an integral predictive nonlinear h control structure for a quadrotor helicopter this paper presents an integral predictive and nonlinear robust control strategy to solve the path following problem for a quadrotor helicopter the dynamic motion equations are obtained by the lagrange euler formalism the proposed control structure is a hierarchical scheme consisting of a model predictive controller mpc to track the reference trajectory together with a nonlinear h controller to stabilize the rotational movements in both controllers the integral of the position error is considered allowing the achievement of a null steady state error when sustained disturbances are acting on the system simulation results in the presence of aerodynamic disturbances parametric and structural uncertainties are presented to corroborate the effectiveness and the robustness of the proposed strategy

discrete time nonlinear h control with measurement feedback abstract this paper deals with the problem of h control via measurement feedback with internal stability for discrete time nonlinear systems using the theory of discrete time dissipative systems and differential game we first present a parameterization of a family of static state feedback h nonlinear controllers then we provide sufficient conditions for the existence of a dynamic output compensator which solves the problem of disturbance attenuation with internal stability for discrete time nonlinear systems the theory developed in this paper incorporates the well known results for discrete time linear systems and generalizes some recent advances in h control of continuous time nonlinear systems to their discrete time counterparts

h sub infinity optimal control with state feedback a h sub infinity optimal control problem in which the measured outputs are the states of the plant is considered the main result shows that the infimum of the norm of the closed loop transfer function using linear static state feedback equals the infimum of the norm of the closed loop transfer function over all stabilizing dynamic even nonlinear time varying state feedback controllers

stabilization and disturbance rejection for the beam equation we consider a system described by the one dimensional linear wave equation in a bounded domain with appropriate boundary conditions to stabilize the system we propose a dynamic boundary controller applied at the free end of the system the transfer function of the proposed controller is a proper rational function of the complex variable and may contain a single pole at the origin and a pair of complex conjugate poles on the imaginary axis provided that the residues corresponding to these poles are nonnegative the rest of the transfer function is required to be a strictly positive real function we then show that depending on the location of the pole on the imaginary axis the closed loop system is asymptotically stable we also consider the case where the output of the controller is corrupted by a disturbance and show that it may be possible to attenuate the effect of the disturbance at the output if we choose the controller transfer function appropriately we also present some numerical simulation results which support this argument

convergence of an iterative method for total variation denoising in total variation denoising one attempts to remove noise from a signal or image by solving a nonlinear minimization problem involving a total variation criterion several approaches based on this idea have recently been shown to be very effective particularly for denoising functions with discontinuities this paper analyzes the convergence of an iterative method for solving such problems the iterative method involves a lagged diffusivity approach in which a sequence of linear diffusion problems are solved global convergence in a finite dimensional setting is established and local convergence properties including rates and their dependence on various parameters are examined

fuzzy output tracking control of semi linear first order hyperbolic pde systems with matched perturbations abstract this paper considers the design problem of a fuzzy output tracking controller via a finite number of actuators for a class of nonlinear distributed parameter systems with unknown matched perturbations described by semi linear first order hyperbolic partial differential equations pdes firstly a t s fuzzy hyperbolic pde model is assumed to be used to accurately represent the semi linear first order hyperbolic pde system subsequently based on the t s fuzzy pde model the classic variable structure control technique is adopted to develop a fuzzy output tracking controller such that the output of the semi linear pde system exponentially tracks a desired reference and the state of the system is uniformly bounded in the filippov sense by constructing a strict lyapunov function the sufficient condition on the existence of the fuzzy output tracking controller is derived and presented in terms of algebraic linear matrix inequalities lmis in space with an equality constraint it has been shown that when these algebraic lmis with an equality constraint are feasible fuzzy tracking control design can be obtained via the existing convex optimization techniques finally the developed design methodology is successfully applied to the control of a semi linear lotka volterra pde system and the achieved results illustrate its effectiveness

admissibility of unbounded control operators for linear systems described by dot x t ax t bu t where a generates a semigroup on the state space x and b is an unbounded operator some necessary as well as some sufficient conditions are given for b to be admissible i e for any t the state x t should be in x and should depend continuously on the input u in l p this approach begins with an axiomatic description of such a system in terms of a functional equation the results are applied to the wave equation on a bounded interval

synchronization and secure communication of uncertain chaotic systems based on full order and reduced order output affine observers this paper deals with the problems of chaos synchronization and secure communication for a class of uncertain chaotic systems the uncertain chaotic systems under consideration are subject to modeling uncertainties and depend affinely on a set of measurable system outputs two types of observer are proposed to achieve chaos synchronization and secure communication first a full order output affine observer is proposed to simultaneously estimate the system states and the message signals second a reduced order output affine observer is proposed to simultaneously estimate the unmeasured system states and the message signals a numerical example is given for a chaotic system to show the design procedure and the effectiveness of the proposed observers the simulation results indicate that the proposed observers work well

acceleration methods for total variation based image denoising in this paper we apply a fixed point method to solve the total variation based image denoising problem an algebraic multigrid method is used to solve the corresponding linear equations krylov subspace acceleration is adopted to improve convergence in the fixed point iteration a good initial guess for this outer iteration at finest grid is obtained by combining fixed point iteration and geometric multigrid interpolation successively from the coarsest grid to the finest grid numerical experiments demonstrate that this method is efficient and robust even for images with large noise to signal ratios

