antenna array pattern synthesis via convex optimization we show that a variety of antenna array pattern synthesis problems can be expressed as convex optimization problems which can be numerically solved with great efficiency by recently developed interior point methods the synthesis problems involve arrays with arbitrary geometry and element directivity constraints on far and near field patterns over narrow or broad frequency bandwidth and some important robustness constraints we show several numerical simulations for the particular problem of constraining the beampattern level of a simple array for adaptive and broadband arrays

adaptive systems and time varying plants abstract the behaviour of four adaptive algorithms lms equation error output error identification and the goodwin ramadge caines adaptive control algorithm are examined in the face of plant parameter variations the key point to note is that persistency of excitation conditions in the time invariant parameter case guarantees exponential convergence then standard and newly developed lyapunov stability results allow us to guarantee tracking error and parameter error boundedness when the plant parameters are actually time varying

stability analysis of an adaptive system with unmodelled dynamics stability bounds for fast and slow adaptation are derived for a simple adaptive system with one unmodelled parasitic pole which is approximated by a right half plane zero in fast adaptation the product of the adaptive gain and power of the reference input must be smaller than the parasitic pole in slow adaptation most of the input signal energy must be in the frequency range lower than the square root of the parasitic pole it is shown that a plant bypass ensures a global stability property by making the linear time invariant part of the adaptive loop strictly positive real spr the price paid is an increase of the tracking error at very low frequencies and with slow adaptation when the equilibrium of the system without bypass is exponentially stable

robustness of adaptive control for stochastic systems robustness of the stochastic adaptive systems with unmodelled dynamics and external disturbances is discussed in this paper an adaptive controller is designed using the els algorithm except for the finite switches it is shown that the closed loop system is globally stable both the estimation error and the tracking error approach their minima when the unmodelled dynamics diminish that is the asymptotically adaptive system operating with the els algorithm has a good robustness with respect to unmodelled dynamics and external disturbances

a robust direct adaptive controller this paper proposes a new direct adaptive control algorithm which is robust with respect to additive and multiplicative plant unmodeled dynamics the algorithm is designed based on the reduced order plant which is assumed to be minimum phase and of known order and relative degree but is analyzed with respect to the overall plant which due to the unmodeled dynamics may be nonminimum phase and of unknown order and relative degree it is shown that if the unmodeled dynamics are sufficiently small in the low frequency range then the algorithm guarantees boundedness of all signals in the adaptive loop and small residual tracking errors for any bounded initial conditions in the absence of unmodeled dynamics the residual tracking error is shown to be zero

application of convex relaxation to array synthesis problems a general procedure to solve efficiently non convex array synthesis problems is presented it is based on the semidefinite relaxation sdr technique the way to properly relax the constraints in order to formulate the synthesis of shaped beams phase only arrays and reconfigurable arrays as semidefinite programming problems is detailed these so approximated array synthesis problems are then convex easy to implement and can be efficiently solved using off the shelf numerical routines the conditions under which the relaxed problems provide the optimal solution to the original non convex synthesis problems are specified various representative numerical comparisons with arrays designed by other approaches show the validity of the proposed method and illustrate its potentialities

a simple algorithm to achieve desired patterns for arbitrary arrays a simple iterative algorithm which can be used to find array weights that produce array patterns with a given look direction and an arbitrary sidelobe specification is presented the method can be applied to nonuniform array geometries in which the individual elements have arbitrary and differing radiation patterns the method is iterative and uses sequential updating to ensure that peak sidelobe levels in the array meet the specification computation of each successive pattern is based on the solution of a linearly constrained least squares problem the constraints ensure that the magnitude of the sidelobes at the locations of the previous peaks takes on the prespecified values phase values for the sidelobes do not change during this process and problems associated with choosing a specific phase value are therefore avoided experimental evidence suggests that the procedure terminates in remarkably few iterations even for arrays with significant numbers of elements

particle smoothing for hidden diffusion processes adaptive path integral smoother smoothing methods are used for inference of stochastic processes given noisy observations the estimation of the marginal posterior distribution given all observations is typically a computationally intensive task we propose a novel algorithm based on path integral control theory to efficiently estimate the smoothing distribution of continuous time diffusion processes from partial observations in particular we use an adaptive importance sampling method to improve the effective sampling size of the posterior and the reliability of the estimation of the marginals this is achieved by estimating a feedback controller together with an adaptive initialization and an annealing scheme to sample efficiently from the joint smoothing distribution we compare the results with estimations obtained from the standard forward filter backward simulator ffbsi for two diffusion processes of different complexity we show that the proposed method gives more accurate estimates than the standard ffbsi

