between a prespecified set of operating conditions linear controllers are designed at setpoints along this scheduling trajectory to satisfy bounded amplitude performance constraints this paper discusses an approach to analyze the switched system behavior under practical assumptions on the structure of the switching rule the approach combines the scheduling parameter with lpv system properties to derive bounds on the switching behavior of the system these estimates are then used to construct a logical model of the switched system behavior in the form of a timed automaton in this respect this paper presents a way of extracting logical models of continuous time system behavior

one approach to the control of uncertain dynamical systems we present a controller design methodology for uncertain systems which is based on the constructive use of lyapunov stability theory the uncertainties which are deterministic are characterized by certain structural conditions and known as well as unknown bounds as a consequence of the lyapunov approach the methodology is not restricted to linear or time invariant systems the robustness of these controllers in the presence of singular perturbations is considered the situation in which the full state of the system is not available for measurement is also considered as are other generalizations

monotone discrete newton iterations and elimination abstract the improvement in convergence by means of accurate functional elimination in the context of the monotone newton theorem is further analyzed and extended to discrete approximations of the newton method

continuous robust control design for nonlinear uncertain systems without a priori knowledge of control direction in this paper a robust control scheme is proposed for a class of nonlinear systems that have not only additive nonlinear uncertainties but also unknown multiplicative signs these signs are called control directions since they represent effectively the direction of motion under any given control except for the unknown control directions the class of systems satisfy the generalized matching conditions nonlinear robust control is designed to identify on line unknown control directions and to guarantee global stability of uniform ultimate boundedness without the knowledge of nonlinear dynamics except their size bounding functions it is also shown that the proposed robust control can be made continuous through utilizing the so called shifting laws that change smoothly and accordingly the signs of robust controls and that no matter what time constants and gains of the shifting laws are global stability is always ensured the analysis and design is done using lyapunov s direct method

robust stabilization of the angular velocity of a rigid body the problem of robust control for the angular velocity of a rigid body subject to external disturbances is addressed it is shown that if the disturbances are matched there exists a control law attenuating the effect of the disturbances whereas in the case of non matched disturbances no such a feedback law generically exists hence a new concept of disturbance attenuation is introduced and it is proved that the aforementioned problem is solvable in this weaker sense explicit expressions of the control laws solving the proposed robust stabilization problems are given

linear and nonlinear stabilizing continuous controllers of uncertain dynamical systems including state delay the problem of robust stabilization of a class of time varying dynamical systems with disturbance uncertain parameters and a bounded time varying state delay is considered two classes of stabilizing continuous controllers are proposed the proposed controllers can guarantee the existence of the solution to the dynamical system in the usual sense and can also be directly implemented in the practical control problems moreover since the proposed controllers are completely independent of the time delay which is only assumed to be any nonnegative bounded and continuous function the results developed in this note are applicable to a class of dynamical systems with uncertain time delays finally a numerical example is given to demonstrate the validity of the results

an adaptive control strategy for mechanical manipulators this paper focuses on the study of an adaptive perturbation control which tracks a desired time based trajectory as close as possible for all times over a wide range of manipulator motion and payloads the proposed adaptive control is based on the linearized perturbation equations in the vicinity of a nominal trajectory the controlled system is characterized by feedforward and feedback components which can be computed separately and simultaneously the feedforward component computes the nominal torques from the newton euler equations of motion to compensate all the interaction forces among the various joints the feedback component consisting of recursive least square identification and an optimal adaptive self tuning control algorithm for the linearized system computes the perturbation torques which reduce the position and velocity errors of the manipulator along the nominal trajectory a computer simulation study was conducted to evaluate the performance of the proposed adaptive control

output tracking control of nonlinear systems with mismatched uncertainties abstract this paper addresses the output tracking problem of a class of nonlinear systems given input output linearizability of the class of nonlinear systems a robust output tracking controller derived via a lyapunov based approach is proposed here the model uncertainties do not need to satisfy the conventional matching condition but states and tracking error remain bounded furthermore the magnitude of the tracking error will bear dominant dependence on the magnitude of the mismatched uncertainties