an algebraic riccati equation approach to h optimization abstract this paper considers the general so called four block h optimal control problem with the assumption that system states are available for feedback it is shown that infimization of the h norm of the closed loop transfer function over all linear constant i e nondynamic stabilizing state feedback laws can be completely characterized via an algebraic riccati equation it is further shown that the optimal norm is not improved by allowing feedback to be dynamic thus the general state feedback h optimal control problem can be solved by iteratively solving one are and the controller can be chosen to be static gain

discrete time cal h _ infty control problem for nonlinear descriptor systems this note presents an explicit solution to the problem of disturbance attenuation with internal stability for discrete time nonlinear descriptor systems both the static state feedback and dynamic output feedback cases are considered in particular we characterize a family of hinfin controllers solving the problem locally around a neighborhood of the origin to do this we first derive two stability criteria for discrete time nonlinear descriptor systems and then a version of a bounded real lemma is also developed based on the concepts of dissipation inequality and differential game after that the results are used to derive the hinfin control theory for nonlinear discrete time descriptor systems the approach taken is mainly algebraic and hence is simple and clear

a rigorous reduction of the l2 stability of the solutions to a nonlinear binary reaction diffusion system of pde s to the stability of the solutions to a linear binary system of ode s abstract a basic peculiar lyapunov functional v is introduced for the dynamical systems generated by a pair of nonlinear reaction diffusion pde s with nonconstant coefficients the sign of v and of its derivative along the solutions is linked through an immediate simple relation to the eigenvalues by using v and the l 2 norm the non linear l 2 stability instability is rigorously reduced to the stability instability of the solutions to a linear binary system of ode s

controller discretization a gap metric framework for analysis and synthesis although techniques for directly synthesising sampled data sd compensators are available in the literature feedback controller design is perhaps best understood in a purely continuous time setting as such a feedback controller is often designed in the continuous time domain and then discretized for digital implementation it is important for the discretization step involved to yield an sd approximation which captures the essential features of the original controller from the perspective of closed loop behavior in this note a gap metric framework is developed for studying the controller discretization problem for linear time invariant lti plants and controllers importantly knowledge of a gap metric distance between an lti controller and an sd approximation permits explicit characterization of the possible difference in closed loop performance with any lti plant for which the lti controller is known to work well accounting for intersample behavior the central result of the new framework gives rise to an algorithm for computing a gap metric measure of the distance between an lti controller and a given discretization and a technique for synthesising a sd approximation which is optimal with respect to this metric

brief a receding horizon approach to the nonlinear h control problem the receding horizon rh methodology is extended to the design of a robust controller of h type for nonlinear systems using the nonlinear analogue of the fake h algebraic riccati equation we derive an inverse optimality result for the rh schemes for which increasing the horizon causes a decrease of the optimal cost function this inverse optimality result shows that the input output map of the closed loop system obtained with the rh control law has a bounded l 2 gain robustness properties of the nonlinear h control law in face of dynamic input uncertainty are considered

robust h sub spl infin control for a class of cascaded nonlinear systems this paper is concerned with the problem of robust h sub spl infin control for a class of nonlinear systems with parameter uncertainty the system under consideration is composed of two cascaded subsystems a zero input asymptotically stable nonlinear one and a linearizable one which is controllable the uncertain parameters are from a known compact set and are allowed to enter the system nonlinearly based on a lyapunov approach a nonlinear static state feedback controller is designed such that the l sub 2 gain of the closed loop system is below a prespecified value for all admissible uncertainties furthermore the closed loop system is shown to be robust input to state stable under some conditions

h sup infinity control for nonlinear systems with output feedback the basic question of nonlinear h sup infinity control theory is to decide for a given two port system when feedback that makes the full system dissipative and internally stable exists this problem can also be viewed as a question about circuits and after translation also has a game theoretic statement several necessary conditions for solutions to exist are presented and sufficient conditions for a certain construction to lead to a solution are given

adaptive controller design for tracking and disturbance attenuation in parametric strict feedback nonlinear systems the authors develop a systematic procedure for obtaining robust adaptive controllers that achieve asymptotic tracking and disturbance attenuation for a class of nonlinear systems which are described in the parametric strict feedback form and are subject to additional exogenous disturbance inputs their approach to adaptive control is performance based where the objective for the controller design is not only to find an adaptive controller but also to construct an appropriate cost functional compatible with desired asymptotic tracking and disturbance attenuation specifications with respect to which the adaptive controller is worst case optimal three main issues of the paper are the backstepping methodology worst case identification schemes and singular perturbations analysis closed form expressions have been obtained for an adaptive controller and the corresponding value function a numerical example involving a third order system is given

brief paper boundary control with integral action for hyperbolic systems of conservation laws stability and experiments a strict lyapunov function for boundary control with integral actions of hyperbolic systems of conservation laws that can be diagonalised with riemann invariants is presented the time derivative of this lyapunov function can be made strictly negative definite by an appropriate choice of the boundary conditions and the integral control gains previous stability results are extended to guarantee the local convergence of the state towards a desired set point furthermore the control can be implemented as a feedback of the state measured only at the boundaries the control design method is illustrated with a hydraulic application namely the level and flow regulation in a reach of the sambre river and in the micro channel of valence respectively through simulations and experimentations

mixed h 2 h control via state feedback for nonlinear systems this paper studies a mixed h 2 h control problem with internal stability by means of memoryless state feedback for smooth nonlinear control systems the problem consists of combining the performance requirements of quadratic optimal controllers with the robustness properties of h controllers it is shown that under appropriate assumptions the problem is solvable if a pair of cross coupled hamilton jacobi isaacs equations allows smooth solutions our approach to the mixed h 2 h nonlinear control problem is drawn from the concepts of non zero sum differential game lasalle s invariance principle and completion of squares analogous results are also developed for discrete time nonlinear systems by using the taylor expansion argument finally all the results obtained in affine systems are generalized to non affine nonlinear systems

