system structure and singular control the general continuous time linear quadratic control problem is considered it is shown that recently developed linear system theoretic properties and algorithms play an important role in solving this singular control problem

stochastic linear quadratic control with conic control constraints on an infinite time horizon this paper is concerned with a stochastic linear quadratic lq control problem in the infinite time horizon where the control is constrained in a given arbitrary closed cone the cost weighting matrices are allowed to be indefinite and the state is scalar valued first the mean square conic stabilizability of the system is defined which is then characterized by a set of simple conditions involving linear matrix inequalities lmis next the issue of well posedness of the underlying optimal lq control which is necessitated by the indefiniteness of the problem is addressed in great detail and necessary and sufficient conditions of the well posedness are presented on the other hand to address the lq optimality two new algebraic equations a la riccati called extended algebraic riccati equations eares along with the notion of their stabilizing solutions are introduced for the first time optimal feedback control as well as the optimal value are explicitly derived in terms of the stabilizing solutions to the eares moreover several cases when the stabilizing solutions do exist are discussed and algorithms of computing the solutions are presented finally numerical examples are provided to illustrate the theoretical results established

dynamic mean variance portfolio selection with no shorting constraints this paper is concerned with mean variance portfolio selection problems in continuous time under the constraint that short selling of stocks is prohibited the problem is formulated as a stochastic optimal linear quadratic lq control problem however this lq problem is not a conventional one in that the control portfolio is constrained to take nonnegative values due to the no shorting restriction and thereby the usual riccati equation approach involving a completion of squares does not apply directly in addition the corresponding hamilton jacobi bellman hjb equation inherently has no smooth solution to tackle these difficulties a continuous function is constructed via two riccati equations and then it is shown that this function is a viscosity solution to the hjb equation solving these riccati equations enables one to explicitly obtain the efficient frontier and efficient investment strategies for the original mean variance problem an example illustrating these results is also presented

linear matrix inequalities riccati equations and indefinite stochastic linear quadratic controls this paper deals with an optimal stochastic linear quadratic lq control problem in infinite time horizon where the diffusion term in dynamics depends on both the state and the control variables in contrast to the deterministic case we allow the control and state weighting matrices in the cost functional to be indefinite this leads to an indefinite lq problem which may still be well posed due to the deep nature of uncertainty involved the problem gives rise to a stochastic algebraic riccati equation sare which is however fundamentally different from the classical algebraic riccati equation as a result of the indefinite nature of the lq problem to analyze the sare we introduce linear matrix inequalities lmis whose feasibility is shown to be equivalent to the solvability of the sare moreover we develop a computational approach to the sare via a semi definite programming associated with the lmis finally numerical experiments are reported to illustrate the proposed approach

list decoding tensor products and interleaved codes we design the first efficient algorithms and prove new combinatorial bounds for list decoding tensor products of codes and interleaved codes we show that for every code the ratio of its list decoding radius ldr to its minimum distance stays unchanged under the tensor product operation rather than squaring as one might expect this gives the first efficient list decoders and new combinatorial bounds for some natural codes including multivariate polynomials where the degree in each variable is bounded we show that for every code its ldr remains unchanged under m wise interleaving for an integer m this generalizes a recent result of dinur et al in proceedings of the 40th acm symposium on theory of computing stoc 08 2008 pp 275 284 who proved such a result for interleaved hadamard codes equivalently linear transformations using the notion of generalized hamming weights we give better list size bounds for both the tensoring and interleaving of binary linear codes by analyzing the weight distribution of these codes we reduce the task of bounding the list size to one of bounding the number of close by low rank codewords for decoding linear transformations using rank reduction together with other ideas we obtain list size bounds that are tight over small fields our results give better bounds on the ldr than what is obtained from the johnson bound and yield rather general families of codes decodable beyond the johnson radius

risk sensitive control with hara utility a control methodology based on the hyperbolic absolute risk averse hara utility function is presented as an alternative to the exponential of an integral approach to finding robust controllers the work is inspired by the intuition that hara controllers while being robust may give better performance than exponential controllers in normal situations the hara problem is shown to be equivalent to a certain differential game and the asymptotic properties of the hara problem and this differential game are studied as an example a linear quadratic hara problem is studied where the problem of finding a robust hara controller is proved to be equivalent to solving a standard linear quadratic problem for a system with a higher noise intensity this reveals an interesting relationship between robustness and uncertainty