stabilizing controllers for uncertain linear systems with additive disturbances this paper is concerned with the problem of designing stabilizing controllers for linear systems containing uncertainty the uncertainty is time varying with values lying in a specified set and enters through the system matrix through the input connection matrix and additively a method is presented for obtaining a linear state feedback controller which guarantees that the system response ultimately lies in a prespecified neighbourhood of the origin in some situations this neighbourhood can be made arbitrarily small and practical stability is achieved the solution of an algebraic riccati equation is used to generate the feedback gains for the linear controller several examples are included to illustrate the application of the method

regular splittings and monotone iteration functions in this paper we introduce the set of so called monotone iteration functions mi functions belonging to a given function we prove necessary and sufficient conditions in order that a given mi function is in a precisely defined sense at least as fast as a second one regular splittings of a function which were initially introduced for linear functions by r s varga in 1960 are generating mi functions in a natural manner for linear functions every mi function is generated by a regular splitting for nonlinear functions however this is generally not the case

multiple surface sliding control of a class of uncertain nonlinear systemsm we develop a multiple surface sliding control for a class of single input single output nonlinear systems whose uncertainties do not satisfy the standard matching condition a coordinate dependence condition on the uncertainty bound is assumed a computed normal form is defined to handle such uncertainties instead of the normal form used in conventional input output linearization a control algorithm which can be applied to global tracking problems has been developed and evaluated for a benchmark example

the vss approach to the model reference control of nonminimum phase linear plants a nontrivial application of the discontinuous control system theory based on filippov s solution concept is presented the problem addressed is the model reference output feedback control of linear plants with non hurwitzian numerator in the transfer function a solution in the case of known systems is presented first an error state equation whose state is accessible is then derived for the case in which the plant parameters are unknown in the case in which some bounds on the plant characteristics are supposed known a pair of discontinuous signals acting on both the plant and the model is chosen causing the error state to vanish asymptotically

further results on the observer design problem abstract in this paper the observer design problem for nonlinear systems is considered sufficient lyapunov like conditions are presented for the existence of a nonlinear observer the theory we develop considerably improves and extends the results of our recent work 14

decentralized variable structure control for tracking in non linear systems the problem of tracking time varying trajectories in non linear systems is considered these trajectories could be generated on line by a reference model the problem is tackled by considering the overall system as a set of decentralized linear sub systems which can be modelled as a set of double integrators and treating the non linearities as uncertainties with known bounds on their magnitudes a variable structure controller is designed based on the theory of uncertain dynamical systems the system is shown to track a class of trajectories generated by the reference mode a set of double integrators to within a specified tolerance some analysis is presented to explain the dynamic behaviour of the closed loop system and bounds are derived linking the rate of convergence and the tracking ability to system parameters such as available control and magnitude of the uncertainty simulation results are presented to validate the conclusions

a comparison principle for state constrained differential inequalities and its application to time optimal control in this paper we present a comparison principle that characterizes the maximal solutions of state constrained differential inequalities in terms of solutions of certain differential equations with discontinuous right hand sides for the sake of completeness we show through some set valued analysis that the differential equations determining the maximal solutions have the unique solutions in the carathe spl acute odory sense in spite of discontinuity of their right hand sides we apply our comparison principle to the explicit characterization of the solution to a time optimal control problem for a class of state constrained second order systems which includes the dynamic equations of robotic manipulators with geometric path constraints as well as single degree of freedom mechanical systems with friction specifically we show that the time optimal trajectory is uniquely determined by two curves that can be constructed by solving two scalar ordinary differential equations with continuous right hand sides hence the time optimal trajectory can be found in a computationally efficient way through the direct use of the well known euler or runge kutta methods another interesting feature is that our method to solve the time optimal control problem works even when there exist an infinite number of switching points finally some simulation results using a two degrees of freedom dof robotic manipulator are presented to demonstrate the practical use of our complete characterization of the time optimal solution