h sub spl infin control for asymptotically stable nonlinear systems this paper deals with the problem of h sub spl infin control for a class of nonlinear systems the system under consideration is assumed to be globally asymptotically stable with a known lyapunov function based on this lyapunov function and using the notion of dissipativeness a state feedback controller is designed which renders the closed loop system globally asymptotically stable with a prescribed bound on the l sub 2 gain from the disturbance input to the controlled output the proposed controller design method is based on the explicit construction of a lyapunov function for the closed loop system which represents a significant advantage over existing methods

brief paper singular h suboptimal control for a class of nonlinear cascade systems in the present paper singular state feedback h suboptimal control for a class of nonlinear cascade systems is addressed under the assumption that a regular state feedback h suboptimal control problem is solvable for a particular subsystem of the cascade system an auxiliary nonlinear system is defined it is shown that a state feedback solution to the singular h suboptimal control problem for the auxiliary system also applies to the original problem the advantage of the auxiliary problem to the original problem is that the auxiliary penalty variable has lower dimension than the original penalty variable it is shown how this fact can simplify the problem considerably for the case when the auxiliary system can be strongly input output decoupled the theory is applied to a problem of a rigid spacecraft with actuator dynamics application to the special case when a subsystem of the nonlinear cascade system is passive is also considered

nonlinear h infinity control and related problems of homogeneous systems in this paper the problems of h infinity control and related l2 gain of nonlinear homo geneous systems are considered first of all l2 gains of homogeneous stable systems are estimated with a method in light of hamilton jacobi inequalities secondly by virtue of hamilton jacobi isaacs hji inequality the nonlinear h infinity induced l2 gain problem of a class of systems with homogeneous vector fields is discussed and global control law is given under an assumption similar to the one of stabilizability of linear systems then following the previous results homogeneous systems with higher degree perturbed terms are studied finally the analysis of finite test of homogeneous systems with perturbed parameter is presented

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

disturbance attenuation via state feedback for systems with a saturation nonlinearity in the control channel we study the problem of disturbance attenuation via state feedback for asymptotically stable systems with a saturation nonlinearity in the control channel the disturbance is assumed to be bounded with the bound known this amounts to adding a saturation nonlinearity in the disturbance channel a sufficient condition is derived in terms of algebraic matrix inequalities which are much simpler to solve than the general hamilton jacobi isaacs partial differential inequality a suboptimal control law is given based on the solution to the riccati inequalities the computational complexity of solving the optimal controller is similar to that of liner h controller design

disturbance attenuation and h sub infinity control via measurement feedback in nonlinear systems a solution to the problem of disturbance attenuation via measurement feedback with internal stability is presented for an affine nonlinear system it is shown that the concept of disturbance attenuation in the sense of truncated l sub 2 norms can be given an interpretation in terms of the response to periodic inputs in the sense of rms amplitude even in the nonlinear setup in the case of state feedback a family of controllers is also provided the proofs of all these results are simple and provide deeper insight even in the analysis of the corresponding linear control problem

classical bounded and almost periodic solutions to quasilinear first order hyperbolic systems in a strip abstract we consider boundary value problems for quasilinear first order one dimensional hyperbolic systems in a strip the boundary conditions are supposed to be of a smoothing type in the sense that the l 2 generalized solutions to the initial boundary value problems become eventually c 2 smooth for any initial l 2 data we investigate small global classical solutions and obtain the existence and uniqueness result under the condition that the evolution family generated by the linearized problem has exponential dichotomy on r we prove that the dichotomy survives under small perturbations in the leading coefficients of the hyperbolic system assuming that the coefficients of the hyperbolic system are almost periodic we prove that the bounded solution is almost periodic also

l sub 2 gain analysis of nonlinear systems and nonlinear state feedback h sub infinity control previously obtained results on l2 gain analysis of smooth nonlinear systems are unified and extended using an approach based on hamilton jacobi equations and inequalities and their relation to invariant manifolds of an associated hamiltonian vector field on the basis of these results a nonlinear analog is obtained of the simplest part of a state space approach to linear h sub infinity control namely the state feedback h sub infinity optimal control problem furthermore the relation with h sub infinity control of the linearized system is dealt with

classical solutions in sobolev spaces for a class of hyperbolic lotka volterra systems this paper considers the global classical solvability well posedness of a mixed initial boundary value problem for semilinear hyperbolic systems with nonlinear reaction coupling of lotka volterra type the reaction nonlinearity is not globally lipschitz in l 2 and has lipschitz properties depending on an l infty norm bound the well posedness problem is reformulated in an abstract setting as a modified cauchy problem with homogeneous boundary conditions and solved based on the banach contraction mapping theorem extra regularity of the local solutions in sobolev spaces is shown based on moser type inequalities it is shown that global existence of classical solutions holds if a uniform a priori bound on the l infty norm of the solution and boundary term exists

backstepping boundary control for first order hyperbolic pdes and application to systems with actuator and sensor delays abstract we consider a problem of boundary feedback stabilization of first order hyperbolic partial differential equations pdes these equations serve as a model for physical phenomena such as traffic flows chemical reactors and heat exchangers we design controllers using a backstepping method which has been recently developed for parabolic pdes with the integral transformation and boundary feedback the unstable pde is converted into a delay line system which converges to zero in finite time we then apply this procedure to finite dimensional systems with actuator and sensor delays to recover a well known infinite dimensional controller analog of the smith predictor for unstable plants we also show that the proposed method can be used for the boundary control of a korteweg de vries like third order pde the designs are illustrated with simulations

