the standard ℋ2 optimal control problem a polynomial solution in this paper we present a solution to the standard 2 control problem the solution presented here is based upon the algebra of polynomials and in particular we use the polynomial equation approach in considering the scalar version of the standard 2 problem we derive a couple of linear polynomial diophantine equations which define the optimal regulator the coefficients of these equations are obtained from polynomial spectral factorization

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

polynomial lq optimization for the standard control structure scalar solution abstract the problem of lq optimization for the standard control structure is studied we obtain a solution for the scalar case of this problem using the polynomial equation approach in solving the optimal regulation problem using polynomial techniques we derive a couple of linear polynomial equations which together define the unique optimal regulator the coefficients of these equations are obtained from polynomial spectral factorization

optimal h robustness and the relationship to lqg design problems a solution to the hx optimal control problem is obtained by employing a standard lqg polynomial based solution procedure the derivation is straightforward and avoids many of the more abstract mathematical results usually employed the relationship between the lqg and hm design methods becomes transparent and the similarities and differences can be identified

lqg control with an h sup infinity performance bound a riccati equation approach an lqg linear quadratic gaussian control design problem involving a constraint on h sup infinity disturbance attenuation is considered the h sup infinity performance constraint is embedded within the optimization process by replacing the covariance lyapunov equation by a riccati equation whose solution leads to an upper bound on l sub 2 performance in contrast to the pair of separated riccati equations of standard lqg theory the h sup infinity constrained gains are given by a coupled system of three modified riccati equations the coupling illustrates the breakdown of the separation principle for the h sup infinity constrained problem both full and reduced order design problems are considered with an h sup infinity attenuation constraint involving both state and control variables an algorithm is developed for the full order design problem and illustrative numerical results are given

brief wiener hopf design of the optimal decoupling control system with state space formulas the optimal decoupling controller minimizing a given quadratic cost function is derived for the generalized plant model with two degree of freedom controller configuration a minimal set of assumptions for the existence of the optimal controller is presented in both the frequency and the state space domains the optimal controller formula is described in the frequency domain and the corresponding state space formula is derived for computational efficiency

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

viscosity solutions for weakly coupled systems of first order partial differential equations abstract we consider viscosity solutions for weakly coupled systems of first order partial differential equations and apply these existence and uniqueness results to examples involving random evolutions

polynomial solution of the standard multivariable spl hscr sub 2 optimal control problem in this work the authors solve the standard multivariable spl hscr sup 2 optimal control problem using polynomial matrix techniques

improved decay estimates in time dependent stokes flow abstract this paper investigates the time dependent stokes flow of a viscous fluid in a channel with nonzero net entry flow assuming the fluid to be initially at rest with entry flow at the finite end of a semi infinite channel energy bounds for the flow are derived it is shown that the flow decays exponentially in energy norm to a transient poiseuille flow as the distance from the finite end tends to infinity the problem was previously investigated by lin saacm 2 1992 249 264 for the case in which the net entry flow was zero our methods are patterned after those of lin but a somewhat better choice of arbitrary constants yields an improved decay rate for lin s problem

optimal multivariable lqg control using a single diophantine equation the general solution of the optimal lqg problem using the polynomial equation approach involves the solution of a couple of two sided matrix polynomial equations the conditions under which a single one sided equation which is related to the original two the implied diophantine equation yields the unique optimal controller are derived in this paper the result has considerable relevance to aspects such as computation and self tuning control applications

optimal switching for ordinary differential equations we consider the problem of controlling an ordinary differential equation subject to positive switching costs and show in particular that the value functions form the viscosity solution cf 6 7 of the dynamic programming quasi variational inequalities this interpretation allows for a rigorous application of various dynamic programming techniques