stochastic monotonicity and realizable monotonicity we explore and relate two notions of monotonicity stochastic and realizable for a system of probability measures on a common finite partially ordered set poset f when the measures are indexed by another poset a we give counterexamples to show that the two notions are not always equivalent but for various large classes of f we also present conditions on the poset a that are necessary and sufficient for equivalence when a f the condition that the cover graph of f have no cycles is necessary and sufficient for equivalence this case arises in comparing applicability of the perfect sampling algorithms of propp and wilson and the first author of the present paper

a lyapunov approach for robust nonlinear state feedback synthesis the authors apply the input output linearization approach for nonlinear state feedback synthesis the model uncertainty under consideration is a class of state model perturbations that satisfy appropriate matching conditions the controller design uses a lyapunov based approach to guarantee uniform ultimate boundedness of the states and the output

dynamic surface control for a class of nonlinear systems a method is proposed for designing controllers with arbitrarily small tracking error for uncertain mismatched nonlinear systems in the strict feedback form this method is another synthetic input technique similar to backstepping and multiple surface control methods but with an important addition spl tau 1 low pass filters are included in the design where spl tau is the relative degree of the output to be controlled it is shown that these low pass filters allow a design where the model is not differentiated thus ending the complexity arising due to the explosion of terms that has made other methods difficult to implement in practice the backstepping approach while suffering from the problem of explosion of terms guarantees boundedness of tracking errors globally however the proposed approach while being simpler to implement can only guarantee boundedness of tracking error semiglobally when the nonlinearities in the system are non lipschitz

quadratic stabilizability of linear systems with structural independent time varying uncertainties the author investigates the problem of designing a linear state feedback control to stabilize a class of single input uncertain linear dynamical systems the systems under consideration contain time varying uncertain parameters whose values are unknown but bounded in given compact sets the method used to establish asymptotical stability of the closed loop system obtained when the feedback control is applied involves the use of a quadratic lyapunov function the author first shows that to ensure a stabilizable system some entries of the system matrices must be sign invariant he then derives necessary and sufficient conditions under which a system can be quadratically stabilized by a linear control for all admissible variations of uncertainties the conditions show that all uncertainties can only enter the system matrices in such a way as to form a particular geometrical pattern called an antisymmetric stepwise configuration for the systems satisfying the stabilizability conditions a computational control design procedure is also provided and illustrated via an example

observer based adaptive control for uncertain time delay systems in this paper we will focus on investigating the observer based controlling problem of time delay systems first we investigate a class of simple time delay systems the corresponding adaptive observer and controller are designed which are both independent of the time delays based on lyapunov stability theory we prove that the closed loop system is asymptotically stable next we further consider the interconnected time delay system case the corresponding adaptive observer and controller are designed we prove that the resulting closed loop system is also asymptotically stable simulations on controlling time delay systems and interconnected systems are investigated and the results show that the designed controllers are feasible and efficient

letter to the editor on the exponential stability of a class of nonlinear systems including delayed perturbations in this letter the problem of robust stabilization of a class of nonlinear dynamical systems with delayed perturbations is considered based on the stability of the nominal systems a new stabilizing control law for exponential stability of the system is designed using lyapunov stability theory

robust semi global output tracking for nonlinear singularly perturbed systems in this work a robust controller design methodology for a broad class of singularly perturbed nonlinear systems with time varying uncertainties is developed when the fast subsystem is stabilizable and the slow subsystem is input output linearizable with input to state stable iss inverse dynamics the developed state feedback controller guarantees boundedness of the trajectories of the closed loop system and robust output tracking with arbitrary degree of asymptotic attenuation of the effect of uncertainty on the output for initial conditions and uncertainties in an arbitrarily large compact set so long as the singular perturbation parameter is sufficiently small the controller is a continuous function of the state of the system and its construction requires the knowledge of bounding functions on the size of uncertainty the developed method is applied to a non isothermal continuous stirred tank reactor with fast jacket dynamics