fault tolerant control for a class of switched linear hyperbolic systems this paper considers the fault tolerant control ftc problem for switched systems described by linear hyperbolic partial differential equations with the process and boundary faults the effect of

global h sub spl infin controllers for a class of nonlinear systems in this note the problem of state feedback h sub spl infin control for a class of nonlinear systems is considered the class under study is a generalization of the well known lur e systems the h sub spl infin problem is addressed via a class of storage functions of the lur e postnikov type whose integral term is parameterized by a nonlinear scalar function the related h sub spl infin controllers consist of a linear term which is designed for the underlying linearized system plus a nonlinear term which depends on the nonlinear function a simple geometrical criterion is provided for the characterization of the set of controllers which ensure a given level of l sub 2 performance globally some guidelines for an effective design of the controller within this set are discussed via two examples

adaptive dynamic output feedback neural network control of uncertain mimo nonlinear systems with prescribed performance an adaptive dynamic output feedback neural network controller for a class of multi input multi output affine in the control uncertain nonlinear systems is designed capable of guaranteeing prescribed performance bounds on the system s output as well as boundedness of all other closed loop signals it is proved that simply guaranteeing a boundedness property for the states of a specifically defined augmented closed loop system is necessary and sufficient to solve the problem under consideration the proposed dynamic controller is of switching type however its continuity is guaranteed thus alleviating any issues related to the existence and uniqueness of solutions simulations on a planar two link articulated manipulator illustrate the approach

lur e systems with multilayer perceptron and recurrent neural networks absolute stability and dissipativity sufficient conditions for absolute stability and dissipativity of continuous time recurrent neural networks with two hidden layers are presented in the autonomous case this is related to a lur e system with multilayer perceptron nonlinearity such models are obtained after parametrizing general nonlinear models and controllers by a multilayer perceptron with one hidden layer and representing the control scheme in standard plant form the conditions are expressed as matrix inequalities and can be employed for nonlinear h sub spl infin control and imposing closed loop stability in dynamic backpropagation

inverse optimal design of input to state stabilizing nonlinear controllers we show that input to state stabilizability as defined by sontag 1989 1995 is both necessary and sufficient for the solvability of a hamilton jacobi isaacs equation associated with a meaningful differential game problem similar to but more general than the nonlinear h sub spl infin problem the significance of the result stems from the fact that constructive solutions to the input to state stabilization problem are available presented in the paper and that as shown here inverse optimal controllers possess margins on input to state stability against a certain class of input unmodeled dynamics rather than completion of squares the main tools in our analysis are legendre fenchel transformations and the general form of young s inequality

state feedback ℋ control for stochastic time delay nonlinear systems with state and disturbance dependent noise this article focuses on the state feedback control problem for the stochastic nonlinear systems with state and disturbance dependent noise and time varying state delays based on the maxmin optimisation approach both the delay independent and the delay dependent hamilton jacobi inequalities hjis are developed for synthesising the state feedback controller for a general type of stochastic nonlinear systems it is shown that the resulting control system achieves stochastic stability in probability and the prescribed disturbance attenuation level for a class of stochastic affine nonlinear systems the delay independent as well as delay dependent matrix valued inequalities are proposed the resulting control system satisfies global asymptotic stability in the mean square sense and the required disturbance attenuation level by modelling the nonlinearities as uncertainties in corresponding stochastic time delay systems the sufficient conditions in terms of a linear matrix inequality lmi and a bili

perturbations of superstable linear hyperbolic systems abstract the paper deals with initial boundary value problems for linear non autonomous first order hyperbolic systems whose solutions stabilize to zero in a finite time we prove that problems in this class remain exponentially stable in l 2 as well as in c 1 under small bounded perturbations to show this for c 1 we prove a general smoothing result implying that the solutions to the perturbed problems become eventually c 1 smooth for any l 2 initial data

prescribed performance adaptive control for multi input multi output affine in the control nonlinear systems we consider the tracking problem of unknown robustly stabilizable multi input multi output mimo affine in the control nonlinear systems with guaranteed prescribed performance by prescribed performance we mean that the tracking error converges to a predefined arbitrarily small residual set with convergence rate no less than a prespecified value exhibiting maximum overshoot as well as undershoot less than some sufficiently small preassigned constants utilizing an output error transformation we obtain a transformed system whose robust stabilization is proven necessary and sufficient to achieve prescribed performance guarantees for the output tracking error of the original system provided that initially the transformed system is well defined consequently a switching robust control lyapunov function rclf based adaptive state feedback controller is designed to solve the stated problem the proposed controller is continuous and successfully overcomes the problem of computing the control law when the approximation model becomes uncontrollable simulations illustrate the approach

h control by state feedback an iterative algorithm and characterization of high gain occurrence we present an iterative algorithm to compute the achievable h norm by state feedbak for a standard regular problem and give a characterization when high gain feedback is necessary to approach the optimal value if there is no need for high gain components to approximate the optimal value we can reduce the problem to the computation of the h norm of a certain stable transfer matrix

