stable inversion of continuous time nonlinear systems by finite difference methods introduces finite difference methods for stable inversion of continuous time nonlinear systems a relationship between the new finite difference methods and the existing picard methods is established a damped newton finite difference method is shown to possess superior convergence properties and its effectiveness is illustrated with an inverted pendulum example

stable inversion of abel equations stable inversion plays a key role in the solution of the exact tracking control problem in nonminimum phase systems however the general methods developed so far for the computation of stable inverses require backwards time numeric integration of the internal dynamics equation which yields high sensitivity to external disturbances and or structured uncertainties this article introduces an iterative technique that provides periodic closed form analytic expressions uniformly convergent to the exact periodic solution of a certain class of abel ode written in the normal form the method is then applied to the output voltage tracking of periodic references in dc dc boost power converters through a state feedback indirect control scheme the procedure lies on a number of assumptions for which sufficient conditions involving system parameters and reference candidates are derived it also allows one to attenuate the effect of bounded piecewise constant load disturbances using dynamic compensation simulation results validate the proposed algorithm

a new approach to inversion based feedforward control design for nonlinear systems the finite time transition between stationary setpoints of nonlinear siso systems is considered as a scenario for the presentation of a new design approach for inversion based feedforward control design techniques which are based on a stable system inversion result in input trajectories with pre and or post actuation intervals the presented approach treats the considered transition task as a two point boundary value problem bvp and yields causal feedforward trajectories which are constant outside the transition interval the main idea of this approach is to provide free parameters in the desired output trajectory to solve the bvp of the internal dynamics thereby a standard matlab function can be used for the numerical solution of the bvp feedforward control design techniques are illustrated by simulation results for a simple example

approximated stable inversion for nonlinear systems with nonhyperbolic internal dynamics a technique to achieve output tracking for nonminimum phase nonlinear systems with nonhyperbolic internal dynamics is presented the present paper integrates stable inversion techniques that achieve exact tracking with approximation techniques that modify the internal dynamics to circumvent the nonhyperbolicity of the internal dynamics this nonhyperbolicity is an obstruction to applying presently available stable inversion techniques the theory is developed for nonlinear systems and the method is applied to a two cart with inverted pendulum example

tracking nonlinear non minimum phase systems using sliding control nonlinear systems affine in the input and having a well defined vector relative degree are considered the invertibility of the input output dynamics can be used to achieve tracking of smooth desired trajectories if the associated zero dynamics are stable we consider tracking in nonlinear systems with unacceptable zero dynamics i e non minimum phase systems the desired trajectories are assumed to be generated by some exosystem we use sliding control to achieve tracking independent of disturbances entering in the channels of the input the main idea is i to do an output redefinition such that the zero dynamics with respect to this new output are acceptable ii to define a modified desired trajectory for the new output to track such that in the process the original output tracks the original desired trajectory asymptotically

brief mixed internal model based and feedforward control for robust tracking in nonlinear systems the purpose of this paper is to compare different features of two approaches to the problem of tracking prescribed trajectories in a nonlinear system and to propose a possible merger of these approaches in what is called here the problem of asymptotically robust perfect tracking the latter is the problem of designing a feedforward error feedback control law achieving perfect tracking in case the initial conditions of the system exosystem are known and compatible with perfect tracking and asymptotic tracking in all other cases

brief paper swing up of the double pendulum on a cart by feedforward and feedback control with experimental validation the swing up maneuver of the double pendulum on a cart serves to demonstrate a new approach of inversion based feedforward control design introduced recently the concept treats the transition task as a nonlinear two point boundary value problem of the internal dynamics by providing free parameters in the desired output trajectory for the cart position a feedback control is designed with linear methods to stabilize the swing up maneuver the emphasis of the paper is on the experimental realization of the double pendulum swing up which reveals the accuracy of the feedforward feedback control scheme

dynamic inversion for multivariable non affine in control systems via time scale separation this paper presents a tracking design methodology applicable to multivariable non affine in control systems the main focus is on solving the tracking problem for non linear systems whose dynamics depend non linearly on the control input the latter is designed to be faster than the main system dynamics using singular perturbation theory along with the lyapunov stability theorems it is shown that the proposed controller approximates an unknown dynamic inversion based solution with bounded errors provides closed loop stability and solves the tracking problem with bounded errors simulations illustrate the theoretical results

brief paper on the equivalence between stable inversion for nonminimum phase systems and reciprocal transfer functions defined by the two sided laplace transform in this paper the two sided laplace transform a classical but not very common mathematical tool is revived to express the stable inversion for linear nonminimum phase systems that was recently proposed from the viewpoint of state space representations it is demonstrated that those two different expressions for the stable inversion are mathematically equivalent simple examples are presented to illustrate the two sided laplace transform as a direct and intuitive approach to stable inversion the two sided laplace transform approach is also applied to the development of an iterative learning control for nonminimum phase systems that needs neither a precise inversion model nor fourier transform computations but instead requires only measuring the system response with time reversals

