Showing papers on "Riccati equation published in 2012"
TL;DR: It is shown that the sigma point function evaluations can be used in the classical EKF rather than an explicitly linearized model, and a less cited version of the EKf based on a second-order Taylor expansion is shown to be quite closely related to UKF.
Abstract: The unscented Kalman filter (UKF) has become a popular alternative to the extended Kalman filter (EKF) during the last decade. UKF propagates the so called sigma points by function evaluations using the unscented transformation (UT), and this is at first glance very different from the standard EKF algorithm which is based on a linearized model. The claimed advantages with UKF are that it propagates the first two moments of the posterior distribution and that it does not require gradients of the system model. We point out several less known links between EKF and UKF in terms of two conceptually different implementations of the Kalman filter: the standard one based on the discrete Riccati equation, and one based on a formula on conditional expectations that does not involve an explicit Riccati equation. First, it is shown that the sigma point function evaluations can be used in the classical EKF rather than an explicitly linearized model. Second, a less cited version of the EKF based on a second-order Taylor expansion is shown to be quite closely related to UKF. The different algorithms and results are illustrated with examples inspired by core observation models in target tracking and sensor network applications.
325 citations
TL;DR: A Newton-based extremum seeking algorithm for the multivariable case that allows all the parameters to converge with the same speed, yielding straight trajectories to the extremum even with maps that have highly elongated level sets, in contrast to curved ''steepest descent'' trajectories of the gradient algorithm.
236 citations
01 Dec 2012
TL;DR: The proposed method can be implemented in two different ways: as an event-based scheme where transmit decisions are made online, or as a time-based periodic transmit schedule if a periodic solution to the switching Riccati equation is found.
Abstract: An event-based state estimation scenario is considered where a sensor sporadically transmits observations of a scalar linear process to a remote estimator. The remote estimator is a time-varying Kalman filter. The triggering decision is based on the estimation variance: the sensor runs a copy of the remote estimator and transmits a measurement if the associated measurement prediction variance exceeds a tolerable threshold. The resulting variance iteration is a new type of Riccati equation with switching that corresponds to the availability or unavailability of a measurement and depends on the variance at the previous step. We study asymptotic properties of the variance iteration and, in particular, asymptotic convergence to a periodic solution.
214 citations
TL;DR: The proposed stochastic optimal control method uses an adaptive estimator (AE) and ideas from Q-learning to solve the infinite horizon optimal regulation of unknown NCS with time-varying system matrices and produces an optimal control scheme that operates forward-in-time manner for unknown linear systems.
195 citations
TL;DR: In this paper, the Riccati equation approach was used to design a full-order observer for one-sided Lipschitz nonlinear systems, and the reduced-order observers were designed for the same purpose.
144 citations
TL;DR: The resulting nonlinear equation for the evolution of weakly nonlinear hydrodynamic disturbances on a static cosmological background with self-focusing in a two-dimensional nonlinear Schrodinger (NLS) equation was transformed to an ordinary differential equation, which depended only on one function ξ and can be solved.
138 citations
TL;DR: In this article, the fractional derivatives in the sense of modified Riemann-Liouville derivative and the Backlund transformation of fractional Riccati equation are employed for constructing the exact solutions of nonlinear fractional partial differential equations.
114 citations
TL;DR: In this article, three control strategies are used for controlling the trajectory of the system: state dependent Riccati Equation (SDRE), optimal linear feedback control, and fuzzy sliding mode control.
Abstract: In this work, we deal with a micro electromechanical system (MEMS), represented by a micro-accelerometer. Through numerical simulations, it was found that for certain parameters, the system has a chaotic behavior. The chaotic behaviors in a fractional order are also studied numerically, by historical time and phase portraits, and the results are validated by the existence of positive maximal Lyapunov exponent. Three control strategies are used for controlling the trajectory of the system: State Dependent Riccati Equation (SDRE) Control, Optimal Linear Feedback Control, and Fuzzy Sliding Mode Control. The controls proved effective in controlling the trajectory of the system studied and robust in the presence of parametric errors.
92 citations
TL;DR: In this article, a new integrable equation derived recently by V.S.Novikov was investigated, and sufficient conditions on the initial data were established to guarantee the formulation of singularities in finite time.
Book•
16 Nov 2012
TL;DR: The authors develop theory for a control problem with ordinary differential equations subject to boundary conditions of equality and inequality type and for mixed state-control constraints of equality type.