neural network based online simultaneous policy update algorithm for solving the hji equation in nonlinear h_ infty control it is well known that the nonlinear h state feedback control problem relies on the solution of the hamilton jacobi isaacs hji equation which is a nonlinear partial differential equation that has proven to be impossible to solve analytically in this paper a neural network nn based online simultaneous policy update algorithm spua is developed to solve the hji equation in which knowledge of internal system dynamics is not required first we propose an online spua which can be viewed as a reinforcement learning technique for two players to learn their optimal actions in an unknown environment the proposed online spua updates control and disturbance policies simultaneously thus only one iterative loop is needed second the convergence of the online spua is established by proving that it is mathematically equivalent to newton s method for finding a fixed point in a banach space third we develop an actor critic structure for the implementation of the online spua in which only one critic nn is needed for approximating the cost function and a least square method is given for estimating the nn weight parameters finally simulation studies are provided to demonstrate the effectiveness of the proposed algorithm

robustness of nonlinear state feedback a survey a survey of robustness of nonlinear state feedback is given for series perturbations there are fairly complete results showing that under mild restrictions an optimal controller can tolerate an infinite increase in gain for gain reductions there are some results for systems linear in the control in particular there is a 50 reduction tolerance if the control penalty is quadratic usually the optimal controller cannot be computed exactly there are some results showing the effects of truncation on the robustness essentially robustness is maintained but in a reduced computable part of the state space

approximated solutions to nonlinear discrete time h sub spl infin control it is shown that there exists an analytic solution to the discrete hamilton jacobi equation arising in the nonlinear discrete time h sub spl infin control problem if and only if the h sub spl infin control problem associated to the linear approximated system is solvable starting from the solution of the riccati equation associated to this linear problem we show that the nonlinear solution can be computed at any desired degree of approximation on this basis the control solution can be computed iteratively

global asymptotic stabilisation of non linear systems in this article the problem of global asymptotic stabilisation of non linear systems is considered first of all the global asymptotic stability of a class of non linear systems is considered it is proved that the class of non linear systems is globally asymptotically stable under certain appropriate conditions secondly based on the result obtained the global asymptotic stabilisation of a class of non linear systems is investigated and the feedback control laws which globally stabilise the class of systems are designed thirdly by the coordinate change and the results obtained the global stabilisation of the affine non linear systems are studied and then some sufficient conditions of stabilisation are presented finally the global asymptotic stabilisation of partially linear cascade non linear system is considered the sufficient conditions of global stabilisation are obtained and the corresponding feedback control laws which stabilise the non linear systems are designed in addition some

deterministic edge preserving regularization in computed imaging many image processing problems are ill posed and must be regularized usually a roughness penalty is imposed on the solution the difficulty is to avoid the smoothing of edges which are very important attributes of the image in this paper we first give conditions for the design of such an edge preserving regularization under these conditions we show that it is possible to introduce an auxiliary variable whose role is twofold first it marks the discontinuities and ensures their preservation from smoothing second it makes the criterion half quadratic the optimization is then easier we propose a deterministic strategy based on alternate minimizations on the image and the auxiliary variable this leads to the definition of an original reconstruction algorithm called artur some theoretical properties of artur are discussed experimental results illustrate the behavior of the algorithm these results are shown in the field of 2d single photon emission tomography but this method can be applied in a large number of applications in image processing

backstepping design with local optimality matching in nonlinear h sup spl infin optimal control design for strict feedback nonlinear systems our objective is to construct globally stabilizing control laws to match the optimal control law up to any desired order and to be inverse optimal with respect to some computable cost functional our recursive construction of a cost functional and the corresponding solution to the hamilton jacobi isaacs equation employs a new concept of nonlinear cholesky factorization when the value function for the system has a nonlinear cholesky factorization we show that the backstepping design procedure can be tuned to yield the optimal control law

a computationally efficient lyapunov based scheduling procedure for control of nonlinear systems with stability guarantees we propose an alternative to gain scheduling for stabilization of nonlinear systems for a useful class of nonlinear systems the characterization of a region of stability based on a control lyapunov function is computationally tractable in the sense that computation times vary polynomially with the state dimension for a fixed number of scheduling variables using this fact we develop a procedure to expand the region of stability by constructing control lyapunov functions to various trim points of the system a lyapunov based control synthesis algorithm is used to construct a control law that guarantees closed loop stability for initial conditions in the expanded region of state space this control asymptotically recovers the optimal stability margin in the sense of a lyapunov derivative which in turn can be seen as a performance measure robustness to bounded disturbances and stabilization under bounded control are easily incorporated into this framework in the worst case the computational complexity of the analysis problem that develops in the new method is increased by an exponential in the disturbance dimension similarly we can handle control constraints with an increase in computational complexity of no more than an exponential in the control dimension we demonstrate the new control design procedure on an example

convergence of fixed point iteration for deblurring and denoising problem abstract to solve deblurring and denoising problem we present a proof of the global and linear convergence of fixed point iteration as well as an estimate for the rate of convergence is given we show the equivalence among three different iterative methods half quadratic regularization iteration based on bergman distance weiszfeld s method

convergence analysis for reduced order adaptive controller design of uncertain siso linear systems with noisy output measurements we consider in this article a class of uncertain siso linear systems that are subject to system and measurement noises reduced order adaptive controller designs have been proposed before for such systems by the authors and stability analysis of the closed loop systems has been established here we analyse further the robustness properties for these reduced order adaptive control systems by providing detailed convergence analysis results for the key closed loop signals and parameter estimates we rigorously prove that whenever the exogenous disturbance input is of finite energy and bounded and the reference trajectory and its derivatives up to rth order are bounded r being the relative degree of the transfer function of the true system a set of signals including the tracking error the estimation error between the system output and its estimate the projection signal are of finite energy and converge to zero and the system states and their estimates exhibit asymptotic behaviours with certain form