linear time varying system control based on the inversion transformation this paper proposes a new state feedback control design for uniformly controllable linear time varying systems the new design is based on a nonlinear state transformation that converts the stabilization problem of the system state into a destabilization problem of the transformed state such a transformation results in a new control that has two advantages over previous controls 1 in some of the previous control designs forecast of future information of the time varying system matrices over some time interval t t is required to calculate the state feedback gain at any time instant t while in the new control design no such forecast is needed 2 in other previous control designs consecutive time differentiation on the time varying system matrices is required while in the new control design time integration instead of differentiation is applied to the system matrices the new control can therefore be applied to systems with time varying parameters that are piecewise continuous in time

output feedback decentralized control of large scale systems using weighted sensitivity functions minimization this paper considers the problem of achieving stability and desired dynamical transient behavior for linear large scale systems by decentralized control it can be done by making the effects of the interconnections between the subsystems arbitrarily small sufficient conditions for stability and diagonal dominance of the closed loop system are introduced these conditions are in terms of decentralized subsystems and directly make a constructive h control design possible a mixed h pole region placement is suggested such that by assigning the closed loop eigenvalues of the isolated subsystems appropriately the eigenvalues of the overall closed loop system are assigned in desirable range the designs are illustrated by an example

adaptive stabilizing state feedback controllers of uncertain dynamical systems with multiple time delays the problem of robust stabilization for a class of uncertain dynamical systems with multiple delayed state perturbations is considered in this paper it is assumed that each perturbation is bounded by a linear function of delayed state with unknown gains and an adaptation law is proposed to estimate these unknown gains moreover by making use of the updated values of these unknown bounds we propose a memoryless state feedback controller for such a class of uncertain time delay systems based on lyapunov stability theory and lyapunov krasovskii functional it is shown that the closed loop dynamical system resulting from the proposed adaptive robust control schemes is globally stable in the sense of uniform ultimate boundedness finally a numerical example is given to demonstrate the validity of the results

paper linear ultimate boundedness control of uncertain dynamical systems given a state equation whose description includes uncertain parameters it is often desirable to design a feedback controller which renders all solutions uniformly and ultimately bounded when facing such a problem one often has available or assumes an upper bound for the excursions of the uncertain parameters within this framework the objective is to guarantee no matter how nature selects the uncertainty that the state will eventually end up and remain within some pre specified region when this region is a small neighborhood about the origin the concept of uniform ultimate boundedness is tantamount to practical asymptotic stability the objectives of this paper are twofold first and foremost our goal is to show that a class of ultimate boundedness problems which have been solved to date via nonlinear control can in point of fact be solved via linear control this is the main result and is given in theorem 4 1 secondly we show that some of the so called matching assumptions which have been required in the earlier literature can be weakened somewhat this enables one to design controllers for a larger class of dynamical systems than previously considered

decentralized adaptive robust control for a class of large scale systems with uncertainties in the interconnections the problem of decentralized control is considered for a class of time varying large scale systems with uncertainties and external disturbances in the interconnections in this paper the upper bounds of the uncertainties and external disturbances are assumed to be unknown the adaptation laws are proposed to estimate such unknown bounds and by making use of the updated values of these unknown bounds a class of decentralized linear and non linear state feedback controllers are constructed it is shown that by employing the proposed decentralized non linear state feedback controllers the solutions of the resulting adaptive closed loop large scale system can be guaranteed to be uniformly bounded and the states are uniformly asymptotically stable by using the decentralized linear state feedback controllers one can guarantee the uniform ultimate boundedness of the resulting adaptive closed loop large scale system finally a numerical example is given to demonstrate the validity of the results

