a new recursive identification algorithm for singularity free adaptive control reportedly guaranteeing the controllability of the estimated system is a crucial problem in adaptive control in this paper we introduce a least squares based identification algorithm for stochastic siso systems which secures the uniform controllability of the estimated system and presents closed loop identification properties similar to those of the least squares algorithm the proposed algorithm is recursive and therefore easily implementable its use however is confined to cases in which the parameter uncertainly is highly structured

model selection and akaike s information criterion aic the general theory and its analytical extensions during the last fifteen years akaike s entropy based information criterion aic has had a fundamental impact in statistical model evaluation problems this paper studies the general theory of the aic procedure and provides its analytical extensions in two ways without violating akaike s main principles these extensions make aic asymptotically consistent and penalize overparameterization more stringently to pick only the simplest of the true models these selection criteria are called caic and caicf asymptotic properties of aic and its extensions are investigated and empirical performances of these criteria are studied in choosing the correct degree of a polynomial model in two different monte carlo experiments under different conditions

integral action in robust adaptive control conditions are studied under which integral action in robust adaptive control is soundly based the method of analysis amounts to verifying that the key conditions needed for convergence are satisfied a simple strategy is described for choosing the integral constant and global convergence is established for the resultant algorithm this illustrates a proof paradigm which could be similarly applied to other problems the principal assumptions used are that the plant when augmented by an integrator has a known degree of controllability and that an overbounding function is known for the unmodeled system response the continuous time case is treated but the corresponding discrete time results follow mutatis mutandis by simply replacing p d dt by delta q 1 delta l sub 2 by l sub 2 integral by sigma and so on

some integral inequalities for l operator and their applications on self shrinkers abstract in this paper we derive a reilly type inequality for the drifting laplacian operator l on a self shrinker of the mean curvature flow using this reilly type inequality we obtain some new poincare type inequalities not only on the self shrinker but more interestingly also on its boundary moreover we get some eigenvalue estimates for l operator on the compact self shrinker and its boundary and also make some global estimates on generalized mean curvature h on the boundary

a robust direct adaptive controller this paper proposes a new direct adaptive control algorithm which is robust with respect to additive and multiplicative plant unmodeled dynamics the algorithm is designed based on the reduced order plant which is assumed to be minimum phase and of known order and relative degree but is analyzed with respect to the overall plant which due to the unmodeled dynamics may be nonminimum phase and of unknown order and relative degree it is shown that if the unmodeled dynamics are sufficiently small in the low frequency range then the algorithm guarantees boundedness of all signals in the adaptive loop and small residual tracking errors for any bounded initial conditions in the absence of unmodeled dynamics the residual tracking error is shown to be zero

on robustified adaptive minimum variance controller an adaptive regulator of the minimum variance type in the presence of disturbance uncertainly is considered in the paper supposing a linear armax model of the single input single output system a robustified direct adaptive control algorithm is derived using the robust statistical approach named m estimation the derived algorithm differs from the conventional linear algorithms by the insertion of a suitably chosen nonlinear transformation of the prediction error which has to cut off the large noise realizations named outliers the global stability of the proposed control system and self optimizing property of the adaptive regulator is established theoretically using the martingale theory the feasibility of the approach is demonstrated with simulation

a robust indirect adaptive control approach this paper considers the robust design of an indirect adaptive control approach which is applicable when the unknown parameters of a linear time invariant plant lie in a known convex set throughout which no unstable pole zero cancellation occurs in order to achieve the robustness the use of a relative dead zone in the adaptive law is proposed it is shown that with a suitably designed relative dead zone the adaptive control system is globally stable even in the presence of small unmodeled plant uncertainties

on the necessity of identifying the true parameter in adaptive lq control in adaptive control problems one may drop the requirement of identifying the true system in order to simplify the problem of control it will be shown that in the adaptive lq control problem this does not at all lead to an easier problem

