generalized l sub 2 synthesis introduces a general framework for control design which can be used to solve several open problems in robust and optimal control these include systems subject to independently norm bounded disturbances robust stability for systems subject to element by element bounded structured uncertainty certain classes of robust performance problems and systems subject to deterministic white noise disturbances this is achieved by combining concepts such as h infinity optimization linear matrix inequalities and integral quadratic constraints necessary and sufficient conditions for the general problem to have a solution are in terms of a computationally attractive finite dimensional linear matrix inequality

h 2 optimal control with an h constraint the state feedback case in this paper we consider a mixed hz optimal control problem it is assumed that the plant as well as the feedback controller are finite dimensional and linear time invariant and that the plant state is available for feedback more specifically among all the state feedback controllers that minimize the he norm of a closed loop transfer matrix we give necessary and sufficient conditions for the existence of a controller that also satisfies a prescribed h norm bound on some other closed loop transfer matrix when these conditions are met the solution to the above problem is also a global solution to the contrained optimization problem of minimizing an he norm performance measure subject to an h norm constraint we also give state space formulae for computing the solutions some easily checkable sufficient conditions for the existence of solutions are given finally we give an example in which all solutions to the constrained optimization problem are necessarily dynamic i e there is no static gain solution even though plant state is available for feedback

brief a parametric optimization approach to h and h2 strong stabilization this paper presents an approach for designing stable mimo h and h 2 controllers by directly computing the norm constrained stable transfer matrices q in the h and h 2 suboptimal controller parameterizations this is done by first converting the h 2 and h strong stabilization problems into some nonlinear unconstrained optimization problems through explicit parameterization of the norm constrained q s for any fixed order then a two stage numerical search is carried out by using a combination of a genetic algorithm and a quasi newton algorithm in order to reach an optimal solution the effectiveness of the proposed algorithms is illustrated through some benchmark numerical examples

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

gradient estimates for variable coefficient parabolic equations and singular perturbation problems in this article we prove via monotonicity formulas interior and boundary gradient esti mates for solutions to second order parabolic equations in divergence form with dini top order coefficients we then prove uniform lipschitz estimates for solutions of singular perturbation prob lems using the previous results and two phase monotonicity formulas introduction the purpose of this paper is to study the regularity of spatial gradients of solutions to second order uniformly parabolic equations in divergence form with bounded lower order terms and dini continuous coefficients and also to establish uniform spatial lipschitz estimates for some singular perturbation problems in the same context in part 1 we obtain interior and boundary estimates for solutions to these linear equations as is well known the weakest assumption on the modulus of continuity of the top order terms to obtain interior continuity of the gradient of solutions is dini continuity see part 1 for the relevant definitions see for instance g w in the elliptic case the usual approach to such results is to use appropriate potentials here we use a monotonicity formula approach theo rem 1 2 9 which we believe is new the approach has the advantage that it allows us to show that dini continuity of the coefficients at a given point yields bound edness of the gradient at the same point using our monotonicity formula the fact that linear functions are almost solutions and a geometric argument from cl we also obtain under uniform dini continuity of the coefficients a uniform modulus of continuity estimate for gradients of solutions theorem 1 3 1 the fact that the monotonicity formula at a point depends only on the dini continuity at that same point enables us to use a simple reflection argument to extend these results up to the boundary theorem 1 4 5 and theorem 1 4 12 we thus obtain a modulus of continuity estimate up to the boundary for gradients of solutions with smooth dirichlet data under uniform dini continuity of the top order coeffi cients once this is established a compactness argument theorem 1 5 10 and a judicious application of harnack s principle allow us to obtain a hopf maximum principle theorem 1 5 10 corollary 1 5 13 and corollary 1 5 16 for our class of equations

quantum feedback control of linear stochastic systems with feedback loop time delays in a quantum feedback control loop one is often confronted with time delays that mainly originated from the transition delay of signals which may cause the quantum feedback control system unstable the purpose of this paper is to deal with a problem of quantum measurement based feedback control subject to feedback loop time delays a quantum version of delay independent stability criterion as well as an upper bound on a cost function is derived based on quantum it rules we propose one numerical procedure for quantum feedback controller designs which is then illustrated by an example