robustness of discrete time direct adaptive controllers the problem of preserving stability of discrete time adaptive controllers in spite of reduced order modeling and output disturbances is addressed in this paper conditions for global stability convergence of the tracking error with bounded signals are derived for a discrete time pole zero placement adaptive controller where the parameter estimator is modified in terms of normalized signals following an input output perpective the overall system is decomposed into two subsystems reflecting the parameter estimation and modeling errors respectively and its stability is studied using the sector stability and passivity theorems first the analysis is carried for the class of disturbances and reference inputs that are either decaying or can be exactly hulled by a linear controller of the chosen structure in this l 2 framework it is shown that the only substantive assumption to assure stability is the existence of a linear controller such that the closed loop transfer function verifies certain conicity conditions the convergence speed and alertness properties of various parameter adaptation algorithms regarding this condition are discussed the results are further extended to a broader class of l infty disturbances and reference inputs

stochastic optimal control and quantum mechanics classical mechanics is formulated as a kind of deterministic optimal control the simplest from the optimal control point of view stochastic generalization of classical mechanisms is submitted the connections between stochastic mechanics and quantum mechanics are shown thanks to the stochastic optimal control method

robust redesign of adaptive control effects of unmodeled high frequency dynamics on stability and performance of adaptive control schemes are analyzed in the regulation problem global stability properties are no longer guaranteed but a region of attraction exists for exact adaptive regulation the dependence of the region of attraction on unmodeled parasitics is examined first then the general case of model reference adaptive control is considered in which parasitics can destroy stability and boundedness properties a modified adaptive law is proposed guaranteeing the existence of a region of attraction from which all signals converge to a residual set which contains the equilibrium for exact tracking the size of this set depends on design parameters the frequency range of parasitics and the reference input signal characteristics

non linear dynamics in adaptive control chaotic and periodic stabilization abstract in this paper the non linear features of adaptive control algorithms are highlighted using a simple linear discrete time example based on classical design it is demonstrated that in the presence of undermodelling errors non linear phenomena in the feedback gain such as limit cycles and even chaos arise despite these complicated dynamics robust stabilization of the plant can still occur for the class of undermodelling errors considered the set of plants stabilizable by this adaptive controller is completely characterized

a robust adaptive minimum variance controller this paper addresses the twin questions of performance and robustness of an adaptive controller for single input single output linear stochastic systems the authors present an adaptive controller that has the following properties 1 attaining optimal regulation and tracking in the ideal minimum phase known upper bound on system order known sign and lower bound for the leading coefficient b 0 positive real condition on noise case and self tuning in a cesaro sense to a minimum variance regulator in the case of pure regulation 2 providing mean square stability when the system is of minimum phase with known upper bound on order but not necessarily satisfying a positive real condition on the noise 3 providing mean square stability when the system is in a graph topological neighborhood of computable size of an ideal plant as in 1 and the statistical properties of the disturbance are violated 4 continuing to stabilize the system when the adaptation gain is prevented from vanishing

solving quantum stochastic lqr optimal control problem in fock space and its application in finance abstract this paper is an attempt for solving operator valued quantum stochastic optimal control problems in fock space for this purpose the dynamics of the classical system state is described by hudson parthasarathy type quantum stochastic differential equation qsde in fock space and then by associating a quadratic performance criterion with the qsde a quantum stochastic linear quadratic regulator qs lqr optimal control problem is formulated also an algorithm for solving the qs lqr optimal control problem is designed for solving the resulting optimal control problem a new hjb equation is obtained thereby the operator valued control process is obtained two theorems are proved to facilitate the algorithm in this paper for the first time the optimal strategy for trading stock is designed via the presented method for this purpose merton portfolio allocation problem is solved the simulation results show that portfolio optimal performances minimum risk and maximum return are achieved via presented method

optimal array pattern synthesis using semidefinite programming we present algorithms for the solution of two problems in array pattern synthesis the first is the design of nonuniform arrays with a desired magnitude response the second is that of robust design i e design in the presence of uncertainties constraints such as power limitation can be addressed with both problems the algorithms that we present are based on semidefinite programming for which efficient software is readily available we present examples that illustrate the effectiveness of our approach