indirect adaptive control for interconnected systems an indirect adaptive controller for interconnected systems is introduced each subsystem is subject to bounded disturbances and to possibly unbounded interconnections with other subsystems a variable dead zone is incorporated into a gradient estimation scheme to limit the effects of the interconnections and disturbances an adaptive state feedback control law is described which stabilizes the interconnected system forcing the input and output signals of each subsystem to remain bounded

robust adaptive lq control schemes the certainty equivalence principle is used to combine a robust adaptive law with a control structure derived from the linear quadratic lq control problem the resulting adaptive control scheme is applicable to minimum and nonminimum phase continuous time plants and is robust with respect to unmodeled dynamics and bounded disturbances the computational complexity of the continuous time adaptive lq control scheme is improved by using a hybrid adaptive law which requires the solution of an algebraic riccati equation at each interval of time rather than at each time t

construction of complete embedded self similar surfaces under mean curvature flow part i we carry out the first main step towards the construc tion of new examples of complete embedded self similar surfaces under mean curvature flow an approximate solution is obtained by taking two known examples of self similar surfaces and desin gularizing the intersection circle using an appropriately modified singly periodic scherk surface called the core using an inverse function theorem we show that for small boundary conditions on the core there is an embedded surface close to the core that is a solution of the equation for self similar surfaces this provides us with an adequate central piece to substitute for the intersection

robustness of model reference adaptive controllers an input output approach a general input output approach is employed to study the direct model reference adaptive control problem in the presence of parametric and unstructured uncertainty a sufficient condition for the boundedness of the closed loop signals is developed relating an appropriately defined size of the unstructured uncertainty to the size of the parametric uncertainty this condition involves the intuitively appealing gains of various sensitivity operators and allows for the study of the effect of the design parameters on the boundedness properties of the closed loop system the results of this work indicate a direction towards a unified and systematic theory in adaptive control

a note on impact factor distribution revisited abstract motivated by huang 2017 we analyze impact factor data in all subject categories for each year from 2010 to 2015 the results are provided by subject categories and by years the two exponent distribution due to mansilla et al 2007 and the normal distribution are shown to give the best fits for the data sets the best fits are assessed in terms of probability plots quantile plots and five other criteria

bifurcation in model reference adaptive control systems abstract we study the effect of unmodeled dynamics on the performance of a simple model reference adaptive control mechanism exact stability boundaries are computed and different routes to chaotic behavior and global instability are described typically we observed a region of period doubling and hopf bifurcations similar to those observed in the ziegler nichols approach to pid control design the analysis applies to higher order and certain nonlinear systems as well

robust model reference adaptive control we propose a new model reference adaptive control algorithm and show that it provides the robust stability of the resulting closed loop adaptive control system with respect to unmodeled plant uncertainties the robustness is achieved by using a relative error signal in combination with a dead zone and a projection in the adaptive law the extra a priori information needed to design the adaptive law are bounds on the plant parameters and an exponential bound on the impulse response of the inverse plant transfer function

robust pole placement direct adaptive control a pole placement direct adaptive control for not necessarily minimum phase plants is presented which is robust with respect to unmodeled dynamics and bounded disturbances the robustness is achieved by using both a normalized least squares algorithm with dead zone and appropriate nonlinear feedback the resulting closed loop system is shown to be globally stable subject to standard assumptions

regression and time series model selection in small samples summary a bias correction to the akaike information criterion aic is derived for regression and autoregressive time series models the correction is of particular use when the sample size is small or when the number of fitted parameters is a moderate to large fraction of the sample size the corrected method called aicc is asymptotically efficient if the true model is infinite dimensional furthermore when the true model is of finite dimension aicc is found to provide better model order choices than any other asymptotically efficient method applications to nonstationary autoregressive and mixed autoregressive moving average time series models are also discussed

on adaptive state regulation an indirect adaptive state regulator consisting of an adaptive observer and an asymptotic feedback matrix synthesis is discussed in a rigorous analysis lyapunov stability of the resulting closed loop system without the need for external excitation possible global instabilities as well as global convergence subject to sufficient excitation are shown moreover the behavior of the closed loop system is analyzed for cases in which the true plant differs from the assumed linear time invariant model in that it is of higher order contains slight nonlinearities and time variation effects and is subject to plant and measurement disturbances