on a state space approach to nonlinear h control we study the standard h optimal control problem using state feedback for smooth nonlinear control systems the main theorem obtained roughly states that the l2 induced norm from disturbances to inputs and outputs can be made smaller than a constant 0 if the corresponding h norm for the system linearized at the equilibrium can be made smaller than by linear state feedback necessary and sufficient conditions for the latter problem are by now well known e g from the state space approach to linear h optimal control our approach to the nonlinear h optimal control problem generalizes the state space approach to the linear h problem by replacing the hamiltonian matrix and corresponding riccati equation as used in the linear context by a hamiltonian vector field together with a hamiltonian jacobi equation corresponding to its stable invariant manifold

feedback and optimal sensitivity model reference transformations multiplicative seminorms and approximate inverses in this paper the problem of sensitivity reduction by feedback is formulated as an optimization problem and separated from the problem of stabilization stable feedback schemes obtainable from a given plant are parameterized salient properties of sensitivity reducing schemes are derived and it is shown that plant uncertainty reduces the ability of feedback to reduce sensitivity the theory is developed for input output systems in a general setting of banach algebras and then specialized to a class of multivariable time invariant systems characterized by n times n matrices of h infty frequency response functions either with or without zeros in the right half plane the approach is based on the use of a weighted seminorm on the algebra of operators to measure sensitivity and on the concept of an approximate inverse approximate invertibility of the plant is shown to be a necessary and sufficient condition for sensitivity reduction an indicator of approximate invertibility called a measure of singularity is introduced the measure of singularity of a linear time invariant plant is shown to be determined by the location of its right half plane zeros in the absence of plant uncertainty the sensitivity to output disturbances can be reduced to an optimal value approaching the singularity measure in particular if there are no right half plane zeros sensitivity can be made arbitrarily small the feedback schemes used in the optimization of sensitivity resemble the lead lag networks of classical control design some of their properties and methods of constructing them in special cases are presented

stabilization of a system of n 1 coupled first order hyperbolic linear pdes with a single boundary input we solve the problem of stabilization of a class of linear first order hyperbolic systems featuring n rightward convecting transport pdes and one leftward convecting transport pde we design a controller which requires a single control input applied on the leftward convecting pde s right boundary and an observer which employs a single sensor on the same pde s left boundary we prove exponential stability of the origin of the resulting plant observer controller system in the spatial l2 sense

h sub spl infin control of discrete time nonlinear systems this paper presents an explicit solution to the problem of disturbance attenuation with internal stability via full information feedback state feedback and dynamic output feedback respectively for discrete time nonlinear systems the h sub spl infin control theory is first developed for affine systems and then extended to general nonlinear systems based on the concepts of dissipation inequality differential game and lasalle s invariance principle in discrete time a substantial difficulty that v a x b x u e x w respectively v f x u w is no longer quadratic in sub w sup u arising in the case of discrete time nonlinear systems has been surmounted in the paper in the case of a linear system we show how the results reduce to the well known ones recently proposed in the literature

parameterization of nonlinear h state feedback controllers state space formulas are derived for a family of controllers solving the nonlinear h state feedback control problem these controllers are obtained by interconnecting the central controller with an asymptotically stable free system that satisfies one additional cascade condition all proofs given are simple and clear and also provide a deeper insight into the synthesis of the corresponding linear h controllers

brief solutions of nonlinear optimal and robust control problems via a mixed collocation dae s based algorithm a new algorithm for computing the solutions of nonlinear optimal and robust h control problems is proposed the algorithm is based on the use of the collocation method to transform the pde s into ode s some convergence results are given and several examples are presented

h sup spl infin control for more general nonlinear systems the authors consider the standard h sup spl infin control problem for more general nonlinear systems modeled by equations in which the penalty output and the measured output are in general functions of the state the exogenous input and the control input in particular we characterize a family of h sup spl infin controllers via output feedback as well as state feedback solving the problem the results obtained generalize some recent results in the literature

on nonlinear control of euler lagrange systems disturbance attenuation properties abstract in this brief note we analyse the local disturbance attenuation properties of some asymptotically stabilizing nonlinear controllers for euler lagrange systems reported in the literature our objective in this study is twofold first to compare the performance of these schemes from a perspective different from stabilizability second to quantify the basic tradeoff between robust stability and robust performance for these designs we consider passivity based and feedback linearization schemes developed for the control of dc to dc converters and rigid robots for the dc to dc problem we show that for both controllers there exists a lower bound to the achievable attenuation level i e a lower bound to the l 2 gain of the closed loop operator from disturbance to regulated output which is independent of the design parameters also for the passivity based scheme we obtain an upper bound for the disturbance attenuation which is insured provided we sacrifice the convergence rate for rigid robots we show that both approaches yield arbitrarily good disturbance attenuation without compromising the convergence rate

dissipative boundary conditions for one dimensional quasi linear hyperbolic systems lyapunov stability for the c 1 norm this paper is concerned with boundary dissipative conditions that guarantee the exponential stability of classical solutions of one dimensional quasi linear hyperbolic systems we present a comprehensive review of the results that are available in the literature the main result of the paper is then to supplement these previous results by showing how a new lyapunov stability approach can be used for the analysis of boundary conditions that are known to be dissipative for the c 1 norm