hosm observer for a class of non minimum phase causal nonlinear mimo systems a higher order sliding mode observer is proposed for asymptotic identification of the full state vector and the vector of unknown inputs for mimo nonlinear causal systems with unstable internal dynamics the problem is addressed via consistent application of exact higher order sliding mode differentiators in conjunction with the method of stable system center a numerical example illustrates the performance of the proposed algorithm

brief paper inversion of sampled data system approximates the continuous time counterpart in a noncausal framework although correspondence between the poles of a continuous time and sampled data system with a piecewise constant input is simple and desirable from the stability viewpoint the relationship between zeros is intricate inversion of a sampled data system is mostly unstable irrespective of the stability of the continuous time counterpart this makes it difficult to apply inversion based control techniques such as perfect tracking transient response shaping or iterative learning control to sampled data systems although recently developed noncausal inversion techniques help us to circumvent unboundedness of the inversion caused by unstable zeros whether the inversion of sampled data systems approximates the continuous time counterpart or not as the sample period is shortened is still to be determined this article gives a positive conclusion to this problem

stable inversion and parameter variations abstract as part of the process of automatically guiding an aircraft we have been successful in using stable inversion to compute a desired bounded state trajectory and corresponding bounded control in addition to this feedforward control we must also construct a regulator to address modeling errors and disturbances with respect to modeling errors we find that the stable inversion procedures used are so accurate that the regulator can assume a simple form say a linear regulator about the desired trajectory we show that under the appropriate assumptions the bounded state trajectory and bounded control computed through stable inversion depend continuously on the parameters of the system this is a consequence of a mathematical result that we prove about the continuous dependence of the particular solution of a time varying nonlinear system driven by a bounded input this is distinct from the usual continuous dependence of the initial value problem for systems

h2 optimal rejection with preview in the continuous time domain the synthesis of a feedforward unit for h 2 optimal rejection of previewed signals in continuous time invariant linear systems is considered the h 2 optimal compensator herein devised consists of a finite impulse response system working in connection with a standard dynamic unit the design strategy is based on a simple interpretation of the h 2 optimal rejection problem with preview as a compound optimal control problem i e as a problem consisting of a finite horizon lq control problem with constrained final state an infinite horizon lq control problem and the problem of minimizing the global cost functional an explicit description of the compensator is derived by exploiting some results on the parameterization of the solutions of the associated autonomous hamiltonian system

invertibility of switched nonlinear systems this article addresses the invertibility problem for switched nonlinear systems affine in controls the problem is concerned with reconstructing the input and switching signal uniquely from given output and initial state we extend the concept of switch singular pairs introduced recently to nonlinear systems and develop a formula for checking if the given state and output form a switch singular pair a necessary and sufficient condition for the invertibility of switched nonlinear systems is given which requires the invertibility of individual subsystems and the nonexistence of switch singular pairs when all the subsystems are invertible we present an algorithm for finding switching signals and inputs that generate a given output in a finite interval when there is a finite number of such switching signals and inputs detailed examples are included to illustrate these newly developed concepts

stable inversion of lptv systems with application in position dependent and non equidistantly sampled systems abstractmany control applications including feedforward and learning control involve the inverse of a dynamical system for nonminimum phase systems the response of the inverse system is unbounded for linear time invariant lti nonminimum phase systems a bounded noncausal inverse response can be obtained through an exponential dichotomy for general linear time varying ltv systems such a dichotomy does not exist in general the aim of this paper is to develop an inversion approach for an important class of ltv systems namely linear periodically time varying lptv systems which occur in e g position dependent systems with periodic tasks and non equidistantly sampled systems the proposed methodology exploits the periodicity to determine a bounded inverse for general lptv systems conditions for existence are provided the method is successfully demonstrated in several application cases including position dependent and non equidistantly sampled systems

a general framework for approximated model stable inversion abstract in this paper we propose an approximated method for the design of feedforward actions based on model stable inversion in the proposed framework the solution of the model stable inversion is approximated in the least squares sense by a suitable combination of any arbitrary set of basis functions the paper makes use of operator theory to derive a closed form formula to compute such approximation and to provide boundedness properties for the computed solution simulations are provided to show the effectiveness of the proposed method with different families of basis functions

on a nonlinear multivariable servomechanism problem abstract multivariable nonlinear plants with both measured and unmeasured vector disturbance signals are considered output feedback dynamic control laws are designed for the problem of tracking a constant or slowly varying reference input while rejecting constant or slowly varying disturbances