uniqueness of self similar shrinkers with asymptotically conical ends in this paper we show the uniqueness of smooth embedded selfshrinkers asymptotic to generalized cylinders of infinite order also we construct non rotationally symmetric self shrinking ends asymptotic to generalized cylinders with rate as fast as any given polynomial

stability analysis of input constrained continuous time indirect adaptive control abstract stability analysis of continuous time indirect pole placement adaptive control with input constraint is presented in this paper it is shown that the closed loop system for a class of stable type 1 plants is globally stable in the sense that all the signals in the loop remain bounded and that certain degree of robustness with respect to modelling uncertainties and disturbances can be achieved by implementing a simple fixed dead zone in the parameter estimator it is also shown that if the plant is free from modelling uncertainties and disturbances and the control input is not saturated for a finite period of time then the closed loop system will asymptotically be characterized by the desired closed loop poles within this time period

unified treatment of internal model principle based adaptive control algorithms a number of adaptive control algorithms are summarized here for the control of unknown linear discrete time plants with unknown deterministic disturbances adaptive implementation of the internal model principle is used for asymptotical cancellation of the deterministic disturbances the use of the certainty equivalence principle for implementation of these algorithms can be shown to result in a certain type of unmodelled dynamics error for each of these algorithms a unified analysis of these algorithms is given under a common framework of unmodelled dynamics with suitable modification of the parameter estimation algorithm the global convergence and stability of these algorithms are established without the requirement of the persistency of excitation condition some simulation results are provided for support of the analysis

pole placement direct adaptive control for time varying ill modeled plants the problem is discussed of preserving the stability of pole placement direct adaptive control in spite of output bounded disturbances time varying plant model parameters and unmodeled dynamics assumed to be small in the mean the controller parameter estimates are shown to track in the mean their true time varying parameter values such a convergence property is achieved using an ad hoc internally generated excitation sequence that ensures persistent excitation in the ideal case the convergence of the parameter estimates is exponential avoiding in particular possible chaotic phenomena

adaptive robust control for siso systems abstract this paper addresses the problem of nonconservative adaptive robust regulating a siso system allowing for model perturbations in the coprime factor representation of the system as well as external additive bounded disturbance signals the perturbations and disturbances are assumed to belong to a particular parameterized class and are norm bounded the norm bounds are not available for control design but the class knowledge is available the performance measure is the worst possible steady state absolute value of the controlled output over the class of allowable disturbances and model perturbations an identification based adaptive control method is proposed where the identification criterion coincides with the control objective the proposed adaptive scheme achieves near optimal performance simulations comparing the new scheme with an adaptive controller based on classical recursive least squares identification are presented

robust adaptive regulation without persistent excitation a globally convergent adaptive regulator for minimum or nonminimum phase systems subject to bounded disturbances is presented the control strategy is designed for a particular input output representation obtained from the state space representation of the system the leading coefficient of the novel representation is the product of the observability and controllability matrices of the system the controller scheme uses a least squares identification algorithm with a dead zone the dead zone is chosen to obtain convergence properties on the estimates and on the covariance matrix as well this allows the definition of modified estimates which secure well conditioned matrices in the adaptive control law explicit bounds on the plant output are given

on globally stable adaptive control providing l 1 tracking performance for linear discrete time systems abstractexisting adaptive control algorithms at best guarantee that the tracking error is a l2 sequence this paper presents globally stable adaptive control algorithms for linear discrete time systems providing l1 tracking performance two algorithms with different degree of complexity are proposed one for the case of known control directions and a separate algorithm for the case of unknown control directions it is demonstrated that in both cases the tracking error is l1 sequence while the input and output signals are uniformly bounded