iterative adaptive dynamic programming for solving unknown nonlinear zero sum game based on online data h infty control is a powerful method to solve the disturbance attenuation problems that occur in some control systems the design of such controllers relies on solving the zero sum game zsg but in practical applications the exact dynamics is mostly unknown identification of dynamics also produces errors that are detrimental to the control performance to overcome this problem an iterative adaptive dynamic programming algorithm is proposed in this paper to solve the continuous time unknown nonlinear zsg with only online data a model free approach to the hamilton jacobi isaacs equation is developed based on the policy iteration method control and disturbance policies and value are approximated by neural networks nns under the critic actor disturber structure the nn weights are solved by the least squares method according to the theoretical analysis our algorithm is equivalent to a gauss newton method solving an optimization problem and it converges uniformly to the optimal solution the online data can also be used repeatedly which is highly efficient simulation results demonstrate its feasibility to solve the unknown nonlinear zsg when compared with other algorithms it saves a significant amount of online measurement time

brief paper robust h control of uncertain nonlinear systems this paper discusses the robust l 2 gain performance synthesis problem for a class of uncertain nonlinear systems it is shown that the hamilton jacobi equation approach to robust h performance synthesis can be extended to solve this problem based on a positive definite solution of a hamilton jacobi inequality a sufficient condition is given such that the uncertain nonlinear system is robust and stable and its l 2 gain is less than or equal to a prescribed value using this condition a state feedback law and an output feedback law which ensure robust l 2 gain performance of the closed loop system are derived finally an example is given

robust h sub spl infin control for linear discrete time systems with norm bounded nonlinear uncertainties this paper studies the problem of robust control of a class of uncertain discrete time systems the class of uncertain systems is described by a state space model with linear nominal parts and norm bounded nonlinear uncertainties in the state and output equations the authors address the problem of robust h sub spl infin control in which both robust stability and a prescribed h sub spl infin performance are required to be achieved irrespective of the uncertainties it has been shown that instead of the nonlinear uncertain system one may only consider a related linear uncertain system and thus a linear static state feedback control law is designed which is in terms of a riccati inequality

convex design control for practical nonlinear systems this paper describes a new control scheme for approximately optimal control aoc of nonlinear systems convex control design convcd the key idea of convcd is to transform the approximate optimal control problem into a convex semi definite programming sdp problem contrary to the majority of existing aoc designs where the problem that is addressed is to provide a control design which approximates the performance of the optimal controller by increasing the controller complexity the proposed approach addresses a different problem given a controller of fixed complexity it provides a control design that renders the controller as close to the optimal as possible and moreover the resulted closed loop system stable two numerical examples are used to show the effectiveness of the method

a polynomial approach to minimax frequency domain optimization of multivariable feedback systems the properties of a feedback system where the plant has rational transfer matrix h and the compensator has transfer matrix g can be characterized through the system functions s i hg and t g i hg 1 good disturbance attenuation robustness limited bandwidth and compensator roll off may be obtained by minimizing a criterion of the form z where z v s t w1 wls t w2 w2t v with respect to the compensator transfer matrix g here v w1 and w2 are suitable rational weighting matrices the solution of the problem can be reduced to a pair of matrix polynomial equations since the optimal solution is highly non unique special solutions with additional optimality properties are considered as well the paper includes a discussion of the numerical solution of the polynomial equations and of the question how to choose the weighting matrices to ensure required feedback system properties an example illustrates the results

filtering and smoothing in an h sup infinity setting the problems of filtering and smoothing are considered for linear systems in an h sup infinity setting i e the plant and measurement noises have bounded energies are in l sub 2 but are otherwise arbitrary two distinct situations for the initial condition of the system are considered the initial condition is assumed known in one case while in the other the initial condition is not known but the initial condition the plant and measurement noise are in some weighted ball of r sup n xl sub 2 finite horizon and infinite horizon cases are considered necessary and sufficient conditions are presented for the existence of estimators both filters and smoothers that achieve a prescribed performance bound and algorithms that result in performance within the bounds are developed in case of smoothers the optimal smoother is also presented the approach uses basic quadratic optimization theory in a time domain setting as a consequence of which both linear time varying and time invariant systems can be considered with equal ease in the smoothing problem for linear time varying systems one considers only the finite horizon case

policy iterations on the hamilton jacobi isaacs equation for h_ infty state feedback control with input saturation an hinfin suboptimal state feedback controller for constrained input systems is derived using the hamilton jacobi isaacs hji equation of a corresponding zero sum game that uses a special quasi norm to encode the constraints on the input the unique saddle point in feedback strategy form is derived using policy iterations on both players the hji equation is broken into a sequence of differential equations linear in the cost for which closed form solutions are easier to obtain policy iterations on the disturbance are shown to converge to the available storage function of the associated l2 gain dissipative dynamics the resulting constrained optimal control feedback strategy has the largest domain of validity within which l2 performance for a given gamma is guaranteed

reduced complexity nonlinear h sup spl infin control of discrete time systems in this note we describe a reduced complexity solution to the nonlinear h sup spl infin control problem this reduction applies to systems where some of the states are perfectly known and is an intermediate problem between full state feedback and the standard measurement feedback problem the reduction of computational complexity is significant and of practical importance online implementation is feasible with 2003 computer technology for a range of practical engineering design problems

h sub spl infin tuning for task space feedback control of robot with uncertain jacobian matrix the h sub spl infin tuning problem for task space feedback control of a robot with uncertain kinematics and jacobian matrix from joint space to task space is formulated and solved h sub spl infin tuning methods are presented for two task space feedback controllers when the systems are subject to external disturbance it is shown that the conditions for the establishment of h sub spl infin tuning can be obtained in simple forms without solving the hamilton jacobi inequalities even in the presence of kinematics uncertainty