output feedback variable structure control design this paper describes a procedure for variable structure output feedback control vsofc for a class of multivariable linear time invariant systems the equivalent control method of utkin in the output feedback mode yields a reduced order system exhibiting output feedback equivalent dynamics using the kimura davison sufficient conditions for pole placement using output feedback a sufficient condition is derived to assign the eigenvalues of the reduced order system the observability and controllability of the reduced system is discussed two switching surface design algorithms are introduced based on both a static output feedback and on an eigenstructure assignment techniques a control design is discussed as well

exact nonlinear control of large angle rotational maneuvers the rigid body attitude control problem with external torques is transformed into an equivalent linear form implementable by three double integrators the linearizing transformations themselves are formulated in vector algebra requiring no integrators for implementation it is thereby shown that optimal command generation for fast slewing maneuvers can be carried out exactly in the transformed system together with regulator design without gain scheduling for correction of unmodeled disturbances in particular a general rest to rest maneuver is computed in closed form and coupled with a previously obtained exact detumbling maneuver so that arbitrary initial conditions can be accommodated an illustrative simulation is appended

robust output tracking for nonlinear systems with weakly non minimum phase this paper is concerned with the problem of designing a robust output tracking controller for mimo nonlinear systems with weakly non minimum phase based on our system formulation control plants with uncertainties and or with actuator dynamics fall into the class under consideration the controller design here is divided into two phases fast feedback control and slow feedback control so that a final composite control is obtained the former is chosen to stabilize the boundary layer system whereas the latter essentially handles the mismatched uncertainties after the system is reformulated under some mild assumptions it is shown that the overall states are bounded and the tracking errors converge to a residual set whose size is a class k function of e as e 0 the residual set shrinks to the origin an interesting application to a simplified aircraft model with fast actuator dynamics which turns out to be weakly non minimum phase is given the computer simulation has verified the expected satisfac

output feedback decentralized stabilization ilmi approach in this paper the static output feedback decentralized stabilization problem is addressed using a linear matrix inequality approach a necessary and sufficient condition for static output feedback decentralized stabilizability is derived for linear time invariant large scale systems it is proven that the existence of a stabilizing decentralized gain is equivalent to that of the solution of a quadratic matrix inequality the extension of the result to h control is studied an iterative lmi algorithm based on the linear matrix inequality technique is proposed to obtain the decentralized feedback gain examples show the effectiveness of the algorithm

adaptive robust tracking and model following of uncertain dynamical systems with multiple time delays the problem of robust tracking and model following is considered for a class of linear systems with multiple delayed state perturbations time varying uncertain parameters and disturbance in this note it is assumed that the upper bounds of the delayed state perturbations uncertainties and external disturbances are unknown an improved adaptation law with spl sigma modification is proposed to estimate such unknown bounds and on the basis of the updated values of these unknown bounds a class of continuous memoryless state feedback controllers is constructed for robust tracking of dynamical signals the proposed adaptive robust tracking controller can guarantee that the tracking error decreases asymptotically to zero in the presence of multiple delayed state perturbations time varying uncertain parameters and disturbance in addition it is also shown that this improved adaptation law with spl sigma modification can be applied to the general adaptive control problems to obtain some more exact control results finally a numerical example is given to demonstrate the validity of the results

an extension of kemperman s characterization on k independence and its application abstract we present a mixed type multivariate distributional model generalizing the model of k independent identically distributed random variables and give necessary and sufficient conditions for a distribution of a random vector to be the joint distribution of the numbers of successes of q categories in n such dependent trials the model includes as particular cases mixtures of multivariate extremal distributions and models corresponding to ordinal sums of independence and comonotonicity copulas as an application we study the extremal properties of order statistics based on random vectors with known multivariate marginals

on the equivalence between global recurrence and the existence of a smooth lyapunov function for hybrid systems abstract we study a weak stability property called recurrence for a class of hybrid systems an open set is recurrent if there are no finite escape times and every complete trajectory eventually reaches the set under sufficient regularity properties for the hybrid system we establish that the existence of a smooth radially unbounded lyapunov function that decreases along solutions outside an open bounded set is a necessary and sufficient condition for recurrence of that set recurrence of open bounded sets is robust to sufficiently small state dependent perturbations and this robustness property is crucial for establishing the existence of a lyapunov function that is smooth we also highlight some connections between recurrence and other well studied properties like asymptotic stability and ultimate boundedness