stochastic adaptive one step ahead optimal controllers based on input matching optimal adaptive controller based on the els algorithm is established using the input matching technique the control signal is reduced to a constant weighted sum of the measurable information state vector components using a one step ahead quadratic cost function to govern the behavior of the stochastic linear systems the control effort can be estimated globally the algorithm also predicts the convergence rate with no excitation condition the closed loop system is globally stable and the input converges to the one step ahead optimal input

minimum variance beamforming with phase independent derivative constraints a set of first and second order derivative constraints that can be used in minimum variance beamformers to achieve flat main beam response is presented efficient algorithms are derived for the implementation of these constraints in contrast to conventional derivative constraint methods which constrain both the magnitude power and phase responses of the beamformer the method only constrains the magnitude response the unnecessary constraint on the phase is a major drawback to the conventional methods since it causes the beamformer performance to vary with the particular spatial reference point used to define the array element positions this phenomenon is clearly undesirable because the choice of a reference point is generally made for notational convenience as a direct sequence of the phase constraint an inappropriately chosen reference point can easily result in a beamformer response which has undesirably high sidelobes the problem is avoided through the use of phase independent derivative constraints

robust model reference adaptive control we propose a new model reference adaptive control algorithm and show that it provides the robust stability of the resulting closed loop adaptive control system with respect to unmodeled plant uncertainties the robustness is achieved by using a relative error signal in combination with a dead zone and a projection in the adaptive law the extra a priori information needed to design the adaptive law are bounds on the plant parameters and an exponential bound on the impulse response of the inverse plant transfer function

pattern synthesis with multipoint accurate array response control in this paper the problem of pattern synthesis with antenna arrays is addressed and new approaches based on the recently developed accurate array response control textrm a 2 textrm rc algorithm are presented it is shown that the array weight vector obtained by the textrm a 2 textrm rc algorithm to control the normalized response at a single direction in each step belongs to a specific set thus an appropriate weight vector chosen from the intersection of weight vector sets corresponding to the desired responses at multiple directions is capable of simultaneously controlling those responses this results in the so called multipoint accurate array response control textrm ma 2 textrm rc algorithm moreover in order to avoid possible beam axis shift in pattern synthesis a modified textrm ma 2 textrm rc textrm m 2 textrm a 2 textrm rc algorithm is proposed by imposing a derivative constraint on the direction of beam axis representative numerical examples are provided to demonstrate the effectiveness of the proposed textrm ma 2 textrm rc and textrm m 2 textrm a 2 textrm rc algorithms for multipoint responses control and pattern synthesis

optimal polarization synthesis of arbitrary arrays with focused power pattern the joint synthesis of the spatial power pattern and polarization of arbitrary arrays is addressed specifically the proposed approach gives the solution to a frequently encountered problem namely the array design i e the determination of the radiating element weightings to achieve a pattern that is arbitrarily upper bounded while its polarization is optimized in a given angular region any state of polarization elliptical circular and linear can be synthesized and there is no restriction regarding the array geometry and element patterns the synthesis problem is rewritten as a convex optimization problem that is efficiently solved using readily available software this ensures the optimality of the proposed solution various numerical results are presented to validate the proposed method and illustrate its potentialities the synthesis of a sequentially rotated array is first addressed then a linear array of equispaced randomly oriented dipoles is considered finally a conformal and a planar array of patches where the mutual coupling effects are considered are synthesized to radiate a linear and a circular polarization

synthesis of sparse planar arrays using modified real genetic algorithm in array design the positions of sparse array elements is an important concern for optimal performance in terms of its ability to achieve minimum peak sidelobe level sll this paper proposes a modified real genetic algorithm mga based on resetting of chromosome for the element position optimization of sparse planar arrays with rectangular boundary and here the multiple optimization constraints include the number of elements the aperture and the minimum element spacing by simplifying the space between the elements from the actual distance to chebychev distance the mga searches a smaller solution space by means of indirect description of individual and it can avoid infeasible solution during the optimization process by two novel genetic operators finally the simulation results confirming the great efficiency and the robustness of the proposed method are shown in this paper

a numerical pattern synthesis algorithm for arrays a numerical technique for pattern synthesis in arrays is presented for a given set of elements the technique allows one to find a set of array coefficients that steer the main beam in a given direction and yield sidelobes meeting a specified criterion if such a set of array coefficients exists if the pattern specifications cannot be met with the given elements the algorithm finds the best attainable pattern the advantage of this technique is that it can be used with an arbitrary set of array elements different elements in the array can have different element patterns and the array can have arbitrary nonuniform spacing between elements the synthesis technique is based on adaptive array theory the given array elements are assumed to be used as the elements of an adaptive array the main beam is pointed in the proper direction by choosing the steering vector for that direction and the sidelobes are controlled by introducing a large number of interfering signals at many angles throughout the sidelobe region the algorithm iterates on the interference powers until a suitable pattern is obtained

