optimal controllers for finite wordlength implementation when a controller is implemented by a digital computer with a d and d a conversion numerical errors can severely affect the performance of the control system there exist realizations of a given controller transfer function exhibiting arbitrarily large effects from computational errors assuming sufficient excitation of the system the problem of designing an optimal controller in the presence of both external disturbances and internal roundoff errors is solved the results reduce to the standard lqg controller when infinite precision computation is used for finite precision however the separation principle does not hold a penalty is also added to the cost function to penalize the sum of the wordlengths used to compute the fractional part of each state variable of the controller this sum can be used to represent the lower bound on computer memory needed for controller synthesis it measures controller complexity and is minimized penalized here

robustness analysis with full structured uncertainties this paper deals with problems involving full structured rather than block diagonal uncertainty i e uncertainty blocks where each sub block or element may be an independent uncertainty rearranging this problem into standard block diagonal form results in an explosion in the required computation and so a number of researchers have proposed more efficient bounds in particular those based on non similarity scaling for such problems here we show how to map such problems into reduced size standard problems the standard bounds applied to the reduced size problem are then shown to be at least as accurate and require the same computational effort as earlier techniques with the added bonus that the standard upper bound is convex moreover this new approach is applicable in a much more general setting allowing one to efficiently compute both robust stability and robust performance for problems involving multiple real and complex uncertainty blocks any number of which may be full structured

asymptotic stability of the stationary solution to an initial boundary value problem for the mullins equation of fourth order in the present article we first study the existence of the stationary solution to an initial boundary value problem for the mullins equation of fourth order which was proposed by mullins two dimensional motion of idealized grain boundaries j appl phys 27 900 1956 to describe the groove development due to the surface diffusion at the grain boundaries of a heated polycrystal then employing an energy method we prove that this stationary solution is asymptotically stable in a suitable norm as time goes to infinity

energy control of a pendulum with quantized feedback the problem of controlling a nonlinear system to an invariant manifold using quantized state feedback is considered by the example of controlling the pendulum s energy a feedback control law based on the speed gradient algorithm is chosen the main result consisting in precisely characterizing allowed quantization error bounds and resulting energy deviation bounds is presented

some qualitative properties of sampled data control systems the authors consider sampled data control systems which consist of an interconnection of a continuous time nonlinear plant and a digital controller which has quantizers but is otherwise linear along with the required interface elements a d and d a converters in the present paper the authors study the qualitative effects of the quantizers and the plant nonlinearities of these systems

some qualitative properties of multirate digital control systems the authors consider multirate digital control systems which consist of an interconnection of a continuous time nonlinear plant described by ordinary differential equations a digital controller described by ordinary difference equations which has quantizers but is otherwise linear along with the required interface elements a d and d a converters the input to the digital controller consists of the multirate sampled output of the plant in the present paper the authors show that when quantizer nonlinearities are neglected then under reasonable conditions which exclude the critical cases the stability properties in the lyapunov sense of the trivial solution of a nonlinear multirate digital control system can be deduced from the stability properties of the trivial solution of its linearization for such systems we also present a result concerning the existence and construction of stabilizing multirate output digital controllers in the present paper the authors also show that the solutions of a multirate digital feedback control system with nonlinear plant and quantizers are uniformly ultimately bounded if the trivial solution of the corresponding linear system consisting of the linearization of the plant and with the quantization removed from the digital controller is asymptotically stable we also provide a result which compares the response of multirate digital control systems with nonlinear plant and quantizers in the controller with the response of the corresponding nonlinear multirate digital control systems without quantizers in the digital controller

robust non fragile control for uncertain discrete delay large scale systems with a class of controller gain variations this paper considers the problems of robust non fragile control for uncertain discrete delay large scale systems under state feedback gain variations two classes of controller gain variations are considered based on the lyapunov method the state feedback control design for robust stability is given in terms of solutions to a linear matrix inequality lmi the solutions of the lmi can be easily obtained using efficient convex optimization techniques a numerical example is included to illustrate the design procedures