all optimal hankel norm approximations of linear multivariable systems and their l error bounds the problem of approximating a multivariable transfer function g s of mcmillan degree n by s of mcmillan degree k is considered a complete characterization of all approximations that minimize the hankel norm is derived the solution involves a characterization of all rational functions s f s that minimize where s has mcmillan degree k and f s is anticavisal the solution to the latter problem is via results on balanced realizations all pass functions and the inertia of matrices all in terms of the solutions to lyapunov equations it is then shown that where k 1 g s is the k l st hankel singular value of g s and for one class of optimal hankel norm approximations the method is not computationally demanding and is applied to a 12 state model

spatial decay bounds for double diffusive convection in brinkman flow abstract this paper examines the time dependent double diffusive convection in brinkman flow in a semi infinite cylinder under appropriate initial and boundary conditions the authors establish exponential decay of solutions in energy norm with distance from the finite end of the cylinder

linear control theory with an h 0e optimality criterion this expository paper sets out the principal results in bf h infty control theory in the context of continuous time linear systems the focus is on the mathematical theory rather than computational methods

polynomial design of stochastic tracking systems a new technique to design optimal stochastic tracking systems is presented for single input output plants described by rational transfer functions the optimal controller is shown to consist of feedback and feedforward parts and it is designed by solving two couples of linear polynomial equations whose coefficients are obtained by spectral factorization

on general ℋ2 control from frequency to time domain this article presents a general formula for discrete time 2 control it works with the regular and singular case of 2 control i e in the case of possibly non left invertible matrices g 12 and non right invertible matrices g 21 with possible unit circle invariant zeros in the generic case it can be simplified and adapted to work with the plant transfer matrix directly without invoking the matrices of the parameterisation of stabilising controllers a further result of this article is the presented necessary and sufficient conditions for state space 2 control under only stabilisability and detectability assumptions if the conditions are satisfied an observer based 2 controller is constructed the corresponding numerical algorithm consists of solving two discrete time algebraic riccati systems darss and two eigen problems

the parabolic bellman equation where q e q x 0 t for some smooth bounded domain sz c w apq denotes the parabolic boundary of q and each l is a second order uniformly elliptic operator of the form lku afj x t uxixj b x t u ek x r u 1 oandall x t eq iw ck 0 1 k m and also 1 3

optimal multivariable regulation with disturbance measurement feedforward abstract the problem of optimal stochastic regulation based on output feedback and disturbance measurement feedforward for multivariable systems is solved using the polynomial equation approach two independent couples of polynomial matrix equations are derived which yield the feedback and the feedforward parts of the regulator

wiener hopf design of optimal decoupling controllers for plants with non square transfer matrices an important consideration in the design of many control systems is decoupling each command input controlling only one output the two degree of freedom or three degree of freedom controller structure is ideally suited to this task since only one of the degrees of freedom is affected by the decoupling requirement the decoupling constraint on this degree of freedom however can lead to some deterioration in achievable system performance a wiener hopf design procedure which minimizes this performance deterioration is described here for plants with non square transfer matrices moreover the parametrization of the class of all decoupled systems is given for which the cost functional representing system performance remains finite

technical communique wiener hopf approach to derivation of rational doubly coprime factorizations this paper presents a method to construct a stable rational doubly coprime factorization dcf of a transfer matrix proper or improper from a given polynomial dcf wiener hopf factor polynomials are used to rationalize the polynomial dcf matrices it is shown that the suggested construction procedure results in the stable rational dcf description that includes the normalized matrix fractional description mfd and inner coprime mfd as special cases

the optimal projection equations with petersen hollot bounds robust stability and performance via fixed order dynamic compensation for systems with structured real valued parameter uncertainty a feedback control design problem involving structured real valued plant parameter uncertainties is considered a quadratic lyapunov bound suggested by recent work of i r petersen and c v hollot 1986 is utilized in conjunction with the guaranteed cost approach of s s l chang and t k c peng 1972 to guarantee robust stability with robust performance bound necessary conditions that generalize the optimal projection equations for fixed order dynamic compensation are used to characterize the controller that minimizes the performance bound the design equations thus effectively serve as sufficient conditions for synthesizing dynamic output feedback controllers that provide robust stability and performance