cavity type problems ruled by infinity laplacian operator abstract we study a singularly perturbed problem related to infinity laplacian operator with prescribed boundary values in a region we prove that solutions are locally uniformly lipschitz continuous they grow as a linear function are strongly non degenerate and have porous level surfaces moreover for some restricted cases we show the finiteness of the n 1 dimensional hausdorff measure of level sets the analysis of the asymptotic limits is carried out as well

multiobjective output feedback control via lmi optimization this paper presents an overview of a linear matrix inequality lmi approach to the multiobjective synthesis of linear output feedback controllers the design objectives can be a mix of h sub spl infin performance h sub 2 performance passivity asymptotic disturbance rejection time domain constraints and constraints on the closed loop pole location in addition these objectives can be specified on different channels of the closed loop system when all objectives are formulated in terms of a common lyapunov function controller design amounts to solving a system of linear matrix inequalities the validity of this approach is illustrated by a realistic design example

optimal discrete time h γ 0 filtering and control under unknown covariances abstractnew stochastic 0 and mixed h 0 filtering and control problems for discrete time systems under completely unknown covariances are introduced and solved the performance measure 0 is the worst case steady state averaged variance of the error signal in response to the stationary gaussian white zero mean disturbance with unknown covariance and identity variance the performance measure h 0 is the worst case power norm of the error signal in response to two input disturbances in different channels one of which is the deterministic signal with a bounded energy and the other is the stationary gaussian white zero mean signal with a bounded variance provided the weighting sum of disturbance powers equals one in this framework it is possible to consider at the same time both deterministic and stochastic disturbances highlighting their mutual effects our main results provide the complete characterisations of the above performance measures in terms of linear matrix inequalities and therefore both th

necessary and sufficient conditions for mixed h sub 2 and h sub infinity optimal control it is shown that d s bernstein and w m hadad s ibid vol 34 no 3 p 293 1989 necessary condition for full order mixed h sub 2 and h sub infinity optimal control is also sufficient and that j c doyle et al s proc amer control conf p 2065 1989 sufficient condition for full order mixed h sub 2 and h sub infinity optimal control is also necessary they are duals of one another

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

a generalized multi period mean variance portfolio optimization with markov switching parameters in this paper we deal with a generalized multi period mean variance portfolio selection problem with market parameters subject to markov random regime switchings problems of this kind have been recently considered in the literature for control over bankruptcy for cases in which there are no jumps in market parameters see zhu s s li d wang s y 2004 risk control over bankruptcy in dynamic portfolio selection a generalized mean variance formulation ieee transactions on automatic control 49 447 457 we present necessary and sufficient conditions for obtaining an optimal control policy for this markovian generalized multi period mean variance problem based on a set of interconnected riccati difference equations and on a set of other recursive equations some closed formulas are also derived for two special cases extending some previous results in the literature we apply the results to a numerical example with real data for risk control over bankruptcy in a dynamic portfolio selection problem with markov jumps selection problem

up to boundary regularity for a singular perturbation problem of p laplacian type equations in non divergence form abstract we prove interior and up to boundary lipschitz regularity of the viscosity solutions to a singular perturbation problem for a reaction diffusion equation related to the normalized p laplacian equation

probability one homotopy algorithms for solving the coupled lyapunov equations arising in reduced order h2 h modeling estimation and control optimal reduced order modeling estimation and control with respect to combined h 2 h criteria give rise to coupled lyapunov and riccati equations to develop reliable numerical algorithms for these problems this paper focuses on the coupled lyapunov equations which appear as a subset of the synthesis equations in particular this paper systematically examines the requirements of probability one homotopy algorithms to guarantee global convergence homotopy algorithms for nonlinear systems of equations construct a continuous family of systems and solve the given system by tracking the continuous curve of solutions to the family the main emphasis is on guaranteeing transversality for several homotopy maps based upon the pseudogramian formulation of the coupled lyapunov equations and variations based upon canonical forms these results are essential to the probability one homotopy approach by guaranteeing good numerical properties in the computational implementation of the homotopy algorithms