robustness in the presence of mixed parametric uncertainty and unmodeled dynamics continuing the development of the structured singular value approach to robust control design the authors investigate the problem of computing mu in the case of mixed real parametric and complex uncertainty the problem is shown to be equivalent to a smooth constrained finite dimensional optimization problem in view of the fact that the functional to be maximized may have several local extrema an upper bound on mu whose computation is numerically tractable is established this leads to a sufficient condition of robust stability and performance a historical perspective on the development of the mu theory is included

convergence properties of the riccati difference equation in optimal filtering of nonstabilizable systems this paper studies the convergence and properties of the solutions of the riccati difference equation special emphasis is given to systems which are not necessarily stabilizable in the filtering sense particularly those having uncontrollable roots on the unit circle besides generalizing and unifying previous work the results have application to a number of important problems including filtering and control of systems with purely deterministic disturbances such as sinusoids and drift components

optimal realizations of floating point implemented digital controllers with finite word length considerations the closed loop stability issue of finite precision realizations is investigated for digital controllers implemented in floating point arithmetic unlike the existing methods which only address the effect of the mantissa bits in floating point implementation to the sensitivity of closed loop stability the sensitivity of closed loop stability is analyzed with respect to both the mantissa and exponent bits of floating point implementation a computationally tractable fwl closed loop stability measure is then defined and the method of computing the value of this measure is given the optimal controller realization problem is posed as searching for a floating point realization that maximizes the proposed fwl closed loop stability measure and a numerical optimization technique is adopted to solve for the resulting optimization problem simulation results show that the proposed design procedure yields computationally efficient controller realizations with enhanced fwl closed loop stability performance

two approaches based on pole sensitivity and stability radius measures for finite precision digital controller realizations this paper compares the two approaches based on pole sensitivity and the complex stability radius measures respectively for optimizing the closed loop stability robustness of digital controllers with respect to finite word length fwl errors in fixed point implementation design details and related optimization procedures are derived for the two methods the two measures although derived from different motivations can both be regarded as lower bound measures of a true but computationally intractable fwl stability measure in some senses an example is used to verify the theoretical analysis and to illustrate the two designs for determining optimal fwl controller realizations

evolution of phase boundaries by configurational forces an initial boundary value problem modeling the evolution of phase interfaces in materials showing martensitic transformations is studied the model which is derived rigorously from a sharp interface model with phase interfaces driven by configurational forces and which generalizes that model consists of the equations of linear elasticity coupled with a nonlinear partial differential equation of hyperbolic character governing the evolution of the order parameter it is proved that in one space dimension global solutions exist for which the order parameter belongs to the space of functions of bounded variation other models for interface motion by martensitic transformations and by interface diffusion are suggested

viscosity solutions to a new phase field model with neumann boundary condition for solid solid phase transitions abstract we shall study an initial boundary value problem of a new phase field model which is a degenerate parabolic equation coupled to a linear elasticity sub system used to describe the solid solid phase transitions in elastically deformable solid materials we establish a series of approximate solutions to the initial boundary value problem and prove that the viscosity solutions to this initial boundary value problem exist in a one dimensional case

the dual iteration for fixed order control this paper proposes a new heuristic algorithm for fixed order control problems using linear matrix inequalities the authors call the algorithm the dual iteration because it is based on the iteration of two design steps state feedback and filtering which are dual to each other extensive numerical experiments show that the algorithm has a decent performance

finite wordlength controller realisations using the specialised implicit form a specialised implicit state space representation is introduced to deal with finite wordlength effects in controller implementations this specialised implicit form provides a macroscopic description of the algorithm to be implemented so it constitutes a unifying framework allowing to encompass various implementation forms such as the operator the direct form ii transposed observer based and many other realisations usually considered separately in the literature different measures quantifying the finite wordlength effects on the overall closed loop behaviour are defined in this new context they concern both stability and performance the gap with the infinite precision case is evaluated classically through the coefficient sensitivity and roundoff noise analysis the problem of determining a realisation with minimum finite wordlength effects can subsequently be solved using appropriate numerical methods the approach is illustrated with an example