h 2 design of one degree of freedom decoupling controllers for square plants decoupling design of one degree of freedom controllers is treated for the generalised plant model within the h 2 framework the class of all realisable closed loop transfer matrices is parametrised under a mild assumption on non unity feedback sensors a set of compact assumptions is presented to guarantee the existence of the optimal h 2 controller together with the optimal one the class of all h 2 controllers that yield finite h 2 cost is obtained the optimal closed transfer matrix and its associated controller are shown to be strictly proper under the reasonable order assumptions on the generalised plant

the h2 control problem a general transfer function solution a general solution of the h2 control problem is presented for linear systems described by rational transfer matrices not necessarily proper or stable the control system is considered in the standard configuration which includes the synthesis model of the plant and the controller the h2 control problem consists of internally stabilizing the control system while minimizing the h2 norm of its transfer function the notion of internal stability is based on bounded input bounded output stability and means that subsystems defined by any pair of input and output signals within the control system all are bounded input bounded output stable in this manner the optimal control system is devoid of impulsive as well as non decaying exponential modes the solution proceeds in three steps first the set of all controllers that internally stabilize the control system is parameterized then the subset of the stabilizing controllers that achieve a finite value of the h2 norm of the control system transfer matrix is

a general theory for the wiener hopf design of multivariable control systems multivariable control system design in a quadratic cost setting is treated for a completely general configuration the class of all controllers is determined for which the general configuration is internally asymptotically stable and a quadratic cost functional is finite this controller class is parameterized in terms of an arbitrary real rational strictly proper matrix z s which is analytic in the closed right hand side of the s plane the choice z identical to 0 gives the controller which minimizes the quadratic cost functional

fifo stable control systems abstract motivated by the dead beat and shortest correlation control strategies the paper introduces the notion of finite input finite output fifo stability for linear discrete time control systems a simple parametrization of all controllers that fifo stabilize a given plant is obtained the best controller is then chosen for various applications including h 2 optimization disturbance rejection and transfer function shaping

simplified formula for a controller in optimal control problems we derive a simplified frequency domain formula for a controller transfer matrix for lq optimal output feedback control of stochastic systems for this purpose we apply a generalization of the wiener hopf method the generalization is characterized by the following three properties 1 we generalize the usual operator cdot on rational matrices in the traditional wiener hopf approach the same algorithms as for computation of cdot are applicable to compute the new operator 2 the matrices of the youla kuccera parametrization do not appear in the optimal controller transfer matrix bf c they appear only in its derivation even if the plant is unstable 3 unlike the traditional wiener hopf method d c youla h a jabr and j j bongiorno jr ieee trans automat control ac 21 1976 pp 319 338 where the spectral factors in the two spectral factorizations are both stable and minimum phase our spectral factors need to be minimum phase only finally three state space applications of the formula are presented

comments on optimizing simultaneously over the numerator and denominator polynomials in the youla kucera parameterization it is noted that the parameterization of the set of stabilizing regulators was first presented in a monograph by larin v b naumenko k i and suntsev v n

the constrained lyapunov problem and its application to robust output feedback stabilization given a dynamical system whose description includes time varying uncertain parameters it is often desirable to design an output feedback controller leading to asymptotic stability of a given equilibrium point when designing such a controller one may consider static i e memoryless or dynamic compensation in this paper we show that solvability of various output feedback design problems is implied by existence of a solution to a certain constrained lyapunov problem clp the clp can be stated in purely algebraic terms once the clp is described we provide necessary and sufficient conditions for its solution to exist subsequently we consider application of the clp to a number of robust stabilization problems involving static output feedback and observer based feedback