iterative control for networked heterogeneous multi agent systems with uncertainties this note addresses the convergence of iterative control for networked heterogeneous multi agent systems where each agent has potentially different dynamics and dissimilar uncertainties the major contribution of this work is to quantify the acceptable modeling uncertainty for ensuring convergence of the proposed iterative approach for collaborative tracking convergence conditions are established for the case when inversion based iterative control of each individual agent designed separately independent of the iterative controllers of the other agents are conjoined using a network graph structure

frequency domain computations for nonlinear steady state solutions steady state analysis and fourier analysis play a major role in linear signal processing in response to a bounded input a steady state solution exists if all the poles of the discrete time linear system are inside the unit circle despite the fact that there is no principle of superposition for nonlinear systems under appropriate sufficient conditions including all poles inside the unit circle for the linear part of the nonlinear system there is a bounded solution for all time in response to a bounded input for all time for a time varying nonlinear difference equation all solutions that start sufficiently close to this unique solution converge to it as time goes to infinity this steady state solution can be computed by applying fourier and inverse fourier transforms to each step in a picard process in this paper we develop an algorithm to compute approximate steady state solutions for discrete time nonlinear difference equations by employing fast fourier transforms and inverse fast fourier transforms at each step of the iterative process simulations are provided to illustrate our algorithm

the fermi golden rule and its form at thresholds in odd dimensions let h be a schrodinger operator on a hilbert space open image in new window such that zero is a nondegenerate threshold eigenvalue of h with eigenfunction 0 let w be a bounded selfadjoint operator satisfying 0 w 0 0 assume that the resolvent h z 1 has an asymptotic expansion around z 0 of the form typical for schrodinger operators on odd dimensional spaces let h h w for 0 and small we show under some additional assumptions that the eigenvalue at zero becomes a resonance for h in the time dependent sense introduced by a orth no analytic continuation is needed we show that the imaginary part of the resonance has a dependence on of the form 2 2 with the integer 1 and odd this shows how the fermi golden rule has to be modified in the case of perturbation of a threshold eigenvalue we give a number of explicit examples where we compute the location of the resonance to leading order in we also give results in the case where the eigenvalue is embedded in the continuum sharpening the existing ones

stable inversion for nonlinear nonminimum phase time varying systems we extend stable inversion to nonlinear time varying systems and study computational issues the technique is applicable to minimum phase as well as nonminimum phase systems the inversion technique is new even in the linear time varying case and relies on partitioning the dichotomic split of the linearized system dynamics into time varying stable and unstable submanifolds this dichotomic split is used to build time varying filters which are in turn the basis of a contraction used to find a bounded inverse input state trajectory finding the inverse input state trajectory allows the development of exact output tracking controllers the method is local to the time varying trajectory and requires that the internal dynamics vary slowly however the method represents a significant advance relative to presently available tracking controllers present techniques are restricted to time invariant nonlinear systems and in the general case track only asymptotically

generalized likelihood adaptive detection of signals deformed by unknown linear filtering in noise with slowly fluctuating power the adaptive detection of signals deformed by unknown linear filtering in noise with slowly fluctuating power is considered a generalized likelihood ratio test is derived this test leads to two agc receivers having the same detection performance the first receiver is comprised of a classical agc that cannot distinguish signal from noise and limits the amplitudes of strong signals the other receiver incorporates a noise alone reference nar agc which is insensitive to strong signals and guarantees a better contrast and more reliable amplitude classification the output contrasts of the two receivers and of a third hypothetical perfect measurement likelihood ratio receiver are compared by means of computer simulations for different signal waveforms and different impulse responses of the linear filter deforming the signal these simulations show that the performance of the second receiver is quite near to the ultimate performance achieved only theoretically by the third receiver moreover unlike the quasi nar agc receiver with the generalized matched and antimatched filters which was defined in a previous paper the nar property of the second receiver is not established at the expense of an increased false alarm probability

inversion of nonlinear time varying systems a procedure for inverting nonlinear systems that presents some computational advantages when applied to flexible robot arms or more generally to mechanical structures is given the procedure is presented in a general setting for nonlinear time varying systems an iterative algorithm that computes a smooth controlled invariant time varying manifold the mathematical properties of which are illustrated and exploited is also proposed an application to a flexible two link manipulator illustrates the algorithm and its computational advantages