brief h controller reduction for nonlinear systems sufficient conditions are proposed for the existence of reduced order fixed order controllers solving the standard nonlinear h output feedback control problem state space formulas for such reduced order h controllers are also derived in terms of the solutions of two hamilton jacobi inequalities the development uses only elementary concepts of dissipativity and differential game thus the proofs given are simple and clear

neurodynamic programming and zero sum games for constrained control systems in this paper neural networks are used along with two player policy iterations to solve for the feedback strategies of a continuous time zero sum game that appears in l2 gain optimal control suboptimal hinfin control of nonlinear systems affine in input with the control policy having saturation constraints the result is a closed form representation on a prescribed compact set chosen a priori of the feedback strategies and the value function that solves the associated hamilton jacobi isaacs hji equation the closed loop stability l2 gain disturbance attenuation of the neural network saturated control feedback strategy and uniform convergence results are proven finally this approach is applied to the rotational translational actuator rtac nonlinear benchmark problem under actuator saturation offering guaranteed stability and disturbance attenuation

infinite dimensional linear systems with unbounded control and observation a functional analytic approach abstract the object of these notes is to develop a unifying framework for the functional analytic representation of infinite dimensional linear systems with unbounded input and output operators on the basis of the general approach new results are derived on the wellposedness of feedback systems and on the linear quadratic control problem the implications of the theory for large classes of functional and partial differential equations are discussed in detail keywords representation of infinite dimensional systems semigroups boundary control feedback linear quadratic control

on the convergence of the lagged diffusivity fixed point method in total variation image restoration in this paper we show that the lagged diffusivity fixed point algorithm introduced by vogel and oman in siam j sci comput 17 1996 pp 227 238 to solve the problem of total variation denoising proposed by rudin osher and fatemi in phys d 60 1992 pp 259 268 is a particular instance of a class of algorithms introduced by voss and eckhardt in computing 25 1980 pp 243 251 whose origins can be traced back to weiszfeld s original work for minimizing a sum of euclidean lengths tohoku math j 43 1937 pp 355 386 there have recently appeared several proofs for the convergence of this algorithm g aubert et al technical report 94 01 informatique signaux et systemes de sophia antipolis 1994 a chambolle and p l lions technical report 9509 ceremade 1995 and d c dobson and c r vogel siam j numer anal 34 1997 pp 1779 1791 here we present a proof of the global and linear convergence using the framework introduced in h voss and u eckhart computing 25 1980 pp 243 251 and give a bound for the convergence rate of the fixed point iteration that agrees with our experimental results these results are also valid for suitable generalizations of the fixed point algorithm

state space solutions to standard h sub 2 and h sub infinity control problems simple state space formulas are derived for all controllers solving the following standard h sub infinity problem for a given number gamma 0 find all controllers such that the h sub infinity norm of the closed loop transfer function is strictly less than gamma it is known that a controller exists if and only if the unique stabilizing solutions to two algebraic riccati equations are positive definite and the spectral radius of their product is less than gamma sup 2 under these conditions a parameterization of all controllers solving the problem is given as a linear fractional transformation lft on a contractive stable free parameter the state dimension of the coefficient matrix for the lft constructed using the two riccati solutions equals that of the plant and has a separation structure reminiscent of classical lqg i e h sub 2 theory this paper is intended to be of tutorial value so a standard h sub 2 solution is developed in parallel

an approach to h control of a class of nonlinear systems this paper considers robust h control of a class of nonlinear systems that can be represented by a heterogeneous model a new controller design method using both state feedback is proposed based on quadratic stability theory a number of necessary and sufficient conditions are derived for quadratic stabilizability with disturbance attenuation of the control system concerned an example is also given to demonstrate the performance of the proposed controller design methods

h sub spl infin control via measurement feedback for general nonlinear systems this paper shows how the problem of local disturbance attenuation via measurement feedback with internal stability can be solved for a nonlinear system of rather general structure the solution of the problem is shown to be related to the existence of solutions of a pair of hamilton jacobi inequalities in n independent variables which are associated with state feedback and respectively output injection design

an iterative adaptive dynamic programming method for solving a class of nonlinear zero sum differential games in this paper a new iterative adaptive dynamic programming adp method is proposed to solve a class of continuous time nonlinear two person zero sum differential games the idea is to use the adp technique to obtain the optimal control pair iteratively which makes the performance index function reach the saddle point of the zero sum differential games if the saddle point does not exist the mixed optimal control pair is obtained to make the performance index function reach the mixed optimum stability analysis of the nonlinear systems is presented and the convergence property of the performance index function is also proved two simulation examples are given to illustrate the performance of the proposed method

lyapunov based boundary control for a class of hyperbolic lotka volterra systems this paper considers a boundary feedback control problem for two first order nonlinearly coupled hyperbolic partial differential equations with lotka volterra type coupling boundary control action is used on one equation to drive the state at the end of the spatial domain to a desired constant reference value static and dynamic boundary controllers are designed based on a special lyapunov functional that is related to an entropy function the time derivative of the entropy function is made strictly negative by an appropriate choice of boundary conditions a unique classical solution is shown to exist globally in time and asymptotic exponential convergence to the desired steady state solution is shown in the norm the boundary control design is illustrated with simulations

h disturbance attenuation for state delayed systems in this note the differential game and dissipation inequality are applied to the disturbance attenuation or h control for linear systems with delayed state firstly a simple sufficient condition on the existence of a suboptimal h state feedback controller is given which is independent of delay and an observer based dynamic output feedback solution is presented in terms of riccati inequalities or riccati equations secondly a sufficient condition on the existence of a delay dependent state feedback is presented and the criterion is presented by a matrix inequality which can be solved by numerical methods