design issues in adaptive control an integrated approach to the design of practical adaptive control algorithms is presented many existing ideas are brought together and the effect of various design parameters available to a user is explored the theory is extended by showing how the problem of stabilizability of the estimated model can be overcome by running parallel estimators it is shown how asymptotic tracking of deterministic set points can be achieved in the presence of unmodeled dynamics

robustness of discrete time adaptive controllers an input output approach a general input output approach that can be used for the design and analysis of robust discrete time adaptive control schemes is presented in particular a model reference adaptive controller is considered the design approach involves the use of the certainty equivalence principle to combine a robust control structure with a robust adaptive law using exponentially weighted i sub 2 norms and exploiting the properties of the adaptive law and the control structure robust stability is established for the closed loop adaptive control scheme

theory and design of robust direct and indirect adaptive control schemes a general approach for designing and the theory for analysing robust direct and indirect adaptive control schemes for continuous time plants is presented the design approach involves the development of a general robust adaptive law and the use of the certainty equivalence principle to combine it with robust model reference and pole placement control structures the global stability properties and robustness of the developed adaptive control schemes are established by using a general theory which relates the properties of signals in the mean sense over intervals of time the developed theory and design approach are used to analyse and compare the robustness properties and performance of a wide class of robust adaptive laws which employ a dead zone fixed e1 and a switching modification as well as their variations

adaptive pole placement without excitation probing signals this paper presents an indirect adaptive control scheme for linear systems which may possibly be a nonminimum phase the control scheme achieves asymptotical pole placement without either introducing persistent excitation probing signals into the systems or assuming any a priori knowledge on the plant parameters the system order is the only a priori knowledge required on the plant the adaptive control law is free from singularities in the sense that the estimated plant model is always controllable the singularities are overcome by a suitable parameter estimates modification which is based upon standard least squares covariance matrix properties the analysis of the stability and the global convergence of a closed loop system is given in detail for both discrete time and continuous time systems

stable model reference adaptive control in the presence of bounded disturbances the adaptive control of a linear time invariant plant in the presence of bounded disturbances is considered in addition to the usual assumptions made regarding the plant transfer function it is also assumed that the high frequency gain k p of the plant and an upper bound on the magnitude of the controller parameters are known under these conditions the adaptive controller suggested assures the boundedness of all signals in the overall system

global stability proofs for continuous time indirect adaptive control schemes this note presents a general stability proof for continuous time adaptive control with very general assumptions on the identifier and controller we show that if the exogenous input signal is rich enough then both the identifier and the controller converge to their true values applications of the proof to pole placement design and design based on the factorization approach are discussed

robust adaptive control of discrete time systems using persistent excitation abstract an important result in the robust adaptive control of continuous time systems using the persistent excitation of the reference input was recently given by narendra and annaswamy 1986 ieee trans aut control ac 31 306 315 according to this result the global boundedness of all the signals in the adaptive system can be assured if the degree of persistent excitation of the reference input is larger than an appropriate bound on the external disturbance the main theorem in narendra and annaswamy 1986 is proved for a class of plants characterized by the property that the reference model used in the adaptive controller could be chosen to be strictly positive real a condition which involves constraints on the relative degree of the plant this paper presents a generalization of the above result to plants of arbitrary relative degree together with the work reported in the earlier paper it demonstrates that the boundedness of all the signals in an adaptive system in the presence of bounded disturbances and arbitrary initial conditions can be assured by increasing the degree of persistent excitation of the reference input

a generalized lqg approach to self tuning control part i aspects of design implicit self tuners based on single stage cost function minimization schemes require exact knowledge of the dead time of the controlled plant explicit pole placement self tuners on the other hand though robust against variations of the time delay are very sensitive to the assumptions made about the model order of the plant wrong assumptions may result in very poor performance an explicit method based on minimization of a multistage cost function and a carima plant model formulated in state space is presented the method extends the design features of the generalized minimum variance scheme to the multistage case these can be used to tailor the closed loop response of the system the approach is shown to be robust against wrong a priori assumptions made about the plant dead time or order thus maintaining good servo and disturbance rejection properties see part ii