global transformations of nonlinear systems recent results have established necessary and sufficient conditions for a nonlinear system of the form dot x t f x t u t g x t with f 0 0 to be locally equivalent in a neighborhood of the origin in rnto a controllable linear system we combine these results with several versions of the global inverse function theorem to prove sufficient conditions for the transformation of a nonlinear system to a linear system in doing so we introduce a technique for constructing a transformation under the assumptions that g ldot f dotg ad n 1 f ldotg span an n dimensional space and that g ldot f ldot g ad n 2 f ldotg is an involutive set

fuzzy dynamical system approach for a dual parameter hybrid order robust control design abstract robust control for uncertain dynamical systems is considered the uncertainty is assumed to be bounded and the fuzzy set theory is adopted to describe the bound a new dual parameter hybrid order robust control design is then proposed in two steps first a class of robust controls is designed taking the advantage of the flexibility in choosing the order and a design parameter the controls are deterministic and are not if then fuzzy rules based deterministic performance including uniform boundedness and uniform ultimate boundedness for the controlled systems is guaranteed second a fuzzy set theoretic based performance index consisting of average and steady state system performance and control cost is proposed a constrained optimization problem is formulated with the intension of minimizing the performance index the objective of the optimization problem is to search for the optimal choice of dual parameters that minimizes the performance index we show that the solution to the optimization problem always exists as a result the resulting control design achieves two concurrent goals guaranteeing deterministic performance as well as minimizing the performance index the theory is illustrated by an unmanned aerial vehicle uav system control design

discrete time robust control via state feedback for single input systems a nonlinear robust state feedback controller for discrete time uncertain systems is proposed the uncertainties in the system must satisfy the matching condition but only their bounds need to be known the controller is designed via the second method of lyapunov the detailed derivation of the controller for single input systems is given the system response remains in the neighborhood of the zero state if uncertainties are small the uncertainty bound for the stability condition is derived

stabilization of linear time invariant interval systems via constant state feedback control this paper investigates the stabilization problem of linear uncertain systems via constant state feedback control the systems under consideration contain time invariant uncertain parameters whose values are unknown but bounded in given compact sets and are thus called interval systems the criterion for the asymptotic stability of the closed loop system obtained when a state feedback control is applied is that all the eigenvalues of the resulting system matrix are in the strict left half of the complex plane first the author shows that to insure an interval system stabilizable some entries of the system matrices must be sign invariant more precisely the number of the least required sign invariant entries in system matrices is equal to the system order then the author studies the stabilizability of a set of interval systems called standard systems which contain sufficient numbers of sign invariant entries in proper locations after dividing all standard systems into some subsets by the uncertainty locations the author then derives necessary and sufficient conditions under which every system in a subset is stabilizable regardless of its parameter varying bounds the conditions show that all uncertain entries in system matrices should form a particular geometrical pattern called a generalized antisymmetric stepwise configuration for an interval system satisfying the stabilizability conditions a computational control design procedure is also provided and illustrated via an example the result is further generalized for nonstandard systems via linear transformation

practical stabilization of nonlinear uncertain dynamic systems with bounded controllers we address the problem of practically stabilizing nonlinear and or uncertain continuous time dynamic systems when the norm of the control input is subject to a given fixed bound we consider a class of systems whose nominal part is linear and whose nonlinear uncertain part does not satisfy the matching condition in this treatment no statistical information regarding the uncertainties is needed only a norm bound on each nonlinear uncertain quantity is assumed we propose a bounded state feedback controller whose design incorporates elements from both variable structure control theory and the deterministic control methodology using the second method of lyapunov we obtain sliding domains regions of uniform ultimate boundedness and estimates of the domain of attraction for systems employing this controller the closed loop stability analysis as well as the design of the controller is facilitated by introducing a special coordinate transformation the approach is illustrated by a numerical example