synthesis of minimax sidelobes for arbitrary arrays this paper presents a synthesis algorithm to minimize the maximum sidelobe level for an arbitrary array similar to dolph chebyshev patterns the minimax array patterns for arbitrary arrays have uniform sidelobes

low dimensional sdp formulation for large antenna array synthesis bounding the sidelobe and mainlobe levels of an array with complex weights is attractive in that it allows direct control of the radiation pattern in this paper we propose an efficient beamforming technique for synthesizing the patterns of large arrays with bound constraints on the sidelobe and mainlobe levels it is shown that the pattern synthesis problem can be posed as a convex semi infinite program sip which is then turned into a semi definite program sdp via a novel linear matrix inequality lmi characterization of semi infinite trigonometric polynomial constraints in contrast to existing sdp formulations which require a large number of additional variables our sdp representation only uses a minimal number of additional variables this subsequently enables the design of patterns for arrays with several hundred elements to be efficiently achieved on a standard personal computer using existing sdp solvers

numerical synthesis of arbitrary discrete arrays a numerical algorithm for the synthesis of arbitrary discrete arrays is given the technique is based on the algorithm of c a olen and r t compton 1990 but employs a different iterative recursive algorithm yielding an optimum convergence rate it is shown that the new algorithm converges to the optimum solution in a significantly reduced number of iterations compared with the technique of olen and compton use of the technique is illustrated by applying the synthesis procedure to a ten element linear array and to a conformal array consisting of ten dipoles located on a parabolic curve

almost exact modelling assumption in adaptive linear control modem adaptive controllers are known to give bounded solutions when the system normalized unmodelled effects are bounded by a small constant this paper studies this unusual characterization of uncertainties we show it encompasses more classical approaches we discuss how feedback and by passing may allow this assumption to be satisfied we conclude by proposing the notion of almost exactly linearly modelled systems

an adaptive generalized sidelobe canceller with derivative constraints an adaptive broad band beamforming structure is presented which employs a gradient based weight adjustment algorithm to minimize output variance subject to a set of j linear constraints on broadband directional derivatives in the desired look direction a generalized sidelobe cancelling structure is employed in which a nonadaptive conventional beamformer operates in parallel with an adaptive beamformer the conventional portion has a broad band beampattern which adheres to the specified constraints while the adaptive path is a cascade of a fixed signal blocking matrix and a set of tapped delay line filters blocking is employed to ensure that all incident waveforms which meet the specified constraints do not reach the tapped delay lines as a result an unconstrained least mean square lms power minimization algorithm is employed to adapt the delay line weights it is shown that with the addition of the directional derivative constraints the beamformer quiescent bcampattern becomes a function of the location of the phase center used to specify the constraints a design criterion for choosing this location is suggested and simulation experiments which illustrate the performance of this new adaptive beamformer are presented

robust adaptive systems and self stabilization a methodology for the global stability analysis and consequently for the design of robust deterministic and stochastic adaptive control filtering and prediction is introduced the methodology represents a mathematical formalization of the self stabilization mechanism which is a natural characteristic of every properly designed adaptive system the underlying idea is the construction of a suitable lyapunov function for different periods of adaptation the effectiveness of the proposed approach is demonstrated by solving the robust deterministic and stochastic adaptive control problems it is shown that very small algorithm gains may produce very large signals in the adaptive loop which are unacceptable for practical applications the intensity of the admissible unmodeled dynamics does not depend on the algorithm gain and it is specified in terms of the corresponding h sup infinity norm in order to establish goal stability persistency exciting conditions are not required in the present results

a finite dimensional quantum model for the stock market abstract we present a finite dimensional version of the quantum model for the stock market proposed in c zhang and l huang a quantum model for the stock market physica a 389 2010 5769 our approach is an attempt to make this model consistent with the discrete nature of the stock price and is based on the mathematical formalism used in the case of the quantum systems with finite dimensional hilbert space the rate of return is a discrete variable corresponding to the coordinate in the case of quantum systems and the operator of the conjugate variable describing the trend of the stock return is defined in terms of the finite fourier transform the stock return in equilibrium is described by a finite gaussian function and the time evolution of the stock price directly related to the rate of return is obtained by numerically solving a schrodinger type equation