nar estimators of spatial covariance matrices for adaptive array detection the theory of noise alone reference nar power estimation is extended to the estimation of spatial covariance matrices a nar covariance estimator insensitive to signal presence is derived the snr signal to noise ratio loss incurred by using this estimator is independent of the input snr and is less than that encountered with the maximum likelihood covariance estimator given that the same number of uncorrelated snapshots is available to both estimators the analysis assumes first a deterministic signal the results are extended and generalized to signals with unknown parameters or random signals for the random signal case generalized and quasi nar covariance estimators are presented

stable inversion for nonlinear systems abstract there have been two recent major developments in output tracking for nonlinear systems and our first main contribution is to relate these under appropriate assumptions we show that the bounded solution of the partial differential equation of isidori and byrnes for each trajectory of an exosystem must be given by an integral representation formula of devasia chen and paden under restrictive hypotheses devasia chen and paden develop a picard process that converges to the solution of the integral equation this solution to the integral equation is also a bounded solution to a dynamical equation driven by the desired outputs in aircraft applications our nonlinear systems are perturbations of pure feedback systems with outputs and we find a solution to the stable inversion problem i e finding bounded controls and bounded state trajectories in response to bounded output signals in two steps the first step ignores the perturbation error and computes the major part of the desired control and corresponding state trajectory the second step computes the remaining control and states by finding a noncausal and stable solution to an error driven dynamical equation in other words the method of devasia chen and paden is applied to an error system and not to the full system this two step procedure is the second main contribution of this paper throughout this paper it is assumed that our nonlinear systems have vector relative degree

switching through singularities asymptotic tracking is studied for systems which are not regular that is the relative degree is not well defined for these systems the input output linearizing control law has singularities we propose a tracking control law which switches between an approximate tracking law hauser et al ieee trans automat control 37 3 1992 392 398 close to the singularities and an exact tracking law away from the singularities and we study the applicability of this law based on the behavior of the system s zero dynamics at the switching boundary as in hauser et al ieee trans automat control 37 3 1992 392 398 the ball and beam example is used to motivate the study

adaptive dynamic inversion via time scale separation this paper presents a full state feedback adaptive dynamic inversion method for uncertain systems that depend nonlinearly upon the control input using a specialized set of basis functions that respect the monotonic property of the system nonlinearities with respect to control input a state predictor is defined for derivation of the adaptive laws the adaptive dynamic inversion controller is defined as a solution of a fast dynamical equation which achieves time scale separation between the state predictor and the controller dynamics lyapunov based adaptive laws ensure that the predictor tracks the state of the nonlinear system with bounded errors as a result the system state tracks the desired reference model with bounded errors benefits of the proposed design method are demonstrated using van der pol dynamics with nonlinear control input

non causal fliess operators and their shuffle algebra fliess operators as a class of non linear operators have been well studied in several respects they have a well developed realization theory and convenient representations in terms of directed infinite products of exponential lie series their interconnection as subsystems has been studied as has their relationship to rational systems they find applications in such diverse areas as discretization methods for controls systems optimal control neural network analysis and the numerical solution of stochastic differential equations one issue concerning fliess operators however that has received little attention is their possible generalization to the non causal case examples of such operators appear implicitly in the literature addressing hilbert adjoints of causal non linear operators and system inversion for the purpose of output tracking but a general systematic treatment of the subject has not appeared in this paper a non causal extension of a fliess operator is developed with the primary focus being on local convergence continuity the associated shuffle algebra and computing adjoint operators

output regulation of non linear systems with more inputs than outputs abstract the necessary and sufficient conditions for the existence of a solution of the non linear regulator problem given by isidori and byrnes 1990 for square systems are extended to the case of systems with more inputs than outputs some examples that stress specific aspects of the solution of the nonlinear regulator problem are given

guaranteed performance in semi global trajectory tracking for matched disturbance nonlinear systems in this article we present a semi global trajectory tracking approach that guarantees a priori computable l 2 and l performance bounds for matched disturbance control affine systems the proposed controller is derived by combining a standard inverse control technique with an extended nonlinear robust state feedback the latter is based on a control lyapunov function used for stabilising one operating point inside the considered state space a difference gradient formulation of this lyapunov function is then applied to prove stabilisation along any trajectory in the considered state space results for l 2 and l bounded disturbances will be presented and further extended to the case of actuator uncertainties and disturbance offsets the theoretical contributions are verified applying them to a numerical example

nonlinear inversion based output tracking an inversion procedure is introduced for nonlinear systems which constructs a bounded input trajectory in the preimage of a desired output trajectory in the case of minimum phase systems the trajectory produced agrees with that generated by hirschorn s inverse dynamic system however the preimage trajectory is noncausal rather than unstable in the nonminimum phase case in addition the analysis leads to a simple geometric connection between the unstable manifold of the system zero dynamics and noncausality in the nonminimum phase case with the addition of stabilizing feedback to the preimage trajectory asymptotically exact output tracking is achieved tracking is demonstrated with a numerical example and compared to the well known byrnes isidori regulator rather than solving a partial differential equation to construct a regulator the inverse is calculated using a picard like interaction when preactuation is not possible noncausal inverse trajectories can be truncated resulting in the tracking error transients found in other control schemes