on the phase portrait of the matrix riccati equation arising from the periodic control problem a comprehensive description is provided of the properties of the matrix riccati differential equation in which the coefficient matrices are t periodic for some t 0 the main results include 1 a classification of all the periodic equilibria t periodic solutions 2 necessary and sufficient conditions for convergence to the uniformly asymptotically stable completely unstable periodic equilibrium as t to infty t to infty 3 necessary and sufficient conditions for a solution to escape in finite forward or backward time 4 a description of every almost periodic solution 5 a proof that every solution which does not escape in finite time is asymptotically almost periodic and an explicit formula for the limiting almost periodic solution

on a model for phase separation in binary alloys driven by mechanical effects this work is concerned with the mathematical analysis of a system of partial differential equations modeling the effect of phase separation driven by mechanical actions in binary alloys like tin lead solders the system combines the quasistationary balance of linear momentum with a fourth order evolution equation of cahn hilliard type for the phase separation and it is highly nonlinearly coupled existence and uniqueness results are shown tel 0382505631 email bonetti dimat unipv it

brief paper robust finite word length controller design a novel finite word length fwl controller design is proposed in the framework of a mixed m theory a robust fwl controller performance measure is first developed which takes into account the standard robust control requirements as well as the fwl implementation considerations and the corresponding controller design problem is naturally reformulated as a mixed m problem which can be treated effectively with the results of the mixed m theory

existence and uniqueness of solutions of nonlinear neumann problems soit d r n un domaine connexe borne lisse et on suppose qu en chaque point x d la normale exterieure n est bien definie soit a une fonction arbitraire continue de holder dans d on etudie les solutions positives du probleme de neumann non lineaire u a x g u 0 dans d u n 0 sur d ou g r r est une fonction de classe c r c 1 r 0 1

positive periodic solutions to an indefinite minkowski curvature equation abstract we investigate the existence non existence multiplicity of positive periodic solutions both harmonic i e t periodic and subharmonic i e kt periodic for some integer k 2 to the equation u 1 u 2 a t g u 0 where 0 is a parameter a t is a t periodic sign changing weight function and g 0 0 is a continuous function having superlinear growth at zero in particular we prove that for both g u u p with p 1 and g u u p 1 u p q with 0 q 1 p the equation has no positive t periodic solutions for close to zero and two positive t periodic solutions a small one and a large one for large enough moreover in both cases the small t periodic solution is surrounded by a family of positive subharmonic solutions with arbitrarily large minimal period the proof of the existence of t periodic solutions relies on a recent extension of mawhin s coincidence degree theory for locally compact operators in product of banach spaces while subharmonic solutions are found by an application of the poincare birkhoff fixed point theorem after a careful asymptotic analysis of the t periodic solutions for

guaranteed cost control for discrete time linear systems under controller gain perturbations abstract this paper considers the problem of guaranteed cost control for discrete time linear systems under state feedback control gain perturbations two classes of perturbations are considered namely additive and multiplicative the state feedback control designs for optimal guaranteed cost control under the two classes of gain perturbations are given in terms of solutions to algebraic riccati equations the designs are such that the cost of the closed loop system is guaranteed to be within a certain bound for all admissible uncertainties numerical examples are included to illustrate the design procedures

on the stability of a class of nonlinear hybrid systems abstract in this paper we propose new conditions for guaranteeing the stability of nonlinear sampled data systems in order to do this we extend lyapunov theory to this class of systems

periodic solutions for a second order differential equation with indefinite weak singularity as a consequence of the main result of this paper efficient conditions guaranteeing the existence of a t periodic solution to the second order differential equation are established here h l t is a piecewise constant sign changing function and the non linear term presents a weak singularity at 0 i e 0 1