disturbance attenuation and h optimization a design method based on the algebraic riccati equation this note presents a method for designing a state feedback control law to reduce the effect of disturbances on the output of a given linear system the problem under consideration involves attenuating the disturbances to a prespecified level the construction of the state feedback control law requires the solution of a certain algebraic riccati equation by applying the procedure with successively smaller values of the prespecifled disturbance level the result also provides an approach to the h infty optimization problem for the state feedback case

parameterization of decoupling controllers in the generalized plant model a diagonal decoupling problem in linear multi variable systems is formulated for the most general setting a necessary and sufficient condition for the existence of a decoupling controller is presented and when a solution exists the class of all decoupling controllers is characterized in terms of free parameters of stable rational vectors

optimal control of partially observable stochastic systems with an exponential of integral performance index the stochastic control problem with linear stochastic differential equations driven by brownian motion processes and as cost functional the exponential of a quadratic form is considered the soluti

wiener hopf design of optimal decoupled multivariable feedback control system an important consideration in the design of many control systems is decoupling each command input controlling only one output the 2dof two degree of freedom or 3dof three degree of freedom structure is ideally suited to this task since only one of the degrees of freedom is affected by the decoupling requirement the decoupling constraint on this degree of freedom however can lead to some deterioration in achievable system performance a design procedure which minimizes this performance deterioration is established the parameterization of the class of all decoupled systems is given for which the cost functional representing system performance remains finite

a feedback theory of two degree of freedom optimal wiener hopf design the design of linear two degree of freedom stabilizing controllers is treated in a quadratic cost setting the class of all such controllers which give finite cost is established and the tradeoff possible between optimum performance tracking cost sensitivity and stability margins is discussed

persistent inputs and the standard h 2 multivariable control problem the h 2 control problem is formulated with exogenous inputs having unstable shape deterministic components such inputs are called persistent some issues in connection with past solutions of the h 2 control problem in this case are carefully described and addressed in particular it is established that two and three degree of freedom 2dof and 3dof systems with persistent inputs cannot be treated within the framework of the standard configuration in addition past treatments of persistent inputs within the framework of the generalised 2dof configuration focused on solutions which yielded stable error transforms without explicitly requiring the same for controller outputs in this article a more general configuration is treated and physical considerations are invoked to justify imposition of the requirement that both the regulated variable z s and the controller output u s be stable a persistent input model for which there exists a stabilising controller that makes both z s and u s stable is cal

multiple objective optimal control of linear systems the quadratic norm case control of a linear system to meet requirements embodied in multiple performance criteria is recognized as the typical design problem the authors study the design of control when every criterion of interest takes the form of an h sub 2 norm defined over certain exogenous inputs and controlled outputs of the system the objective is to find all stabilizing controllers that are noninferior with respect to the defined objectives that is to find the set of pareto optimal controllers the novel feature is the use of the youla parametrization to represent the admissible controllers this representation enables the authors to show that each criterion and hence their weighted sum is convex over the class of admissible controllers since the set of admissible controllers is itself convex the pareto optimal controllers can be determined by the standard scalarization technique it is concluded that in general the controller order is higher than the order of the plant

the general distance problem in h optimal control theory abstract the general distance problem that arises in h optimal control theory is considered transformations that reduce the general h problem to the general distance problem are reviewed and an iterative scheme called iteration is considered in which the general distance problem is reduced to a standard best approximation problem the iteration is viewed as a problem of finding the zero crossing of a function this function is shown to be continuous monotonically decreasing convex and bounded by some very simple functions these properties make it possible to obtain very rapid convergence of the iterative process the issues of model reduction and approximation in h synthesis will also be addressed

optimal parallel model solutions using the polynomial approach solutions to the optimal filtering and open loop control problems using a generalized parallel model scheme are presented the solutions are based on the algebra of polynomial matrices different c

decay estimates for homogeneous boussinesq equations in a semi infinite pipe abstract in this paper we establish the spatial decay bounds for homogeneous boussinesq equations in a semi infinite pipe flow assuming that the entrance velocity and magnetic field data are restricted appropriately and it converges to laminar flow as the distance down the pipe tends to infinity we derive a second order differential inequality that leads to an exponential decay estimate for the energy e z t defined in 27 we also indicate how to establish the explicit bound for the total energy