stochastic controls with terminal contingent conditions abstract this paper considers a nonlinear stochastic control problem where the system dynamics is a controlled nonlinear backward stochastic differential equation and the state must coincide with a given random vector at the terminal time a necessary condition of optimality in the form of a global maximum principle as well as a sufficient condition of optimality are presented the general result is also applied to backward linear quadratic control problem and an optimal control is obtained explicitly as a feedback of the solution to a forward backward equation finally a nonlinear problem with additional integral constraints is discussed and it is shown that the duality gap is zero under the slater condition

adapted solution of a backward stochastic differential equation abstract let wt t 0 1 be a standard k dimensional weiner process defined on a probability space f p and let ft denote its natural filtration given a f1 measurable d dimensional random vector x we look for an adapted pair of processes x t y t t 0 1 with values in rd and rd k respectively which solves an equation of the form x t t 1 f s x s y s ds t 1 g s x s y s dw s x a linearized version of that equation appears in stochastic control theory as the equation satisfied by the adjoint process we also generalize our results to the following equation x t t 1 f s x s y s ds t 1 g s x s y s dw s x under rather restrictive assumptions on g

a general stochastic maximum principle for optimal control problems the maximum principle for nonlinear stochastic optimal control problems in the general case is proved the control domain need not be convex and the diffusion coefficient can contain a control variable

sufficient conditions of optimality for stochastic systems with controllable diffusions this paper studies optimal controls for systems governed by ito s stochastic differential equations both the drift and diffusion terms of the equations are allowed to depend on controls and the systems are allowed to be degenerate it is shown that the necessary conditions of optimality namely the maximum conditions in terms of the spl hscr function which is a generalization of the usual hamiltonian and is quadratic with respect to the diffusion coefficients along with some convexity conditions constitute sufficient conditions of optimality for such controlled systems

stochastic linear quadratic control via semidefinite programming we study stochastic linear quadratic lq optimal control problems over an infinite time horizon allowing the cost matrices to be indefinite we develop a systematic approach based on semidefinite programming sdp a central issue is the stability of the feedback control and we show this can be effectively examined through the complementary duality of the sdp furthermore we establish several implication relations among the sdp complementary duality the generalized riccati equation and the optimality of the lq control problem based on these relations we propose a numerical procedure that provides a thorough treatment of the lq control problem via primal dual sdp it identifies a stabilizing feedback control that is optimal or determines that the problem possesses no optimal solution for the latter case we develop an epsilon approximation scheme that is asymptotically optimal

absolute stability approach to stochastic stability of infinite dimensional nonlinear systems recent applications of absolute stability methods to robustness analysis have led to a rebirth of interest in this topic this paper is concerned with the robust stability of feedback distributed parameter systems against nonlinear and random disturbances our analysis is based on the lyapunov direct method to derive a stochastic lyapunov function we introduce the special stochastic infinite dimensional counterparts of the kalman yakubovich lemma they are proved by use of dynamic programming methods in combination with the properties of hilbert space valued wiener processes examples exhibit extensions of the popov and circle criteria to the feedback stochastic heat and delay equations respectively

relationship between backward stochastic differential equations and stochastic controls a linear quadratic approach it is well known that backward stochastic differential equations bsdes stem from the study on the pontryagin type maximum principle for optimal stochastic controls a solution of a bsde hits a given terminal value which is a random variable by virtue of an it additional martingale term and an indefinite initial state this paper attempts to explore the relationship between bsdes and stochastic controls by interpreting bsdes as some stochastic optimal control problems more specifically associated with a bsde a new stochastic control problem is introduced with the same dynamics but a definite given initial state the martingale term in the original bsde is regarded as the control and the objective is to minimize the second moment of the difference between the terminal state and the terminal value given in the bsde this problem is solved in a closed form by the stochastic linear quadratic lq theory developed recently the general result is then applied to the black scholes model where an optimal mean variance hedging portfolio is obtained explicitly in terms of the option price finally a modified model is investigated where the difference between the state and the expectation of the given terminal value at any time is taken into account

