Catalogue Search | MBRL
Are you sure you want to remove the book from the shelf?
{{itemTitle}}
13,783
result(s) for
"continuous systems"
Sort by:
Kanban change leadership : creating a culture of continuous improvement
\"This book provides an understanding of what is necessary to properly understand change management with Kanban as well as how to apply it optimally in the workplace\"-- Provided by publisher.
Book
Free Energy and Equilibrium States for Families of Interval Maps
We study continuity, and lack thereof, of thermodynamical properties for one-dimensional dynamical systems. Under quite general
hypotheses, the free energy is shown to be almost upper-semicontinuous: some normalised component of a limit measure will have free
energy at least that of the limit of the free energies. From this, we deduce results concerning existence and continuity of equilibrium
states (including statistical stability). Metric entropy, not semicontinuous as a general multimodal map varies, is shown to be upper
semicontinuous under an appropriate hypothesis on critical orbits. Equilibrium states vary continuously, under mild hypotheses, as one
varies the parameter and the map. We give a general method for constructing induced maps which automatically give strong exponential
tail estimates. This also allows us to recover, and further generalise, recent results concerning statistical properties (decay of
correlations, etc.). Counterexamples to statistical stability are given which also show sharpness of the main results.
eBook
The fastest, simplified method of Lyapunov exponents spectrum estimation for continuous-time dynamical systems
Classical method of Lyapunov exponents spectrum estimation for a
n
-th-order continuous-time, smooth dynamical system involves Gram–Schmidt orthonormalization and calculations of perturbations lengths logarithms. In this paper, we have shown that using a new, simplified method, it is possible to estimate full spectrum of
n
Lyapunov exponents by integration of
(
n
-
1
)
perturbations only. In particular, it is enough to integrate just one perturbation to obtain two largest Lyapunov exponents, which enables to search for hyperchaos. Moreover, in the presented algorithm, only very basic mathematical operations such as summation, multiplication or division are applied, which boost the efficiency of computations. All these features together make the new method faster than any other known by the authors if the order of the system under consideration is low. Correctness the method has been tested for three examples: Lorenz system, Duffing oscillator and three Duffing oscillators coupled in the ring scheme. Moreover, efficiency of the method has been confirmed by two practical tests. It has been revealed that for low-order systems, the presented method is faster than any other known by authors.
Journal Article
A constructive design of state observer synthesis for 2-D continuous systems with time-varying delays
There are many observer design approaches that have been developed to estimate the state of a linear time delay system. This paper focuses on the observer design problem for two-dimensional (2-D) continuous systems with delays proposed by Roesser’s state space model. A new sufficient condition for 2-D state observer design of 2-D continuous-time systems with delays is developed. The key point is that the Lyapunov theory that is used here allows us to solve the problem using the technique of linear matrix inequalities, which is used to establish the 2-D state observers with delays. Finally, to illustrate the effectiveness of the proposed methodology, a numerical example is provided.
Journal Article
Nonlinear Continuous-Time System H∞ Control Based on Dynamic Quantization and Event-triggered Mechanism
The
H
∞
state feedback control problem of Takagi–Sugneo (T–S) fuzzy system with dynamic quantization and event-triggered mechanism is studied in this paper. Based on T–S fuzzy model, a new quantization scheme is proposed to solve the problem of synchronous quantization and event-triggered mechanism in continuous-time system. A new event-triggered communication scheme is proposed to improve the utilization rate of network resources. The sufficient conditions for the stability of
H
∞
state feedback control are given by means of linear matrix inequalities. Finally, the effectiveness of the proposed method is verified by a simulation of the spring-mass-damping system.