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

stability robustness bounds for linear state space models with structured uncertainty in this note we consider the robust stability analysis problem in linear state space models we consider systems with structured uncertainty some lower bounds on allowable perturbations which maintain the stability of a nominally stable system are derived these bounds are shown to be less conservative than the existing ones

implied polynomial matrix equations in multivariable stochastic optimal control abstract this paper reports recent work in the theoretical development of the polynomial equation approach to the optimization of multivariable control systems the algebraic properties of the polynomial matrix equations which define the optimal controller are investigated and new results concerned with the numerical solvability of the equations are derived

a coprime factorisation and its application in ℋ2 control given a plant transfer matrix as a fraction of two polynomial matrices we present a doubly coprime factorisation identity over the proper stable rational matrices of the plant transfer matrix and

the lqg ltr procedure for multivariable feedback control design this paper provides a tutorial overview of the lqg ltr design procedure for linear multivariable feedback systems lqg ltr is interpreted as the solution of a specific weighted h2 tradeoff between transfer functions in the frequency domain properties of this solution are examined for both minimum phase and nonminimum phase systems this leads to a formal weight augmentation procedure for the minimum phase case which permits essentially arbitrary specification of system sensitivity functions in terms of the weights while such arbitrary specifications are not possible for nonminimum phase problems a direct relationship between weights and sensitivities is developed for nonminimum phase siso and certain nonminimum phase mimo cases which guides the weight selection process

spatial decay estimates in time dependent double diffusive darcy plane flow this paper considers the time dependent double diffusive convective darcy flow in a semi infinite channel an exponential decay estimate in terms of the distance from the finite end of the channel is obtained from a second order differential inequality for a weighted energy integral the paper also indicates how to bound the total weighted energy

state space formulae for all stabilizing controllers that satisfy and h norm bound and relations to risk sensitivity abstract given a linear system all stabilizing controllers such that a specified closed loop transfer function has h norm less than a given scalar are parametrized this characterization involves the solution to two algebraic riccati equations each with the same order as the system and further gives gives feasible controllers also with this order the relationship to the risk sensitive lqg stochastic control problem is established giving an equivalence between robust and stochastic control

polynomial lqg regulator design for general system configurations a polynomial equation approach to the linear quadratic gaussian lqg regulation problem for a general system configuration is presented the solution is given in terms of a left spectral factorization plus a pair of bilateral diophantine equations the resulting control design procedure is based on an innovations representation of the system this can be obtained from a physical description by solving via polynomial equations a minimum mean square error filtering problem the use in cascade of the above two procedures allows one to generalize previous polynomial design results to general system configurations

h2 optimal control of linear systems with tracking disturbance rejection constraints this paper considers the design of two degree of freedom linear multivariable controllers for four block matrix transfer functions with objectives pertaining to both random and deterministic signals the former are taken into account in the cost functional whereas the latter entail that the controller is constrained to solve a servomechanism problem involving a class of reference signals and two classes of disturbances the cost functional is set up by adding quadratic terms to the usual lqg wiener hopf cost in such a way as to ensure the existence of unique solutions even when the signals to be tracked rejected as well as models have poles on the imaginary axis the solutions of the servomechanism problem are explicitly parametrized by free stable rational and proper parameters under two sets of assumptions one which is necessary and sufficient for the existence of solutions and another stronger set which avoids kronecker products and the associated higher dimensional factorizations involved in