the regulator problem with indefinite quadratic cost for boundary control systems the finite horizon case in this paper we study the finite horizon non standard lq problem for an abstract dynamics which models a large class of hyperbolic like partial differential equations we provide necessary sufficient conditions for finiteness of the value function corresponding to the control problem sharpness of sufficient conditions is shown by means of counterexamples the specific features of the finite in contrast to infinite horizon case are illustrated

discrete time lqg controls with control dependent noise this paper presents some studies on partially observed linear quadratic gaussian lqg models where the stochastic disturbances depend on both the states and the controls and the measurements are bilinear in the noise and the states controls while the separation theorem of standard lqg design does not apply suboptimal linear state estimate feedback controllers are derived based on certain linearizations the controllers are useful for nonlinear stochastic systems where the linearized models include terms bilinear in the noise and states controls and are significantly more accurate than if the bilinear terms are set to zero the controllers are calculated by solving a generalized discrete time riccati equation which in turn has properties relating to well posedness of the associated lqg problem

singular optimal control a geometric approach linear quadratic singular optimal control problem is solved for nonminimum phase and noninvertible systems a state space decomposition is obtained and a reduced order nonsingular subproblem is solved the optimal stabilizing input of the singular problem has been found when there are no transmission zeros on the imaginary axis

measurement scale network sampling scale and groundwater model parameters the scales at which model parameters are measured with local field tests distributed on a sampling network are examined two scales are defined to characterize the problem 1 the measurement scale associated with the resolution of a single field test and 2 the network scale associated with the separation between samples on a network using a spatial filtering approach it is shown that a network of measurements can only resolve a larger scale component of a parameter field the smaller scale component of the parameter field not seen by measurements here called the subgrid component can only vary on scales larger than the measurement scale and smaller than the network scale these unobserved subgrid scales give rise to the so called closure problem and consequent modeling errors when a significant proportion of the parameter variability is contained in the subgrid scales not only will the closure problem be significant but aliasing errors will also pollute the estimate of the large scale component of the parameter field these concepts are illustrated by performing simple analytical and numerical calculations

stochastic linear quadratic regulators with indefinite control weight costs ii in part i of this paper s chen x li and x zhou siam j control optim 36 1998 pp 1685 1702 an optimization model of stochastic linear quadratic regulators lqrs with indefinite control cost weighting matrices is proposed and studied in this sequel the problem of solving lqr models with system diffusions dependent on both state and control variables which is left open in part i is tackled first the solvability of the associated stochastic riccati equations sres is studied in the normal case namely all the state and control weighting matrices and the terminal matrix in the cost functional are nonnegative definite with at least one positive definite which in turn leads to an optimal state feedback control of the lqr problem in the general indefinite case the problem is decomposed into two optimal lqr problems one with a forward dynamics and the other with a backward dynamics the well posedness and solvability of the original lqr problem are then obtained by solving these two subproblems and an optimal control is explicitly constructed examples are presented to illustrate the results

on a class of rational matrix differential equations arising in stochastic control we prove a monotonicity and a comparison theorem for the solutions of a rational matrix differential equation appearing in stochastic control and derive existence and convergence results for the solutions of this differential equation moreover in the time invariant case we present conditions ensuring that the corresponding algebraic matrix equation has a stabilizing solution

stochastic optimal lqr control with integral quadratic constraints and indefinite control weights a standard assumption in traditional deterministic and stochastic optimal minimizing linear quadratic regulator lqr theory is that the control weighting matrix in the cost functional is strictly positive definite in the deterministic case this assumption is in fact necessary for the problem to be well posed because positive definiteness is required to make it a convex optimization problem however it has recently been shown that in the stochastic case when the diffusion term is dependent on the control the control weighting matrix may have negative eigenvalues but the problem remains well posed in this paper the completely observed stochastic lqr problem with integral quadratic constraints is studied sufficient conditions for the well posedness of this problem are given indeed we show that in certain cases these conditions may be satisfied even when the control weighting matrices in the cost and all of the constraint functionals have negative eigenvalues it is revealed that the seemingly nonconvex problem with indefinite control weights can actually be a convex one by virtue of the uncertainty in the system finally when these conditions are satisfied the optimal control is explicitly derived using results from duality theory