control design of uncertain quantum systems with fuzzy estimators an approach of control design using fuzzy estimators fes is proposed for quantum systems with uncertainties two types of quantum control problems are considered 1 control of a pure state quantum system in the presence of uncertainties and 2 control design of quantum systems with initial mixed states and uncertainties for the first type of tasks a partial feedback control scheme with an fe is presented to design controllers in this scheme an fe is trained to estimate the quantum state for feedback control of a quantum system and controlled projective measurement is used to assist in controlling the system for the second type of quantum control tasks a probabilistic fuzzy estimator pfe is trained to estimate the quantum state for control design of a quantum system with an initial mixed state and a corresponding control algorithm is proposed to design a control law that drives the system from the mixed state to a target pure state two examples of two spin 1 2 systems are also presented and analyzed to demonstrate the process of control design and potential applications of the proposed approach

a probabilistic fuzzy logic system for modeling and control in this paper a probabilistic fuzzy logic system pfls is proposed for the modeling and control problems similar to the ordinary fuzzy logic system fls the pfls consists of the fuzzification inference engine and defuzzification operation to process the fuzzy information different to the fls it uses the probabilistic modeling method to improve the stochastic modeling capability by using a three dimensional membership function mf the pfls is able to handle the effect of random noise and stochastic uncertainties existing in the process a unique defuzzification method is proposed to simplify the complex operation finally the proposed pfls is applied to a function approximation problem and a robotic system it shows a better performance than an ordinary fls in stochastic circumstance

quantum risk sensitive estimation and robustness this paper studies a quantum risk sensitive estimation problem and investigates robustness properties of the filter this is a direct extension to the quantum case of analogous classical results all investigations are based on a discrete approximation model of the quantum system under consideration this allows us to study the problem in a simple mathematical setting we close the paper with some examples that demonstrate the robustness of the risk sensitive estimator

ensemble control of bloch equations in this article we study a class of control problems which involves controlling a continuum of dynamical systems with different values of parameters characterizing the system dynamics by using the same control signal we call such problems control of ensembles the motivation for looking into these problems comes from the manipulation of an ensemble of nuclear spins in nuclear magnetic resonance nmr spectroscopy and imaging mri with dispersions in natural frequencies and the strengths of the applied radio frequency rf field from the standpoint of mathematical control theory the challenge is to simultaneously steer a continuum of systems between points of interest with the same control input this raises some new and unexplored questions about controllability of such systems we show that controllability of an ensemble can be understood by the study of the algebra of polynomials defined by the noncommuting vector fields that govern the system dynamics a systematic study of these systems has immediate applications to broad areas of control of ensembles of quantum systems as arising in coherent spectroscopy and quantum information processing the new mathematical structures appearing in such problems are excellent motivation for new developments in control theory

on the canonical forms of the multi dimensional averaged poisson brackets we consider here special poisson brackets given by the averaging of local multi dimensional poisson brackets in the whitham method for the brackets of this kind it is natural to ask about their canonical forms which can be obtained after transformations preserving the physical meaning of the field variables we show here that the averaged bracket can always be written in the canonical form after a transformation of hydrodynamic type in the case of absence of annihilators of initial bracket however in general case the situation is more complicated as we show here in more general case the averaged bracket can be transformed to a pseudo canonical form under some special physical requirements on the initial bracket

transfer function approach to quantum control part i dynamics of quantum feedback systems this paper gives a unified approach to feedback control theory of quantum mechanical systems of bosonic modes described by noncommutative operators a quantum optical closed loop including a plant and controller is developed and its fundamental structural properties are analyzed extensively from a purely quantum mechanical point of view in order to facilitate the use of control theory in microscopic world described by quantum theory in particular an input output description of quantum mechanical systems which is essential in describing the behavior of the feedback systems is fully formulated and developed this would then provide a powerful tool for quantum control and pave an avenue that connects control theory to quantum dynamics this paper is divided into two parts the first part is devoted to the basic formulation of quantum feedback control via quantum communication and local operations on an optical device cavity that can be regarded as a unit of quantum dynamics of bosonic modes the formulation introduced in this paper presents the feature intrinsic in quantum feedback systems based on quantum stochastic differential equations the input output description provides a basis for developing quantum feedback control through the transfer function representation of quantum feedback systems in the follow up paper the quantum mechanical representation of feedback is further elaborated to yield the control theoretical representation of fundamental notions of quantum theory uncertainty principle e g and some applications are presented