wiener hopf design of the general two degree of freedom controllers and the connection to state space formulas h 2 design of the two degree of freedom controller configuration is treated for the generalized plant in both the frequency and state space domains a frequency domain wiener hopf formula is derived first under a set of compact assumptions that gives the entire class of controllers for which the feedback control system is stable and a quadratic cost functional is finite the h 2 design method suggested in this paper allows the reference inputs to include the persistent signals such as step or ramp functions and the class of persistent reference inputs that can be tracked with zero steady state error is characterized explicitly to circumvent the computational difficulties of the wiener hopf formulas the corresponding state space domain formulas are derived by rationalizing the polynomial fractional descriptions it is shown that the well known standard time domain assumptions for the h 2 design problem have the corresponding equivalent frequency domain conditions and this equivalence relationship is show

spatial decay in a double diffusive convection problem in darcy flow this paper deals with a model of time dependent double diffusive convection in darcy flow in particular it is concerned with the spatial decay of solutions when the flow is confined to a semi infinite cylinder decay bounds for an energy expression are derived

general polynomial solution to the optimal feedback feedforward stochastic tracking problem a general solution to the optimal stochastic tracking problem in the presence of both measurable and immeasurable disturbances is obtained using polynomial techniques the plant under consideration includes a coloured measurement noise signal in addition all disturbance and reference sub systems may be unstable the problem formulation involves a cost function which has dynamic weighting elements a feedforward compensator is incorporated in the optimization procedure for the rejection of the measurable disturbance

extension of linear quadratic optimal control theory for mixed backgrounds the problem of finding an optimal controller while both deterministic and stochastic signals are present in the feedback system is addressed a general framework is developed to solve the above problem and to unify conventional frequency domain lq and lqg optimal control theories both the system transient and steady state behaviours are considered and the exact tracking of the arbitrary reference signal is guaranteed the decomposition of a mixed signal into the deterministic and stochastic parts gives a chance to investigate the effect of the weighting factors which were specified in the cost function on the compromise between transient and steady state system performance the solution which characterizes the structure of the optimal controller results in a set of independent diophantine equations instead of a set of coupled ones moreover the number of equations can be reduced under weak conditions finally both transient command tracking and steady state noise rejection capabilities can be op

viscosity solutions for weakly coupled systems of hamilton jacobi equations we obtain comparison results for viscosity solutions of weakly coupled systems of hamilton jacobi equations perron s method is extended to give existence proofs for systems a stronger definition of sub and supersolutions is introduced leading to existence results for continuous solutions the needed sub and supersolutions are constructed for continuous boundary data crandall s and lions notion of viscosity solutions for first order hamilton jacobi equations can be extended in a componentwise way to systems a key tool in obtaining uniqueness comparison and existence results is the maximum principle we obtain such results for weakly coupled systems of hamilton jacobi equations in which the coupling has such a structure to allow the use of maximum principle techniques to motivate the coupling assumptions consider this linear system n

stability radius for structured perturbations and the algebraic riccati equation abstract in this paper we generalize the notion of stability radius introduced in 1 to allow for structured perturbations we then relate the stability radius to the existence of hermitian solutions of an algebraic riccati equation and give some applications of this result

the optimal projection equations for fixed order dynamic compensation first order necessary conditions for quadratically optimal steady state fixed order dynamic compensation of a linear time invariant plant in the presence of disturbance and observation noise are derived in a new and highly simplified form in contrast to the pair of matrix riccati equations for the full order lqg case the optimal steady state fixed order dynamic compensator is characterized by four matrix equations two modified riccati equations and two modified lyapunov equations coupled by a projection whose rank is precisely equal to the order of the compensator and which determines the optimal compensator gains the coupling represents a graphic portrayal of the demise of the classical separation principle for the reduced order controller case

continuous dependence on the soret coefficient for double diffusive convection in darcy flow in this paper the darcy model is used to describe the double diffusive flow of a fluid containing a solute continuous dependence of the solution on the soret coefficient is established