Journal Article
Neural-network-based online optimal control for uncertain non-linear continuous-time systems with control constraints
In this study, an online adaptive optimal control scheme is developed for solving the infinite-horizon optimal control problem of uncertain non-linear continuous-time systems with the control policy having saturation constraints. A novel identifier-critic architecture is presented to approximate the Hamilton–Jacobi–Bellman equation using two neural networks (NNs): an identifier NN is used to estimate the uncertain system dynamics and a critic NN is utilised to derive the optimal control instead of typical action–critic dual networks employed in reinforcement learning. Based on the developed architecture, the identifier NN and the critic NN are tuned simultaneously. Meanwhile, unlike initial stabilising control indispensable in policy iteration, there is no special requirement imposed on the initial control. Moreover, by using Lyapunov's direct method, the weights of the identifier NN and the critic NN are guaranteed to be uniformly ultimately bounded, while keeping the closed-loop system stable. Finally, an example is provided to demonstrate the effectiveness of the present approach.
Journal Article
Transformations of Linear Standard Systems to Positive Asymptotically Stable Linear Ones
New approaches to transformations of linear continuous-time systems to their positive asymptotically stable canonical controllable (observable) forms are proposed. It is shown that, if the system matrix is nonsingular, then the desired transformation matrix can be chosen in block diagonal form. Procedures for the computation of the transformation matrices are proposed and illustrated with simple numerical examples.
Journal Article
Online identification of non-homogeneous fractional order Hammerstein continuous systems based on the principle of multi-innovation
In the process of online identification of non-homogeneous fractional order Hammerstein systems in continuous time, traditional identification algorithms have slow convergence speed and low precision, and it is difficult to simultaneously identify multiple non-homogeneous fractional orders and system parameters. This paper proposes an identification method based on the principle of multi-innovation identification. Firstly, the Hammerstein non-homogeneous fractional order continuous-time system is given, and the parameters to be identified are clarified. Secondly, based on the Riemann–Liouville differential operator, the partial derivative equation of the objective function to non-homogeneous fractional orders in the identification process is given, which ensures that the coefficients of the system and non-homogeneous fractional orders can be identified at the same time. Then, within the given value range of the fractional vector, the partial derivative equation is progressively simplified to make it convenient for online calculation. And the principle of multi-innovation is introduced into the traditional Levenberg–Marquardt algorithm, which improves the convergence speed and convergence precision of the algorithm. Finally, we illustrate the validity of the theory through two experiments, including a numerical simulation example of a fractional-order system and a numerical example of a flexible manipulator system. Experiments prove that the algorithm proposed in this paper has good performance in both simulation examples and actual systems.
Journal Article
Online approximate optimal control for affine non-linear systems with unknown internal dynamics using adaptive dynamic programming
In this study, a novel online adaptive dynamic programming (ADP)-based algorithm is developed for solving the optimal control problem of affine non-linear continuous-time systems with unknown internal dynamics. The present algorithm employs an observer–critic architecture to approximate the Hamilton–Jacobi–Bellman equation. Two neural networks (NNs) are used in this architecture: an NN state observer is constructed to estimate the unknown system dynamics and a critic NN is designed to derive the optimal control instead of typical action–critic dual networks employed in traditional ADP algorithms. Based on the developed architecture, the observer NN and the critic NN are tuned simultaneously. Meanwhile, unlike existing tuning laws for the critic, the newly developed critic update rule not only ensures convergence of the critic to the optimal control but also guarantees stability of the closed-loop system. No initial stabilising control is required, and by using recorded and instantaneous data simultaneously for the adaptation of the critic, the restrictive persistence of excitation condition is relaxed. In addition, Lyapunov direct method is utilised to demonstrate the uniform ultimate boundedness of the weights of the observer NN and the critic NN. Finally, an example is provided to verify the effectiveness of the present approach.
Journal Article
Stabilizing graph-dependent linear switched systems with unstable subsystems
We give sufficient conditions for stability of a continuous-time linear switched system consisting of finitely many subsystems. The switching between subsystems is governed by an underlying graph. The results are applicable to switched systems having some or all non-Hurwitz subsystems. We also present a slow-fast switching mechanism on subsystems comprising simple loops of underlying graph to ensure stability of the switched system.
Journal Article