a state dependent boundary layer design for sliding mode control the use of a boundary layer in sliding mode control has been a common technique to reduce chattering of the control signal however different choices of the boundary layer width lead to conflicting effects a large small boundary layer width can more less effectively alleviate the chattering phenomenon but leads to less more accurate control results this note proposes online adjusting the width of the boundary layer based on the state norm for an uncertain linear system the proposed state dependent boundary layer design can effectively eliminate chattering while at the same time ensuring almost perfect control accuracy

robust tracking control of robots by a linear feedback law for the trajectory following problem of a robot manipulator a simple linear robust fedback control law with constant gain matrix is proposed that makes the resulting error system uniformly ultimately bounded this control law is very easy to implement by simply choosing a feedback gain according to the coefficients of a polynomial function of the tracking errors which is a bounding function for the terms in the lagrange euler formulation in the limit as the gain approaches infinity the error system becomes globally asymptotically stable

robust stabilization of a class of nonlinear time delay systems the problem of robust stabilization for a class of uncertain dynamic systems with multiple delayed state perturbations is considered it is assumed that perturbations of the time delayed sections are not bounded by first order linear functions but bounded by high order functions with unknown gains and the time delay considered is time varying two classes of controllers are proposed when the time derivative of each time varying time delay is less than 1 a class of adaptive state feedback controllers are proposed based on lyapunov krasovskii method which can render the closed loop systems uniformly ultimately bounded stable novel nonlinear feedback controllers are developed by employing razumikhin lemma and the controller also can render the closed loop systems stable in the sense of uniform ultimate boundedness finally several examples are given to show the potential of the proposed techniques

design of softer robust nonlinear control laws abstract we show that the lyapunov function used in backstepping feedback designs for uncertain nonlinear systems leads to unnecessarily hard control laws having undesirable high gain properties we present a new lyapunov function and use it to design softer control laws which exhibit the high gain properties to a much lesser extent we show that the soft designs eliminate the chattering exhibited by the hard designs and achieve the same or better performance with less control effort

sampled data controller design for uncertain systems presents a sampled data controller design methodology for uncertain systems a continuous system with bounded time varying uncertainty is sampled at intervals of length t the controller is designed using a riccati equation approach by neglecting o t sup 2 uncertainty terms in the discretized system stability is verified for this choice of t with the u t sup 2 terms included if there exists a stabilizing continuous controller then there also exists a stabilizing sampled data controller for a sufficiently small choice of t

a new class of stabilizing controllers for uncertain dynamical systems this paper is concerned with the problem of designing a stabilizing controller for a class of uncertain dynamical systems the vector of uncertain parameters q cdot is time varying and its values q t lie within a prespecified bounding set q in r p furthermore no statistical description of q cdot is assumed and the controller is shown to render the closed loop system practically stable in a so called guaranteed sense that is the desired stability properties are assured no matter what admissible uncertainty q cdot is realized within the perspective of previous research in this area this paper contains one salient feature the class of stabilizing controllers which we characterize is shown to include linear controllers when the nominal system happens to be linear and time invariant in contrast in much of the previous literature see for example 1 2 7 and 9 a linear system is stabilized via nonlinear control another feature of this paper is the fact that the

on the state observation and output feedback problems for nonlinear uncertain dynamic systems abstract in this paper we examine the problems of state observation and state trajectory control by output feedback for the class of non linear systems in 3 11 we begin by modifying a known discontinuous variable structure type observer into a continuous type observer that guarantees the observation error is globally exponentially stable ges we then modify a known discontinuous variable structure type output feedback controller into continuous type output feedback controller that forces the state to the origin in the ges sense specific time varying bounds on the observation error and the state trajectory are also developed revealing how the corresponding observer or control parameters can be adjusted to improve the system performance

uncertain systems and fuzzy differential equations the study of fuzzy differential equations is initiated and some typical results are given in order to understand the intricacies involved in incorporating fuzziness in the terms of differential equations