a riccati equation approach to the stabilization of uncertain linear systems this paper presents a method for designing a feedback control law to stabilize a class of uncertain linear systems the systems under consideration contain uncertain parameters whose values are known only to within a given compact bounding set furthermore these uncertain parameters may be time varying the method used to establish asymptotic stability of the closed loop system obtained when the feedback control is applied involves the use of a quadratic lyapunov function the main contribution of this paper involves the development of a computationally feasible algorithm for the construction of a suitable quadratic lyapunov function once the lyapunov function has been obtained it is used to construct the stabilizing feedback control law the fundamental idea behind the algorithm presented involves constructing an upper bound for the lyapunov derivative corresponding to the closed loop system this upper bound is a quadratic form by using this upper bounding procedure a suitable lyapunov function can be found by solving a certain matrix riccati equation another major contribution of this paper is the identification of classes of systems for which the success of the algorithm is both necessary and sufficient for the existence of a suitable quadratic lyapunov function

a polynomial approach to the mimo lq servo and disturbance rejection problems abstract a novel matrix fraction solution to the discrete time lq stochastic tracking and servo problems is extended to the disturbance rejection problem unlike recent contributions here the resulting control law at time t is given in terms of an expectation conditioned to the accessible disturbance given up to time t k if k is positive and large enough the optimal feedforward input can be tightly approximated without requiring any stochastic model for the disturbance if the latter is known also for recurrent or predictable disturbance the optimal feedforward input is obtained by solving a single bilateral diophatine equation

some properties of viscosity solutions of hamilton jacobi equations abstract recently m g crandall and p l lions introduced the notion of viscosity solutions of scalar nonlinear first order partial differential equations viscosity solutions need not be differentiable anywhere and thus are not sensitive to the classical problem of the crossing of characteristics the value of this concept is established by the fact that very general existence uniqueness and continuous dependence results hold for viscosity solutions of many problems arising in fields of application the notion of a viscosity solution admits several equivalent formulations here we look more closely at two of these equivalent criteria and exhibit their virtues by both proving several new facts and reproving various known results in a simpler manner moreover by forsaking technical generality we hereby provide a more congenial introduction to this subject than the original paper author

mixed h2 h problems approximated solutions by galerkin methods this paper presents a galerkin method to solve the mixed h2 h optimal control problem in this method the generator set is built step by step by an optimization procedure algorithm convergence is proved in the setting of weighted hardy spaces some examples are discussed showing the accelerated convergence obtained by this new algorithm and its numerical features a particular quadratic optimal control problem on finite dimensional linear systems under robustness constraints is developed as a motivation for the mixed h2 h problem

feedback properties of multivariable systems the role and use of the return difference matrix for linear time invariant multivariable feedback systems the feedback properties of plant disturbance attenuation sensor noise response stability margins and sensitivity to plant and sensor variation are quantitatively related to the bode magnitude versus frequency plots of the singular values of the return difference matrix i l and of the associated inverse return difference matrix i l 1 implied fundamental limits of feedback performance are quantitatively described and design tradeoffs are discussed the penalty function in the stochastic linear quadratic gaussian lqg optimal control problem is found to be a weighted sum of the singular values with the weights determined by the quadratic cost and noise intensity matrices this enables systematic tuning of lqg cost and noise matrices so that the resulting optimal return difference and inversereturn difference meet inequality constraints derived from design specifications on feedback properties the theory has been used to synthesize a multivariable automatic controller for the longitudinal dynamics of an advanced fighter aircraft

on the wiener hopf approach to optimal feedback design abstract a simple solution is given to the problem of designing a proper feedback which minimizes the h 2 norm of the sensitivity function multiplied by a suitable weighting function

synthesis of linear multivariable regulators this paper generalizes the results obtained by the authors in 1 and presents new results on the construction of proper controllers for linear multivariable regulators these results may lead to efficient computation methods that do not involve smith forms or the order relations used in 1 to construct proper controllers the methods are based on the recently developed theory of generalized polynomials 2 we discuss several numerical algorithms and how they can be applied to the regulator problem we also point out an important computational problem in need of an efficient numerical algorithm