h _ infty tracking control of completely unknown continuous time systems via off policy reinforcement learning this paper deals with the design of an h infty tracking controller for nonlinear continuous time systems with completely unknown dynamics a general bounded l 2 gain tracking problem with a discounted performance function is introduced for the h infty tracking a tracking hamilton jacobi isaac hji equation is then developed that gives a nash equilibrium solution to the associated min max optimization problem a rigorous analysis of bounded l 2 gain and stability of the control solution obtained by solving the tracking hji equation is provided an upper bound is found for the discount factor to assure local asymptotic stability of the tracking error dynamics an off policy reinforcement learning algorithm is used to learn the solution to the tracking hji equation online without requiring any knowledge of the system dynamics convergence of the proposed algorithm to the solution to the tracking hji equation is shown simulation examples are provided to verify the effectiveness of the proposed method

convolution profiles for right inversion of multivariable non minimum phase discrete time systems the problem of the non causal inversion of linear multivariable discrete time systems is analyzed in the geometric approach framework and is solved through the computation of convolution profiles which guarantee perfect tracking under the assumption of infinite length preaction and postaction time intervals it is shown how the shape of the convolution profiles is related to both the relative degree and the invariant zeros of the plant a computational setting for the convolution profiles is derived by means of the standard geometric approach tools feasibility constraints are also taken into account a possible implementation scheme based on a finite impulse response system acting on a stabilized control loop is provided

brief parameter variations relative degree and stable inversion motivated by our prior research on automatic aircraft guidance we address stable inversion for output tracking and prove that this process is continuous with respect to parameter variations even when these variations cause a change in relative degree our earlier simulations indicated that the stable inversion process is extremely accurate and that only a linear regulator about the desired trajectory is required in the face of reasonable modeling error the principal novelty in our technique is that a differential equations point of view is taken as opposed to a state space approach on the driven zero dynamics of the system this is the situation that arises in many applications and it also enables handling the question of changes in relative degree without having to be encumbered by the change in state space dimension as the parameters change linear systems are first studied since the corresponding result is unknown next a corresponding theorem for nonlinear systems proved by using the picard process in conjunction with the result for the linear case the principal contribution of this paper is a result concerning the continuous dependence of a generalized steady state solution of nonlinear driven differential equations with respect to parameter variations which cause the order of the differential equation to change since the notion of steady state is of paramount importance to innumerable engineering situations the contents of this paper have wider scope

a novel approach to control of nonminimum phase nonlinear systems we present an approach to control of nonminimum phase multiple input multiple output mimo nonlinear systems based on a singular perturbation like technique first we show that a mimo nonlinear system can be converted into a singularly perturbed system through magnitude and time scaling transformation in particular the proposed transformation technique can make the hidden or internal dynamics behave like a fast subsystem however the fast subsystem takes a weakly controllable form which implies that a small positive low gain parameter multiplies the control input in the fast subsystem for this reason the well known integral manifold approach is then utilized to decompose the resulting singularly perturbed system into two subsystems in separate timescales each of which is of a lower dimension and more importantly controllable in the sense that the control input will explicitly appear in the boundary layer system the proposed method is particularly useful to make the input output dynamic characteristics of a decouplable nonminimum phase nonlinear system decoupled and linear

constrained reachability and trajectory generation for flat systems we consider the problem of trajectory generation for constrained differentially flat systems based on the topological properties of the set of admissible steady state values of a flat output we derive conditions which allow for an a priori verification of the feasibility of constrained set point changes we propose to utilize this relation to generate feasible reference trajectories to this end we suggest to split the trajectory generation problem into two stages a the planning of geometric reference paths in the flat output space combined with b an assignment of a dynamic reference motion to these paths this assignment is based on a reduced optimal control problem the unique feature of the approach is that due to the specific construction of the reference paths the optimal control problem to be solved is guaranteed to be feasible to illustrate our results we consider a van de vusse reactor as an example

optimal output transitions for linear systems this article addresses the optimal minimum input energy output transition problem for linear systems the goal is to transfer the output from an initial value y t email protected for all time t t f previous methods solve this output transition problem by transforming it into a state transition problem the initial and final states x t i x t f respectively are chosen and a minimum energy state to state transition problem is solved however the choice of the initial and final states can be ad hoc and the resulting output transition cost input energy may not be minimal the contribution of this article is the solution of the optimal output transition problem an example system with elastic dynamics is studied to illustrate the proposed method simulation results are presented that show substantial reduction of transition costs with the use of the proposed method when compared to the use of minimum energy state to state transitions