stability of discrete model reference adaptive control revisited abstract we demonstrate that the model reference adaptive controller is robust with respect to small model plant mismatch the sign and a lower bound on the high frequency gain are known and the control parameters are constrained to belong to a compact set which contains the parameters of a stabilizing controller data normalization and deadzones do not play a role in the analysis a constructive proof is used to develop bounds for the allowable gain of the model mismatch when the algorithm state is far from equilibrium the signals are measured by a decaying exponential the rate of convergence is estimated an expression which can be used to calculate the size of an overbounding set is developed its size scales uniformly with respect to the external disturbances the inverse of the adaptive gain and the reference the ideal case is obtained as these tend to zero this result holds true even when there is a model mismatch

design issues in adaptive control an integrated approach to the design of practical adaptive control algorithms is presented many existing ideas are brought together and the effect of various design parameters available to a user is explored the theory is extended by showing how the problem of stabilizability of the estimated model can be overcome by running parallel estimators it is shown how asymptotic tracking of deterministic set points can be achieved in the presence of unmodeled dynamics

convergence rate of least squares identification and adaptive control for stochastic systems the strong consistency and the convergence rate of least squares identification for the multidimensional armax model are established under some decaying excitation conditions which are satisfied if both input and output do not grow too fast and the attenuating excitation technique is applied the parameter identification results are applied to adaptive control systems with a quadratic loss function the rate of convergence of the loss function to its minimum is also obtained

theory and design of robust direct and indirect adaptive control schemes a general approach for designing and the theory for analysing robust direct and indirect adaptive control schemes for continuous time plants is presented the design approach involves the development of a general robust adaptive law and the use of the certainty equivalence principle to combine it with robust model reference and pole placement control structures the global stability properties and robustness of the developed adaptive control schemes are established by using a general theory which relates the properties of signals in the mean sense over intervals of time the developed theory and design approach are used to analyse and compare the robustness properties and performance of a wide class of robust adaptive laws which employ a dead zone fixed e1 and a switching modification as well as their variations

robust adaptive regulation with minimal prior knowledge a robust adaptive regulator is designed under minimal prior knowledge namely the order of a nominal plant model in a well defined sense the involved robustness means that the closed loop stability is guaranteed in the presence of some class of time varying parameters and unmodeled dynamics the main design feature of the proposed adaptive regulator consists in its self excitation capability together with an appropriate identification stabilization time splitting unlike in the available literature concerning robust adaptive control the involved self excitation is established independently of the parameter estimator properties the use of the robustness oriented modifications as deadzone and parameter projection or contraction which are aimed at achieving the parameter estimates boundedness is no longer required beforehand thereby reducing the underlying prior knowledge

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

pattern synthesis for arbitrary arrays using an adaptive array method this paper presents a new pattern synthesis algorithm for arbitrary arrays based on adaptive array theory with this algorithm the designer can efficiently control both mainlobe shaping and sidelobe levels the element weights optimize a weighted l sub 2 norm between desired and achieved patterns the values of the weighting function in the l sub 2 norm interpreted as imaginary jammers as in olen and compton s 1990 method are iterated to minimize exceedance of the desired sidelobe levels and minimize the absolute difference between desired and achieved mainlobe patterns the sidelobe control can be achieved by iteration only on sidelobe peaks in comparison to olen and compton s method the new algorithm provides a great improvement in mainlobe shaping control example simulations including both nonuniform linear and planar arrays are shown to illustrate the effectiveness of this algorithm

pattern synthesis of narrowband conformal arrays using iterative second order cone programming a new design method is proposed for the power or shaped beam pattern synthesis problem of narrowband conformal arrays where only the magnitude response is specified the proposed method iteratively linearizes the non convex power pattern function to obtain a convex subproblem in the design variables which can be solved optimally using second order cone programming socp in addition a wide variety of magnitude constraints such as non convex lower bound magnitude constraints can be incorporated an efficient technique for determining a reasonably good initial guess to the problem is also proposed to further improve the reliability of the method computer simulations show that the initial guesses so obtained converge to satisfactory solutions while satisfying various prescribed magnitude constraints design results show that the performance of the proposed method is comparable to the optimal solution previously obtained for uniform linear arrays with isotropic elements moreover we show by means of examples that the proposed method is also applicable to general non convex power pattern synthesis problems involving arbitrary array geometries arbitrary polarization characteristics and mutual coupling effect