a duality based approach to the multiobjective h 2 h optimisation problem in this article a duality approach to multiobjective h 2 h problems is pursued in which real rational para hermitian multipliers and real valued ones are associated to h and as usual h 2 constraints respectively it is shown that the maximisation of a dual functional over all such multipliers yields the optimal value of the original multiobjective h 2 h problem to compute lower bounds on the latter and the corresponding approximate solutions to the original problem the maximisation of the dual functional over linearly parameterised finite dimensional classes of real rational multipliers is shown to be equivalent to semi definite linear programming problems once the optimal multipliers in such a class are obtained the corresponding approximate solutions can be computed from an unconstrained h 2 problem iterative modification of such classes is discussed to obtain increasing sequences of lower bounds on the optimal value of the original problem this is done on the basis of locally incr

coherent quantum lqg control based on a recently developed notion of physical realizability for quantum linear stochastic systems we formulate a quantum lqg optimal control problem for quantum linear stochastic systems where the controller itself may also be a quantum system and the plant output signal can be fully quantum such a control scheme is often referred to in the quantum control literature as coherent feedback control it distinguishes the present work from previous works on the quantum lqg problem where measurement is performed on the plant and the measurement signals are used as the input to a fully classical controller with no quantum degrees of freedom the difference in our formulation is the presence of additional non linear and linear constraints on the coefficients of the sought after controller rendering the problem as a type of constrained controller design problem due to the presence of these constraints our problem is inherently computationally hard and this also distinguishes it in an important way from the standard lqg problem we propose a numerical procedure for solving this problem based on an alternating projections algorithm and as an initial demonstration of the feasibility of this approach we provide fully quantum controller design examples in which numerical solutions to the problem were successfully obtained for comparison we also consider the case of classical linear controllers that use direct or indirect measurements and show that there exists a fully quantum linear controller which offers an improvement in performance over the classical ones

quantum optical realization of classical linear stochastic systems abstract the purpose of this paper is to show how a class of classical linear stochastic systems can be physically implemented using quantum optical components quantum optical systems typically have much higher bandwidth than electronic devices meaning faster response and processing times and hence have the potential for providing better performance than classical systems a procedure is provided for constructing the quantum optical realization the paper also describes the use of the quantum optical realization in a measurement feedback loop some examples are given to illustrate the application of the main results

reliable mixed l2 h fuzzy static output feedback control for nonlinear systems with sensor faults this paper is concerned with the design of reliable mixed l 2 h static output feedback sof fuzzy controllers for nonlinear continuous time systems with complete sensor faults the takagi and sugeno t s fuzzy model is employed to represent a nonlinear system a sufficient condition for the existence of reliable mixed l 2 h sof fuzzy controllers is presented in terms of a set of quadratic matrix inequalities qmis which not only guarantees that the closed loop fuzzy system satisfies a desired h disturbance attenuation constraint for all admissible operating regimes including the normal and sensor fault cases but also provides different upper bounds on the l 2 performance criterion for different operating regimes a suboptimal reliable fuzzy controller is obtained by the proposed iterative linear matrix inequality ilmi algorithm for minimizing the normal l 2 performance bound while maintaining acceptable lower levels of the bounds in the sensor fault cases finally a numerical example is given to illustrate the effectiveness of the proposed design method

scaling of general quadratic matrix equations a scaling framework for general quadratic algebraic matrix equations is presented all algebraic quadratic equations can be considered as special cases of a single generalized algebraic quadratic matrix equation gqme hence the paper is focused on the analysis and solution of the scaling problem of that gqme the presented scaling method is based on the assignment of predetermined values of the coefficients and the unknown matrices of the gqme the proposed framework is independent of any numerical method and therefore its use is general implementations are presented for the special case of matrix algebraic riccati equations ares some new results of matrix algebraic identities considering kronecker and hadamard products are also reported