Abstract: This book is devoted to the theory and applications of second-order necessary and sufficient optimality conditions in the calculus of variations and optimal control. The authors develop theory for a control problem with ordinary differential equations subject to boundary conditions of equality and inequality type and for mixed state-control constraints of equality type. The book is distinctive in that necessary and sufficient conditions are given in the form of no-gap conditions; the theory covers broken extremals where the control has finitely many points of discontinuity; and a number of numerical examples in various application areas are fully solved. Audience: This book is suitable for researchers in calculus of variations and optimal control and researchers and engineers in optimal control applications in mechanics; mechatronics; physics; economics; and chemical, electrical, and biological engineering. Contents: List of Figures; Notation; Preface; Introduction; Part I: Second-Order Optimality Conditions for Broken Extremals in the Calculus of Variations; Chapter 1: Abstract Scheme for Obtaining Higher-Order Conditions in Smooth Extremal Problems with Constraints; Chapter 2: Quadratic Conditions in the General Problem of the Calculus of Variations; Chapter 3: Quadratic Conditions for Optimal Control Problems with Mixed Control-State Constraints; Chapter 4: Jacobi-Type Conditions and Riccati Equation for Broken Extremals; Part II: Second-Order Optimality Conditions in Optimal Bang-Bang Control Problems; Chapter 5: Second-Order Optimality Conditions in Optimal Control Problems Linear in a Part of Controls; Chapter 6: Second-Order Optimality Conditions for Bang-Bang Control; Chapter 7: Bang-Bang Control Problem and Its Induced Optimization Problem; Chapter 8: Numerical Methods for Solving the Induced Optimization Problem and Applications; Bibliography; Index.
TL;DR: In this paper, the Lie classical method was used to study the coupled Higgs field equation and Hamiltonian amplitude equation, and the travelling wave solutions were derived by hyperbolic, trigonometric and rational functions.
Abstract: In this paper, coupled Higgs field equation and Hamiltonian amplitude equation are studied using the Lie classical method. Symmetry reductions and exact solutions are reported for Higgs equation and Hamiltonian amplitude equation. We also establish the travelling wave solutions involving parameters of the coupled Higgs equation and Hamiltonian amplitude equation using (G′/G)-expansion method, where G = G(ξ) satisfies a second-order linear ordinary differential equation (ODE). The travelling wave solutions expressed by hyperbolic, trigonometric and the rational functions are obtained.
Posted Content•
TL;DR: In this paper, a linear-quadratic optimal control problem for mean-field stochastic differential equations with constant coefficients in an infinite horizon is considered, and the stabilizability of the control system is studied followed by the discussion of the wellposedness of the LQ problem.
Abstract: A linear-quadratic (LQ, for short) optimal control problem is considered for mean-field stochastic differential equations with constant coefficients in an infinite horizon. The stabilizability of the control system is studied followed by the discussion of the well-posedness of the LQ problem. The optimal control can be expressed as a linear state feedback involving the state and its mean, through the solutions of two algebraic Riccati equations. The solvability of such kind of Riccati equations is investigated by means of semi-definite programming method.
TL;DR: In this article, the robust Kalman filtering problem for discrete-time nonlinear systems with norm-bound parameter uncertainties is studied and a Riccati equation is derived in the presence of both the parameter uncertainties and the linearization errors.
TL;DR: In this paper, some new traveling wave solutions of the (4 + 1)-dimensional Fokas equation, (3 + 1-dimensional Jumbo-Miwa equation and (2 + 1]-dimensional Boiti-Leon-Pempinelli equation are obtained through the (1 − 1)-expansion technique, which is very effective and powerful for solving higher-dimensional nonlinear problems arising in mathematical physics.
01 Jan 2012
TL;DR: It is shown that it is possible to stabilize perturbed flows described by Navier-Stokes equations by designing a stabilizing controller based on a corresponding linear-quadratic optimal control problem.
Abstract: We consider optimal control-based boundary feedback stabilization of flow problems for incompressible fluids. We follow an analytical approach laid out during the last years in a series of papers by Barbu, Lasiecka, Triggiani, Raymond, and others. They have shown that it is possible to stabilize perturbed flows described by Navier-Stokes equations by designing a stabilizing controller based on a corresponding linear-quadratic optimal control problem. For this purpose, algorithmic advances in solving the associated algebraic Riccati equations are needed and investigated here. The computational complexity of the new algorithms is essentially proportional to the simulation of the forward problem.
TL;DR: A high gain like observer with updated gain is proposed for a class of cascade nonlinear and non triangular systems that are observable for any input to perform an admissible tradeoff between state reconstruction dynamics and noise amplification.
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TL;DR: This paper derives the maximum principle for the leader's global Stackelberg solution under the adapted closed-loop memoryless information structure, where the term global signifies theLeader's domination over the entire game duration.
Abstract: This paper obtains the maximum principle for both stochastic (global) open-loop and stochastic (global) closed-loop Stackelberg differential games. For the closed-loop case, we use the theory of controlled forward-backward stochastic differential equations to derive the maximum principle for the leader's optimal strategy. In the special case of the open-loop linear quadratic Stackelberg game, we consider the follower's Hamiltonian system as the leader's state equation, derive the related stochastic Riccati equation, and show the existence and uniqueness of the solution to the Riccati equation under appropriate assumptions. However, for the closed-loop linear quadratic Stackelberg game, we can write the related Riccati equation consisting of forward-backward stochastic differential equations, while leaving the existence of its solution as an open problem.