optimal inversion based control for the set point regulation of nonminimum phase uncertain scalar systems we propose an optimal inversion based control for the set point constrained regulation of nonminimum phase uncertain scalar systems this approach is based on a new control architecture where the main purpose of the feedback is to reduce the sensitivity to parametric plant uncertainties permitting in such a way the effective use of a feedforward action determined via a stable dynamic inversion essential constituents of the architecture are a parameterized family of transition polynomials to shape ideal output transfers and a parameterized controller ensuring the internal model principle the methodology is then centered on the optimal combined design of the feedback controller and of the inversion based command signal in order to minimize the worst case settling time subject to an amplitude constraint on the control variable and to arbitrarily assigned overshoot and undershoot bounds finally an approximate or suboptimal solution to the resulting nonlinear optimization problem can be obtained by genetic algorithms a worked example highlights the effectiveness of the overall methodology

a behavioral approach to inversion based control abstract a new simplified behavior theory is proposed to address inversion based control for linear nonminimum phase siso systems the chosen space of signals is the set of piecewise c functions and input output pairs as weak solutions satisfy a differential integral equation with additional smoothness requirements a related key result is the output input or inverse representation of the behavior set that leads to the solution of a general stable inversion problem where polynomially unbounded noncausal desired outputs are allowed it is shown that this problem has a solution if and only if the smoothness degree of the desired output is greater than or equal to the system relative degree minus one when this straightforward condition is satisfied a closed form expression provides the inverse input then an analysis on preaction and postaction control follows two examples are included showing the relevance of output signal design in control applications

driven dynamics of time varying linear systems motivated by applications to automatic control of aircraft we consider the problem of output tracking for time varying linear systems the signals to be tracked are bounded on spl infin spl infin and our goal is to compute bounded controls and bounded state trajectories that result in the desired tracking a convolution integral representation for the desired solution is given in the literature and we show that certain integrability assumptions can be eliminated from the associated results despite the fact that our system is time varying and our signals do not necessarily have fourier transforms in the classical sense we show that computations can be carried out using generalized fourier transforms we also consider an output tracking problem in which the driven dynamical equation is an ordinary differential equation

brief optimal noncausal set point regulation of scalar systems this paper presents a novel system inversion approach to the set point regulation of linear scalar minimum phase systems this approach uses closed form expressions of cause effect pairs that make possible an arbitrarily smooth transition between two given output set points the cause effect pairs are based on the introduced concept of transition polynomials simple optimization procedures are then proposed to solve the relevant optimal output synthesis and optimal input synthesis the potentiality of the method is highlighted by the examples presented namely a synthesis of elevator velocity profiles and the performance improving of a pid controller

using stable input output inversion for minimum time feedforward constrained regulation of scalar systems the paper approaches the feedforward minimum time smooth control of non minimum phase linear scalar systems for set point regulation the aim is to synthesize a bounded input subject to non saturating constraints on the input and its derivatives till a prespecified arbitrary order the provided solution relies on a stable input output dynamic inversion technique and an ad hoc parameterized family of output transition functions the synthesized minimum time input that exhibits pre and post actuation is determined by means of easily implementable closed form expressions examples are given to illustrate the methodology

asymptotic state tracking in a class of nonlinear systems via learning based inversion describes a learning approach to asymptotic state tracking in a class of nonlinear systems the tracking problem considered concerns the case when the tracking error dynamics are described by a set of time varying nonlinear differential equations which are periodic in time with a known period our iterative update scheme is based on the specific property that the learning system tends to oscillate in steady state in fact our approach extends in a very natural manner the idea of the well known iterative learning control for the case of finite time tracking problems to the case of infinite time asymptotic tracking problems the best advantage of the proposed leaning approach is that it is computationally simple and does not require one to solve any complicated equations based on full system dynamics we explore the conditions under which a periodic nonlinear system exhibits a steady state oscillation our work also can be viewed to provide a learning based solution to the input state inversion problem the generality and practicality of our work is demonstrated through rigorous performance analysis and simulation using a robot manipulator

a pseudoinverse based iterative learning control learning control is a very effective approach for tracking control in processes occurring repetitively over a fixed interval of time in this paper an iterative learning control ilc algorithm is proposed to accommodate a general class of nonlinear nonminimum phase plants with disturbances and initialization errors the algorithm requires the computation of an approximate inverse of the linearized plant rather than the exact inverse an advantage of this approach is that the output of the plant need not be differentiated a bound on the asymptotic trajectory error is exhibited via a concise proof and is shown to grow continuously with a bound on the disturbances the structure of the controller is such that the low frequency components of the trajectory converge faster than the high frequency components