characterization and efficient computation of the structured singular value the concept of structured singular value was recently introduced by doyle 1 as a tool for the analysis and synthesis of feedback systems with structured uncertainties it is a key to the design of control systems under joint robustness and performance specifications and it very nicely complements the h infty approach to control system design in this paper it is shown that the structured singular value can be obtained as the solution of several smooth optimization problems properties of these optimization problems are exhibited leading to a fast algorithm that always yields the structured singular value for block structures of size no larger than 3 and often does for block structures of larger size

synthesis of linear coherent quantum control systems using a differential evolution algorithm we propose a new method to construct an optimal linear coherent quantum controller based on an evolutionary optimization method namely a differential evolution algorithm the aim is to provide a straightforward approach to deal with both nonlinear and nonconvex constraints arising in the coherent quantum controller synthesis the solution to this control problem involves a complex algebraic riccati equation which corresponds to a physical realizability condition for the coherent quantum controller the proposed method is demonstrated through an example of an entanglement control problem for a quantum network comprising two cascaded optical parametric amplifiers

a modified genetic algorithm for optimal control problems abstract this paper studies the application of a genetic algorithm to discrete time optimal control problems numerical results obtained here are compared with ones yielded by gams a system for construction and solution of large and complex mathematical programming models while gams appears to work well only for linear quadratic optimal control problems or problems with short horizon the genetic algorithm applies to more general problems equally well

minimization of the root of a quadratic functional under an affine equality constraint we present a way of solving the problem of minimizing the root of quadratic functional subject to an affine constraint we give an explicit formula for computing the solutions of such a problem this is of interest for solving significant problems of financial economics as well as some classes of feasibility and optimization problems which frequently occur in tomography and other fields

mixed spl hscr sub 2 and spl hscr sub spl infin performance objectives ii optimal control this paper considers the analysis and synthesis of control systems subject to two types of disturbance signals white signals and signals with bounded power the resulting control problem involves minimizing a mixed spl hscr sub 2 and spl hscr sub spl infin norm of the system it is shown that the controller shares a separation property similar to those of pure spl hscr sub 2 or spl hscr sub spl infin controllers necessary conditions and sufficient conditions are obtained for the existence of a solution to the mixed problem explicit state space formulas are also given for the optimal controller

pareto suboptimal controllers in multi objective disturbance attenuation problems abstract a multi objective disturbance attenuation problem is considered as a novel framework for control and filtering problems under multiple exogenous disturbances there are n potentially possible disturbance inputs of a system on each of which may act a disturbance from a certain class a disturbance attenuation level is defined for each channel as an induced norm of the operator mapping signals of the corresponding class to the objective output of the system necessary conditions of the pareto optimality are derived it is established that the optimal solutions with respect to a multi objective cost parameterized by weights from an n dimensional simplex are pareto suboptimal solutions and their relative losses compared to the pareto optimal ones do not exceed 1 n n these results are extended to the case when the disturbances acting on different inputs are combined into coalitions the approach is applied to multiple classes of l 2 bounded and impulsive disturbances for which the h 0 optimal controllers as the pareto suboptimal solutions are synthesized in terms of linear matrix inequalities lmis illustrative examples demonstrate the effectiveness of the approach proposed

mixed control the discrete time case abstract a stochastic h and a mixed stochastic h 2 h control problem for discrete time systems are considered and solved conditions for existence of a solution are derived based on the solvability of an equivalent minimax problem in this framework it is possible to consider at the same time both stochastic and deterministic disturbances highlighting their mutual effects the controller can be designed by solving a system of three coupled riccati equations such equations display how the h 2 type minimization problem and the h type constraint influence each other