TL;DR: The explicit form of the optimal control is derived from a linear anticipated forward–backward stochastic differential delayed equation and the optimal state feedback regulator is studied in two special cases.
TL;DR: In this article, a time-consistent optimal control problem is formulated and studied for a controlled linear ordinary differential equation with quadratic cost functional, and a notion of equilibrium control is introduced, which can be regarded as a timeconsistent solution to the original time-inconsistent problem.
Abstract: A time-inconsistent optimal control problem is formulated and studied for a controlled linear ordinary differential equation with quadratic cost functional. A notion of equilibrium control is introduced, which can be regarded as a time-consistent solution to the original time-inconsistent problem. Under certain conditions, we constructively prove the existence of such an equilibrium control which is represented via a forward ordinary differential equation coupled with a backward Riccati--Volterra integral equation. Our constructive approach is based on the introduction of a family of $N$-person non-cooperative differential games.
TL;DR: In this paper, a generalization of the Gaussian wave packet solution for the harmonic oscillator and the corresponding creation and annihilation operators is presented that also applies for wave packets with time-dependent width as they occur for systems with different initial conditions, timedependent frequency or in contact with a dissipative environment.
Abstract: Based on the Gaussian wave packet solution for the harmonic oscillator and the corresponding creation and annihilation operators, a generalization is presented that also applies for wave packets with time-dependent width as they occur for systems with different initial conditions, time-dependent frequency or in contact with a dissipative environment. In all these cases the corresponding coherent states, position and momentum uncertainties and quantum mechanical energy contributions can be obtained in the same form if the creation and annihilation operators are expressed in terms of a complex variable that fulfills a nonlinear Riccati equation which determines the time-evolution of the wave packet width. The solutions of this Riccati equation depend on the physical system under consideration and on the (complex) initial conditions and have close formal similarities with general superpotentials leading to isospectral potentials in supersymmetric quantum mechanics. The definition of the generalized creation and annihilation operator is also in agreement with a factorization of the operator corresponding to the Ermakov invariant that exists in all cases considered.
TL;DR: In this article, the modified simple equation method is applied to construct exact solutions of the modified equal width (MEW) equation and the Fisher equation, and the nonlinear Telegraph equation and Cahn-Allen equation.
TL;DR: In this article, the effect of input time delay on the stability of a controlled high-dimensional aeroelastic system in an incompressible flow field was revealed and a new optimal control law was proposed to suppress the flutter of the high dimensional annealing system with time delay in the control loop.
TL;DR: In this article, the authors apply the Exp-function method to find exact solutions for two nonlinear partial differential equations (NPDE) and a nonlinear ordinary differential equation (NODE), namely, Cahn-Hilliard equation, Allen-Cahn equation and Steady-State equation, respectively.
TL;DR: In this article, the dynamical behavior of positive solution for a system of a rational third-order difference equation is studied, where positive solution is defined as a positive solution of the third order difference equation.
Abstract: In this paper, we study the dynamical behavior of positive solution for a system of a rational third-order difference equation
TL;DR: The so-called information-based pruning algorithm is proposed, which utilizes the information matrices of the sensors and the monotonicity of the Riccati equation to minimize the estimation error over multiple time steps in a computationally tractable fashion.
Abstract: In the considered linear Gaussian sensor scheduling problem, only one sensor out of a set of sensors performs a measurement. To minimize the estimation error over multiple time steps in a computationally tractable fashion, the so-called information-based pruning algorithm is proposed. It utilizes the information matrices of the sensors and the monotonicity of the Riccati equation. This allows ordering sensors according to their information contribution and excluding many of them from scheduling. Additionally, a tight lower is calculated for branch-and-bound search, which further improves the pruning performance.
TL;DR: By using the subsidiary ordinary differential equation method, many explicit Jacobian elliptic periodic solutions of the cubic-quintic nonlinear optical transmission equation with higher-order dispersion nonlinear terms and self-steepening term are obtained as mentioned in this paper.
Abstract: By using the subsidiary ordinary differential equation method, many explicit Jacobian elliptic periodic solutions of the cubic-quintic nonlinear optical transmission equation with higher-order dispersion nonlinear terms and self-steepening term are obtained. The results are discussed.
TL;DR: In this paper, the structure of the singular set for a C1 smooth surface in the 3-dimensional Heisenberg group ℍ1 was studied and a Codazzi-like equation for the p-area element along the characteristic curves on the surface was discovered.
Abstract: In this paper, we study the structure of the singular set for a C1 smooth surface in the 3-dimensional Heisenberg group ℍ1. We discover a Codazzi-like equation for the p-area element along the characteristic curves on the surface. Information obtained from this ordinary differential equation helps us to analyze the local configuration of the singular set and the characteristic curves. In particular, we can estimate the size and obtain the regularity of the singular set. We understand the global structure of the singular set through a Hopf-type index theorem. We also justify the Codazzi-like equation by proving a fundamental theorem for local surfaces in ℍ1.