approximation of trajectories of non linear systems by iterates of systems with linear state dynamics abstract a modification of an iterative picard process is proposed to approximate the output of a non linear system by a concatenation of systems with linear state dynamics and non linear outputs a local uniform convergence result is given the motivating example is a non linear system that arises in surface plasmon resonance experiments to determine protein protein interaction constants we show with simulations that for this example the approximants converge not only locally but over the full time interval of interest in the application

nonlinear tracking control of vibration amplitude for a parametrically excited microcantilever beam abstract in this paper a feedback control algorithm to regulate oscillation amplitude of a microelectromechanical mems cantilever beam operated at parametric resonances is developed the control objective is to drive the oscillation amplitude of the micro beam which is amplified using parametric excitation to the desired values the principle of the control algorithm is to establish an output tracking control based on the nonlinear dynamic model of the micro beam where the supply voltage is considered as a control input the tracking control algorithm is designed to solve the singularities resulting from the zero deflection state of the micro beam the galerkin method is applied in order to reduce the partial differential equation describing the dynamics of the beam into a set of ordinary differential equations odes uniformly ultimate boundedness stability of the control system is proved using lyapunov method the effectiveness of the proposed control algorithm is illustrated via numerical simulations

practical output tracking of nonlinear systems with uncontrollable unstable linearization the paper focuses on the problem of having the output of nonlinear systems track a prescribed c sup 1 reference signal it is proved that under mild assumptions global practical output tracking is achievable by smooth state feedback although asymptotic output tracking is usually not possible even locally because the linearized system has uncontrollable modes whose eigenvalues are on the right half plane smooth feedback controllers which solve the problem of global practical output tracking are explicitly constructed based on a modified adding a power integrator approach this feedback design method also leads to solutions to challenging benchmark control problems including practical output tracking of an underactuated unstable two degrees of freedom mechanical system

should model based inverse inputs be used as feedforward under plant uncertainty bounds on the size of the plant uncertainties are found such that the use of the inversion based feedforward input improves the output tracking performance when compared to the use of feedback alone the output tracking error is normalized by the size of the desired output and used as a measure of the output tracking performance the worst case performance is compared for two cases 1 with the use of feedback alone and 2 with the addition of the feedforward input it is shown that inversion based feedforward controllers can lead to performance improvements at frequencies w where the uncertainty spl delta jw in the nominal plant is smaller than the size of the nominal plant g sub 0 jw divided by its condition number k sub g0 jw i e spl par spl delta jw spl par sub 2 spl par g sub 0 jw spl par sub 2 k sub g0 jw a modified feedforward input is proposed that only uses the model information in frequency regions where plant uncertainty is sufficiently small the use of this modified inverse with any feedback results in improvement of the output tracking performance when compared to the use of the feedback alone

detection of broadband planewaves in the presence of gaussian noise of unknown covariance asymptotically optimum tests using the 2 d autoregressive noise model this paper addresses the problem of detecting a broadband planewave in noise of unknown spatial and temporal covariance at a linear array of sensors results of asymptotic detection theory are applied to derive detectors that approach optimal performance for large data records a parametric approach is used to model the statistics of the data a 2 d autoregressive 2dar model is chosen to model the noise process two broadband planewave signal models are considered both models represent the signal as a sum of monochromatic planewaves in the gaussian model the amplitudes are assumed to be gaussian with a single variance parameter whereas in the deterministic assumption they are individual unknown parameters detectors based on asymptotic theory are derived for both models as part of the development of the asymptotically as optimum detector the fisher information matrix fim is derived a proof of the locally asymptotic normal lan property is provided for the gaussian model probability density function pdf both detectors however are as equivalent to the generalized likelihood ratio test glrt are as of constant false alarm rate cfar and perform as as well as the glrt constructed with full knowledge of the noise statistics the performance of both detectors are compared with each other and to a standard spatially normalized beamformer in a computer simulation

technical communique a note on the differential regulator equation for non minimum phase linear systems with time varying exosystems some control problems in practice are often formulated as a linear output regulation problem with time varying exosystems although this problem has been studied recently an explicit and constructive solution has been given only for minimum phase systems this paper presents a solution for non minimum phase systems whose zero dynamics is hyperbolic or has an exponentially dichotomic split in the case of time varying zero dynamics the idea is inspired by the non causal stable inversion