brief is set modeling of white noise a good tool for robust h2 analysis recently a new deterministic characterization of the h 2 norm has been proposed using a new norm w h based on approximate set membership modeling of white noise the main result shows that under mild conditions for a fixed system the gap between the h 2 and w h norms can be made arbitrarily small motivated by these results it has been argued that the w h norm provides a useful tool for analyzing robust h 2 controllers specially since in this context lmi based necessary and sufficient conditions for robust performance are available unfortunately as we show here with an example involving a very simple plant the worst case w h m norm can be conservative by at least a factor of m where m denotes the dimension of the exogenous signal for the original robust h 2 problem moreover the same example shows that competing state space based bounds also exhibit a similar degree of conservatism thus at this point the problem of finding non conservative bounds on the worst h 2 norm under lti or slowly varying ltv perturbations still remains open

c1 α local regularity of weak solutions of degenerate elliptic equations abstract it is demonstrated the local c 1 alpha nature of weak solutions of elliptic equations of the type 1 1 in the introduction under the degeneracy or singularity assumptions a sub 1 a sub 3

the impact of model risk on dynamic portfolio selection under multi period mean standard deviation criterion abstract we quantify model risk of a financial portfolio whereby a multi period mean standard deviation criterion is used as a selection criterion in this work model risk is defined as the loss due to uncertainty of the underlying distribution of the returns of the assets in the portfolio the uncertainty is measured by the kullback leibler divergence i e the relative entropy in the worst case scenario the optimal robust strategy can be obtained in a semi analytical form as a solution of a system of nonlinear equations several numerical results are presented which allow us to compare the performance of this robust strategy with the optimal non robust strategy for illustration we also quantify the model risk associated with an empirical dataset

suboptimal robust mixed h2h controller design for uncertain descriptor systems with distributed delays abstract this paper is concerned with the design problem of the optimal robust mixed h 2 h controllers for descriptor systems with time varying uncertainties and distributed delays in our method no decomposition of the coefficient matrix is needed the designed controller can guarantee regularity nonimpulsiveness and internal stability of the closed loop system and simultaneously minimizes an upper bound of the h2 performance measure satisfying an h norm bound constraint the control design problem is transformed into the solvability of a set of strict lmis which can be effectively solved by using interior point algorithms

a newton like method for solving rank constrained linear matrix inequalities this paper presents a newton like algorithm for solving systems of rank constrained linear matrix inequalities though local quadratic convergence of the algorithm is not a priori guaranteed or observed in all cases numerical experiments including application to an output feedback stabilization problem show the effectiveness of the algorithm

derivation of the maximum entropy h controller and a state space formula for its entropy the problem of maximizing the entropy of a stabilized closed loop system is solved the solution exploits the parametrization of all closed loop systems that meet an h norm bound the central solution of this set is shown to maximize the entropy at infinity and for this case a particularly simple formula is derived for the maximum value of the entropy

mixed h sub 2 h sub infinity control a convex optimization approach the problem of finding an internally stabilizing controller that minimizes a mixed h sub 2 h sub infinity performance measure subject to an inequality constraint on the h sub infinity norm of another closed loop transfer function is considered this problem can be interpreted and motivated as a problem of optimal nominal performance subject to a robust stability constraint both the state feedback and output feedback problems are considered it is shown that in the state feedback case one can come arbitrarily close to the optimal even over full information controllers mixed h sub 2 h sub infinity performance measure using constant gain state feedback moreover the state feedback problem can be converted into a convex optimization problem over a bounded subset of n n and n q where n and q are respectively the state and input dimensions real matrices using the central h sub infinity estimator it is shown that the output feedback problem can be reduced to a state feedback problem in this case the dimension of the resulting controller does not exceed the dimension of the generalized plant