solutions to a model with nonuniformly parabolic terms for phase evolution driven by configurational forces we prove the existence of solutions global in time to an initial boundary value problem for a system of partial differential equations which consists of the equations of linear elasticity and a nonlinear nonuniformly parabolic equation of second order the problem models the behavior in time of materials with martensitic phase transformations this model with diffusive phase interfaces was derived from a model with sharp interfaces whose evolution is driven by configurational forces and can be considered to be a regularization of that model our existence proof which contributes to the verification of the model is only valid in one space dimension

pairs of positive periodic solutions of second order nonlinear equations with indefinite weight abstract we study the problem of the existence and multiplicity of positive periodic solutions to the scalar ode u a t g u 0 0 where g x is a positive function on r superlinear at zero and sublinear at infinity and a t is a t periodic and sign indefinite weight with negative mean value we first show the nonexistence of solutions for some classes of nonlinearities g x when is small then using critical point theory we prove the existence of at least two positive t periodic solutions for large some examples are also provided

an improved closed loop stability related measure for finite precision digital controller realizations the pole sensitivity approach is employed to investigate the stability issue of the discrete time control system where a digital controller implemented with finite word length fwl is used a stability related measure is derived which is more accurate in estimating the closed loop stability robustness of an fwl implemented controller than some existing measures for the pole sensitivity analysis this improved stability measure thus provides a better criterion to find the optimal realizations for a generic controller structure that includes output feedback and observer based controllers a numerical example is used to verify the theoretical analysis and to illustrate the design procedure

quantization and overflow effects in digital implementations of linear dynamic controllers the stability of a class of single input single output siso digital feedback control systems is investigated the systems considered contain a linear dynamic plant a digital controller and suitable d a digital to analog and a d converters the design of such systems is usually accomplished by ignoring the nonlinear effects caused by quantization and overflow truncation simulations of specific examples establish the quantization in such systems can lead to loss of asymptotic stability of the origin obtained results prove that when quantization is taken into account but overflow is neglected one only has convergence to some small neighborhood about the origin the results also prove that for initial conditions sufficiently far from the origin overflow effects can lead to unbounded solutions in particular this is the case for observable systems with at least one eigenvalue in the open right half plane rhp the case of systems with no eigenvalues in the open rhp but with eigenvalues on the j omega axis is still unresolved

robust output feedback controller design via local bmi optimization the problem of designing a globally optimal full order output feedback controller for polytopic uncertain systems is known to be a non convex np hard optimization problem that can be represented as a bilinear matrix inequality optimization problem for most design objectives in this paper a new approach is proposed to the design of locally optimal controllers it is iterative by nature and starting from any initial feasible controller it performs local optimization over a suitably defined non convex function at each iteration the approach features the properties of computational efficiency guaranteed convergence to a local optimum and applicability to a very wide range of problems furthermore a fast but conservative lmi based procedure for computing an initially feasible controller is also presented the complete approach is demonstrated on a model of one joint of a real life space robotic manipulator

regularity of solutions to a model for solid solid phase transitions driven by configurational forces abstract in a previous work we prove the existence of weak solutions to an initial boundary value problem with h 1 initial data for a system of partial differential equations which consists of the equations of linear elasticity and a nonlinear degenerate parabolic equation of second order this problem models the behavior in time of materials with martensitic phase transitions this model with diffusive phase interfaces was derived from a model with sharp interfaces whose evolution is driven by configurational forces and can be regarded as a regularization of that model assuming in this article the initial data is in h 2 we investigate the regularity of weak solutions that is difficult due to the gradient term which plays a role of a weight our proof in which the difficulties are caused by the weight in the principle term is only valid in one space dimension

on periodic solutions of second order differential equations with attractive repulsive singularities abstract sufficient conditions for the existence of a solution to the problem u t g t u t h t u t f t for a e t 0 u 0 u u 0 u are established