controllability of quantum systems with switching control this article focuses on wavefunction controllability of a class of quantum systems with switching control first we present a specific quantum system which is not wavefunction controllable under the action of any one of two controllers with different fixed structures however we prove that the system is wavefunction controllable if the control input is allowed to switch between the two controllers then we present a sufficient condition for wavefunction controllability of a class of quantum systems with switching control and briefly discuss the problem of control design for such quantum control systems finally two illustrative examples are presented to demonstrate a possible control design process for the proposed method

stabilizing feedback controls for quantum systems no quantum measurement can give full information on the state of a quantum system hence any quantum feedback control problem is necessarily one with partial observations and can generally be converted into a completely observed control problem for an appropriate quantum filter as in classical stochastic control theory here we study the properties of controlled quantum filtering equations as classical stochastic differential equations we then develop methods using a combination of geometric control and classical probabilistic techniques for global feedback stabilization of a class of quantum filters around a particular eigenstate of the measurement operator

analysis and synthesis of attractive quantum markovian dynamics we propose a general framework for investigating a large class of stabilization problems in markovian quantum systems building on the notions of invariant and attractive quantum subsystem we characterize attractive subspaces by exploring the structure of the invariant sets for the dynamics our general analysis results are exploited to assess the ability of open loop hamiltonian and output feedback control strategies to synthesize markovian generators which stabilize a target subsystem subspace or pure state in particular we provide an algebraic characterization of the manifold of stabilizable pure states in arbitrary finite dimensional markovian systems that leads to a constructive strategy for designing the relevant controllers implications for stabilization of entangled pure states are addressed by example

spatially constrained fuzzy clustering based sensor placement for spatiotemporal fuzzy control system many industrial processes are spatiotemporal dynamic systems a three dimensional fuzzy logic controller 3 d flc has been recently developed to process the inherent capability of spatiotemporal dynamic systems sensor placement which is always crucial to the control of spatiotemporal dynamic systems is also critical to the design of the 3 d flc in this paper a new sensor placement strategy is developed its main feature is to position the sensor by utilizing the main characteristics of spatial distribution the key technique is to use a spatial constrained fuzzy c means algorithm to extract the characteristics of spatial distribution for an easy implementation a systematic sensor placement design scheme in four steps i e data collection dimension reduction data clustering and sensor locating is developed finally control of a catalytic packed bed reactor is taken as an application to demonstrate the effectiveness of the proposed sensor placement scheme

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

systems control with generalized probabilistic fuzzy reinforcement learning reinforcement learning rl is a valuable learning method when the systems require a selection of control actions whose consequences emerge over long periods for which input output data are not available in most combinations of fuzzy systems and rl the environment is considered to be deterministic in many problems however the consequence of an action may be uncertain or stochastic in nature in this paper we propose a novel rl approach to combine the universal function approximation capability of fuzzy systems with consideration of probability distributions over possible consequences of an action the proposed generalized probabilistic fuzzy rl gpfrl method is a modified version of the actor critic ac learning architecture the learning is enhanced by the introduction of a probability measure into the learning structure where an incremental gradient descent weight updating algorithm provides convergence our results show that the proposed approach is robust under probabilistic uncertainty while also having an enhanced learning speed and good overall performance