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

an improved closed form solution for the constrained minimization of the root of a quadratic functional the problem of minimizing the root of a quadratic functional subject to a system of affine constraints occurs in investment portfolio selection insurance risk theory tomography and other areas we provide a solution that improves on the current published solution by being considerably simpler in computational terms in particular a succession of partitions and inversions of large matrices is avoided our solution method employs the lagrangian multiplier method and we give two proofs one of which is based on the solution of a related convex optimization problem a geometrically intuitive interpretation of the objective function and of the optimization solution is also given

mixed lqg and h coherent feedback control for linear quantum systems the purpose of this paper is to study the mixed linear quadratic gaussian lqg and h optimal control problem for linear quantum stochastic systems where the controller itself is also a quantum s

quantum ito s formula and stochastic evolutions using only the boson canonical commutation relations and the riemann lebesgue integral we construct a simple theory of stochastic integrals and differentials with respect to the basic field operator processes this leads to a noncommutative ito product formula a realisation of the classical poisson process in fock space which gives a noncommutative central limit theorem the construction of solutions of certain noncommutative stochastic differential equations and finally to the integration of certain irreversible equations of motion governed by semigroups of completely positive maps the classical ito product formula for stochastic differentials with respect to brownian motion and the poisson process is a special case

minimax optimal control of stochastic uncertain systems with relative entropy constraints this paper considers a new class of discrete time stochastic uncertain systems in which the uncertainty is described by a constraint on the relative entropy between a nominal noise distribution and the perturbed noise distribution this uncertainty description is a natural extension to the case of stochastic uncertain systems of the sum quadratic constraint uncertainty description this paper solves problems of worst case robust performance analysis and output feedback minimax optimal controller synthesis in a general nonlinear setting specializing these results to the linear case leads to a minimax linear quadratic gaussian lqg optimal controller this controller is defined by riccati difference equations and a kalman filter like state equation the paper also shows that the minimax lqg problem will have a solution if and only if a corresponding h sup spl infin control problem has a solution a linear example is presented to illustrate the minimax lqg methodology

h infty control of linear quantum stochastic systems the purpose of this paper is to formulate and solve a h infin controller synthesis problem for a class of noncommutative linear stochastic systems which includes many examples of interest in quantum technology the paper includes results on the class of such systems for which the quantum commutation relations are preserved such a requirement must be satisfied in a physical quantum system a quantum version of standard classical dissipativity results are presented and from this a quantum version of the strict bounded real lemma is derived this enables a quantum version of the two riccati solution to the h infin control problem to be presented this result leads to controllers which may be realized using purely quantum purely classical or a mixture of quantum and classical elements this issue of physical realizability of the controller is examined in detail and necessary and sufficient conditions are given our results are constructive in the sense that we provide explicit formulas for the hamiltonian function and coupling operator corresponding to the controller

coherent feedback control of linear quantum optical systems via squeezing and phase shift the purpose of this paper is to present a theoretic and numerical study of utiliz ing squeezing and phase shift in coherent feedback control of linear quantum optical systems a quadrature representation with built in phase shifters is proposed for such systems fundamen tal structural characterizations of linear quantum optical systems are derived in terms of the new quadrature representation these results reveal considerable insights into the issue of the physical realizability of such quantum systems the problem of coherent quantum linear quadratic gaussian lqg feedback control studied in h i nurdin m r james and i r petersen automatica ifac 45 2009 pp 1837 1846 g zhang and m r james ieee trans automat control 56 2011 pp 1535 1550 is reinvestigated in depth first the optimization methods in these papers are extended to a multistep optimization algorithm which utilizes ideal squeezers second a two stage optimization approach is proposed on the basis of controller parametrization numerical studies show that closed loop systems designed via the second approach may offer lqg control performance even better than that when the closed loop systems are in the vacuum state when ideal squeezers in a closed loop system are replaced by more realistic degenerate parametric amplifiers a sufficient condition is derived for the asymptotic stability of the resultant new closed loop system the issue of performance convergence is also discussed in the lqg control setting

stratification of free boundary points for a two phase variational problem abstract in this paper we prove the local lipschitz regularity of the minimizers of the two phase bernoulli type free boundary problem arising from the minimization of the functional j u u p p u 0 p u 0 1 p here r n is a bounded smooth domain and are positive constants such that p p 0 furthermore we show that for p 1 the free boundary has locally finite perimeter and the set of non smooth points of the free boundary is of zero n 1 dimensional hausdorff measure for this our approach is new even for the classical case p 2

an introduction to quantum filtering this paper provides an introduction to quantum filtering theory an introduction to quantum probability theory is given focusing on the spectral theorem and the conditional expectation as a least squares estimate and culminating in the construction of wiener and poisson processes on the fock space we describe the quantum ito calculus and its use in the modeling of physical systems we use both reference probability and innovations methods to obtain quantum filtering equations for system probe models from quantum optics