the difference periodic ricati equation for the periodic prediction problem gives a comprehensive treatment of several important aspects of the discrete time periodic riccati equation dpre arising from the prediction problem for linear discrete time periodic systems the authors analyze the symmetric periodic positive semidefinite spps solution of the dpre under appropriate assumptions of stabilizability and detectability of the periodic system among the results obtained are necessary and sufficient conditions for the existence and uniqueness of the spps solution and the stability of the resulting closed loop system some of these results can be seen as extensions of the corresponding results for the time invariant case however a number of them contain contributions to the time invariant case as well the paper also gives a numerical algorithm based on an iterative linearization procedure for computing the spps solution the algorithm is a periodic version of kleinman s algorithm for the time invariant case

stabilizability and detectability of linear periodic systems abstract in this paper four characterizations of stabilizability and detectability of linear periodic systems are considered two of them look as natural extensions of the classical definitions given for time invariant systems the remaining two are modal characterizations which turn out to be useful in the analysis of the periodic lyapunov and riccati equations it is shown that all these notions of stabilizability and detectability are in fact equivalent to each other one of the various definitions calls for the existence of the kalman canonical decomposition of periodic systems this issue is addressed in the appendix

solvability via viscosity solutions for a model of phase transitions driven by configurational forces abstract this article is concerned with an initial boundary value problem for an elliptic parabolic coupled system arising in martensitic phase transition theory of elastically deformable solid materials e g steel this model was proposed in alber and zhu 2007 4 and investigated in alber and zhu 2006 3 the existence of weak solutions which are defined in a standard way however the key technique used in alber and zhu 2006 3 is not applicable to multi dimensional problem one of the motivations of this study is to solve this multi dimensional problem and another is to investigate the sharp interface limits thus we define weak solutions in a way which is different from alber and zhu 2006 3 by using the notion of viscosity solution we do prove successfully the existence of weak solutions in this sense for one dimensional problem yet the multi dimensional problem is still open

on the structure of digital controllers with finite word length consideration it is well known that a stable discrete time control system may become unstable when the digital controller is actually implemented with a digital control processor due to the finite word length effects and that the stability behavior of the system depends on the structure of the digital controller due to the difficulties in adopting the existing stability robustness measures a new measure is derived which is tractable and hence enables us to handle the digital controller structure problem easily the optimal controller structure problem is formulated by maximizing this measure an analytical solution is presented an algorithm is developed for finding sparser structures

local superlinearity and sublinearity for indefinite semilinear elliptic problems in this paper the usual notions of superlinearity and sublinearity for semilinear problems like du f x u are given a local form and extended to indefinite nonlinearities here f x s is allowed to change sign or to vanish for s near zero as well as for s near infinity some of the well known results of ambrosetti bre zis cerami are partially extended to this context

periodic solutions to second order indefinite singular equations abstract the efficient conditions guaranteeing the existence of a t periodic solution to the second order differential equation u h t g u are established in the paper here g is a positive and decreasing function which has a strong singularity at the origin and the weight h l r t z is a sign changing function the obtained results have the form of relation between the multiplicities of the zeroes of the weight function h and the order of the singularity of the nonlinear term the approach is based on leray schauder degree theory proving that no t periodic solution of a certain homotopy appears on the boundary of an unbounded open set during the deformation to an autonomous problem

estimates of asymptotic trajectory bounds in digital implementations of linear feedback control systems estimates are established for trajectory bounds which are easy to calculate applicable to general controller topologies and dependent on parameters i e eigenvalues and eigenvectors of the idealized linear system i e the control system model neglecting quantizers the approach utilizes the comparison principle in the lyapunov theory and the properties of minimal matrix norms the applicability of the results are demonstrated by means of a specific example

a µ based optimal finite word length controller design a novel optimal finite word length fwl controller design is proposed in the framework of m theory a computationally tractable close loop stability measure with fwl implementation considerations of the controller is derived based on the m theory and the optimal fwl controller realizations are obtained by solving the resulting optimal fwl realization problem using linear matrix inequality techniques