is measurement based feedback still better for quantum control systems in this paper we put forward a fundamental question concerning feedback control of quantum systems is measurement based feedback control still better than open loop control in contrast to the classical control theory the answer is far from obvious this is because measurement based feedback needs measurement to reduce the system uncertainty whereas the measurement on a quantum system will inevitably increase the system uncertainty in turn in fact there is a complicated tradeoff between the uncertainty introduced and the information gained by the measurement on a quantum system to investigate this fundamental problem we will only focus on a typical model of coherent control mode with and without the decoherence term in the paper by establishing some fundamental limits on the performances of both the open loop and measurement based feedback controls we will demonstrate via simulation that the measurement based feedback control of quantum systems is still superior to the open loop control in some sense for the typical model under consideration

parallelization of a fuzzy control algorithm using quantum computation quantum computation is proposed for the parallelization of a fuzzy logic control flc algorithm quantum computation speeds up the fuzzy inference since serial operations between matrices of large dimensionality are now replaced by a one step quantum addition or a quantum subtraction the unitarity properties of the algorithm prove that the flc stands for a simulator of a quantum computing machine

robust incoherent control of qubit systems via switching and optimisation a robust incoherent quantum control scheme via projective measurements plus unitary transformations is proposed for driving a qubit system from an unknown initial mixed state to an arbitrary target pure state this scheme consists of two main steps projective measurement on the initial mixed state and optimal control between two pure states the first step projects the initial state into an eigenstate of the qubit system by projective measurement and guarantees that the proposed scheme is robust to different initial mixed states the second step finds a set of suitable optimal controls to drive the qubit system from the conditional eigenstate to the target pure state the connection between the two steps is accomplished by a switching strategy to accomplish the second step two approaches are presented in detail these approaches are time optimal transition with unbounded control and bang bang control with minimal switches the minimal time and minimal number of switches in these approaches can be calcu

feedback stabilization of isospectral control systems on complex flag manifolds application to quantum ensembles the convex set of density operators of an n level quantum mechanical system foliated as a complex flag manifold where each leaf is identified with the adjoint unitary orbit of the eigenvalues of a density matrix for an isospectral bilinear control system evolving on such an orbit the state feedback stabilization problem admits a natural lyapunov based time varying feedback design a global description of the domain of attraction of the closed loop system can be provided based on a ldquoroot spacerdquo like structure of the cone of density operators the converging conditions are time independent but depend on the topology of the flag manifold it is shown that the closed loop must have a number of equilibria at least equal to the euler characteristic of the manifold thus imposing topological obstructions to global stabilizability

feedback control of quantum state reduction feedback control of quantum mechanical systems must take into account the probabilistic nature of quantum measurement we formulate quantum feedback control as a problem of stochastic nonlinear control by considering separately a quantum filtering problem and a state feedback control problem for the filter we explore the use of stochastic lyapunov techniques for the design of feedback controllers for quantum spin systems and demonstrate the possibility of stabilizing one outcome of a quantum measurement with unit probability

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

a three dimensional fuzzy control methodology for a class of distributed parameter systems the traditional fuzzy set is two dimensional 2 d with one dimension for the universe of discourse of the variable and the other for its membership degree this 2 d fuzzy set is not able to handle the spatial information the traditional fuzzy logic controller flc developed from this 2 d fuzzy set should not be able to control the distributed parameter system that has the tempo spatial nature a three dimensional 3 d fuzzy set is defined to be made of a traditional fuzzy set and an extra dimension for spatial information based on concept of the 3 d fuzzy set a new fuzzy control methodology is proposed to control the distributed parameter system similar to the traditional flc it still consists of fuzzification rule inference and defuzzification operations different to the traditional flc it uses multiple sensors to provide 3 d fuzzy inputs and possesses the inference mechanism with 3 d nature that can fuse these inputs into a so called ldquospatial membership function rdquo thus a simple 2 d rule base can still be used for two obvious advantages one is that rules will not increase as sensors increase for the spatial measurement the other is that computation of this 3 d fuzzy inference can be significantly reduced for real world applications using only a few more sensors the proposed flc is able to process the distributed parameter system with little complexity increased from the traditional flc the 3 d flc is successfully applied to a catalytic packed bed reactor and compared with the traditional flc the results demonstrate its effectiveness to the nonlinear unknown distributed parameter process and its potential to a wide range of engineering applications