invariant slow manifold approach for exact dynamic inversion of singularly perturbed linear mechanical systems with admissible output constraints abstract we propose an approach for the exact dynamic inversion of singularly perturbed second order linear systems through asymptotic expansion in a singular parameter we show that the inversion solution corresponding to the invariant slow manifold can be expressed as a converging infinite series under desired output constraints composed of exponential support functions in the complex domain we provide systematic mathematical procedures to obtain the closed form invariant slow manifold along with required admissible boundary conditions numerical examples are given to validate the proposed approach

stable inversion for nonlinear discrete time systems we solve the exact output tracking problem for square nonlinear discrete time systems through stable inversion this stable inversion problem involves finding a bounded solution of a dynamical system driven by a bounded signal such a solution is given by a difference representation formula whose existence under the proper assumptions can be proven using a picard process

brief iterative learning control for linear discrete time nonminimum phase systems this paper investigates iterative learning control for linear discrete time nonminimum phase systems first iterative learning control with advanced output data is considered for maximum phase systems next the results are extended to nonminimum phase systems the stability of the inverse mapping from the desired output to the input is proven based on the results for maximum phase systems the input should be updated with the output which is more advanced than the input by the sum of the relative degree of the system and the number of nonminimum phase zeros an example is given to indicate the importance of proper advances of output in the input update law

multi objective optimal trajectory design and tracking with non periodic tracking transition switching for non minimum phase linear systems abstractin this paper the problem of trajectory design and tracking of non periodic tracking transition switching for non minimum phase linear systems is considered such a problem exists in various applications where the output trajectory consists of application dependent tracking sessions and to be designed transition sessions the challenge arises when multiple control objectives are considered including the smooth transition from one output tracking session to the next one without large oscillations during the transition smooth tracking transition switching without inducing pre and or post switching oscillations input energy minimisation without saturation under amplitude constraint and furthermore minimisation of the overall transition time the proposed approach extends the previous work that attained smooth output transition and smooth tracking transition switching to further achieve amplitude constrained input energy minimisation and transition time minimisation first the constrained inp

global approximate output tracking for nonlinear systems addresses the global output tracking problem for nonlinear systems with singular points for nonlinear systems which satisfy a suitable observability condition the authors identify a class of smooth output trajectories which the system can track using continuous open loop controls this class includes all output trajectories generated by smooth state feedback they then study the problem of approximate output tracking using discontinuous time varying feedback controllers given a smooth output trajectory for which exact tracking is possible the authors construct a discontinuous feedback controller which achieves robust tracking of the desired output trajectory in the face of perturbations finally it is shown that their results can be applied to the control of a chain system and some numerical results are presented to illustrate the performance of their controller

brief tracking in a class of nonminimum phase systems with nonlinear internal dynamics via sliding mode control using method of system center a method of asymptotic output tracking in a class of causal nonminimum phase uncertain nonlinear systems is considered local asymptotic stability of output tracking error dynamics are provided for the specified class of systems with the nonlinear hyperbolic at the origin internal dynamics forced by a reference output profile and external disturbances defined by a known linear exosystem the nonlinear vector field of the internal dynamics is expanded in a power series obtained at a selected operational point in the internal dynamics state space the presented technique employs some linear algebraic methods and sliding mode control approach the solution is a complete constructive algorithm

feedforward control design for finite time transition problems of non linear mimo systems under input constraints a new approach is presented for the feedforward control design of non linear systems with the application to finite time setpoint transitions under input constraints this contribution extends recently presented results for the siso case to non linear quadratic mimo systems the inversion based design treats the transition task as a two point boundary value problem bvp defined in the input output coordinates of the considered system for its solvability free parameters are provided in ansatz functions for the highest output derivatives this concept allows the direct incorporation of input constraints within the formulation of the bvp the resulting bvp with free parameters can be solved e g with a standard matlab function the load transport of an overhead crane serves as an example to illustrate the concept

on a switching control scheme for nonlinear systems with ill defined relative degree this paper discusses the applicability of a switching control scheme for a nonlinear system with ill defined relative degree the control scheme switches between exact and approximate input output linearisation control laws unlike a linear system under a switching control scheme the equilibria of a nonlinear system may change with the switching it is pointed out that this is not sufficient to cause instability when the region of the approximate linearisation control law is attractive to the exact zero dynamics it is possible that the closed loop system under the switching control scheme is still stable the results in this paper shows that the switching control scheme proposed in tomlin and sastry systems control lett 35 3 1998 145 is applicable for a wider class of nonlinear systems

output feedback tracking a separation principle approach we study the practical and asymptotic tracking problems for nonlinear systems when only the output of the plant and the reference signal are available for feedback we provide sufficient conditions and a control topology yielding practical tracking in the special case when the reference signal is generated by an exosystem and there exists an internal model satisfying suitable observability properties tracking becomes asymptotic

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