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

relations between maximum entropy h control and combined h lqg control abstract the maximum entropy h control problem and a combined h lqg control problem are presented in a unified way and shown to be equivalent in the case of a full order controller and equalized h lqg weights the result links two separate approaches which have distinctly different methods of solution only two decoupled algebraic riccati equations are needed to state the controller maximum value of the entropy and minimum value of the auxiliary cost

up to boundary regularity for a singular perturbation problem of p laplacian type abstract in this paper we are interested in establishing up to boundary uniform estimates for the one phase singular perturbation problem involving a nonlinear singular degenerate elliptic operator our main result states if r n is a c 1 domain f c 1 for some 0 1 and u e verifies div a x u e u e e u e in 0 u e 1 in u e f on where e 0 e t 1 e t e and 0 t b 0 t 1 r e t d t m 0 with some positive constants b and m then there exists a constant c 0 independent of e such that u e l c

direct and indirect couplings in coherent feedback control of linear quantum systems the purpose of this paper is to study and design direct and indirect couplings for use in coherent feedback control of a class of linear quantum stochastic systems a general physical model for a nominal linear quantum system coupled directly and indirectly to external systems is presented fundamental properties of stability dissipation passivity and gain for this class of linear quantum models are presented and characterized using complex lyapunov equations and linear matrix inequalities lmis coherent h and lqg synthesis methods are extended to accommodate direct couplings using multistep optimization examples are given to illustrate the results

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

on a class of approximate solutions to multi objective h 2 h problems a class of matrix function optimization problems is considered in which the cost functional is the h 2 norm of an affine function of the decision variables and there are several constraints involving h 2 and h x norms of other affine functions such problems arise naturally in feedback control theory as closed loop transfer functions are affine functions of the socalled youla parameter and control objectives can often be expressed as prescribed upper bounds on the h 2 and h x norms of these functions a procedure for obtaining approximate solutions to such problems is described which involves solving a sequence of h 2 problems with a single weighted h 2 constraint this procedure hinges upon a weighting updating scheme in which roughly speaking a multiplication operator is applied to an additively corrected version of the weighting function at each step with both the operator and the additive correction being defined on the basis of the solution of the current auxiliary quadratic problem it is shown

duality and basis functions for robust h 2 performance analysis the robust h2 performance of a plant with a prescribed uncertain component refers to its white noise rejection level in the worst case with respect to its uncertainty set in this paper we derive a dual formulation for the computation of the robust h2 performance of a plant with unit gain structured uncertainty the dual framework gives a tight lower bound on robust h2 performance with no duality gap with respect to the primal approach paganini 1995a we also show how the upper and lower bounds for the robust h2 performance of a plant may be computed using semidefinite programming linear matrix inequality type formulae based on basis functions and provide an example which enables us to demonstrate the relative merits and the complementary nature of the basis function and the gridding approaches to robust h2 performance analysis for both the primal and the dual formulations

multiperiod mean standard deviation time consistent portfolio selection we study a multiperiod portfolio selection problem in which a single period mean standard deviation criterion is used to construct a separable multiperiod selection criterion using this criterion we obtain a closed form optimal strategy which depends on selection schemes of investor s risk preference as a consequence we develop a multiperiod portfolio selection scheme in doing so we adapt a pseudo dynamic programming principle from other existing results the analysis is performed in the market of risky assets only however we allow both market transitions and intermediate cash injections and offtakes