brief robust control of nonlinear systems with parametric uncertainty probabilistic robustness analysis and synthesis for nonlinear systems with uncertain parameters are presented monte carlo simulation is used to estimate the likelihood of system instability and violation of performance requirements subject to variations of the probabilistic system parameters stochastic robust control synthesis searches the controller design parameter space to minimize a cost that is a function of the probabilities that design criteria will not be satisfied the robust control design approach is illustrated by a simple nonlinear example a modified feedback linearization control is chosen as controller structure and the design parameters are searched by a genetic algorithm to achieve the tradeoff between stability and performance robustness

comparison theorems for monotone newton fourier iterations and applications in functional elimination abstract convergence is improved in the context of the monotone newton theorem if the starting points are chosen as close to the root as possible it follows that accurate partial functional elimination can be applied in order to accelerate the convergence of the newton and the newton fourier iterations

combined adaptive and variable structure control for constrained robots abstract this paper addresses the problem of controller design for constrained robots a control algorithm described as a combination of the direct adaptive and the variable structure method is presented for the trajectory tracking of an end effector on a constrained surface with specified constraint forces this scheme has certain advantages both with respect to computational efficiency and with respect to design with respect to computational efficiency the calculation of the regressor is avoided with respect to design since the number of parameter update laws required in the adaptation is independent of the number of links of the robot the difficulty of tuning numerous adaptation gains is avoided

adaptive robust stabilisation of uncertain nonlinear dynamical systems an improved backstepping approach abstractthe main purpose of this paper is to propose a design approach by which some simple adaptive robust controllers can be synthesised for a class of uncertain nonlinear dynamical systems which can be transformed into uncertain strict feedback nonlinear systems in this paper an improved backstepping design approach is presented to synthesising a class of continuous adaptive robust state feedback controllers with a rather simple structure the improved backstepping design approach can avoid the repeated differentiation problem which appears in using the conventional backstepping algorithm in particular it is not required to know the nonlinear upper bound functions of uncertainties in the light of the presented approach the state feedback controllers can be constructed to be linear in the state with the time varying control gains which can be self tuned by the adaptive laws similar to the conventional backstepping algorithm the improved backstepping approach can be extended to a rather large cl

robust static and dynamic output feedback stabilization deterministic and stochastic perspectives three parallel gaps in robust feedback control theory are examined sufficiency versus necessity deterministic versus stochastic uncertainty modeling and stability versus performance deterministic and stochastic output feedback control problems are considered with both static and dynamic controllers the static and dynamic robust stabilization problems involve deterministically modeled bounded but unknown measurable time varying parameter variations while the static and dynamic stochastic optimal control problems feature state control and measurement dependent white noise general sufficiency conditions for the deterministic problems are obtained using lyapunov s direct method while necessary conditions for the stochastic problems are derived as a consequence of minimizing a quadratic performance criterion the sufficiency tests are then applied to the necessary conditions to determine when solutions of the stochastic optimization problems also solve the deterministic robust stability problems as an additional application of the deterministic result the modified riccati equation approach of petersen and hollot is generalized in the static case and extended to dynamic compensation

on ultimate boundedness control of uncertain systems in the absence of matching assumptions this paper describes an approach to ultimate boundedness control under hypotheses less stringent than heretofore required instead of imposing the so called matching conditions of previous authors a certain decomposition of the dynamics is performed the resulting decomposed system has two parts a matched portion and a mismatched portion a certain measure of mismatch m is defined and it is shown that effective control is possible as long as m does not exceed some critical mismatch threshold m it is seen that this threshold depends on the choice of feedback hence it becomes possible to investigate the tradeoffs between the size of the mismatch threshold and the sizes of the feedback gains which achieve the desired ultimate boundedness of solutions

elimination and fixed point iterations abstract we show that under convenient hypotheses partial elimination in nonlinear systems can be used to improve convergence in the jacobi gauss seidel and newton iterations