A mathematical framework for new fault detection schemes in nonlinear stochastic continuous-time dynamical systems

n this work, a mathematical unifying framework for designing new fault detection schemes in nonlinear stochastic continuous-time dynamical systems is developed. These schemes are based on a stochastic process, called the residual, which reflects the system behavior and whose changes are to be detected. A quickest detection scheme for the residual is proposed, which is based on the computed likelihood ratios for time-varying statistical changes in the Ornstein–Uhlenbeck process. Several expressions are provided, depending on a priori knowledge of the fault, which can be employed in a proposed CUSUM-type approximated scheme. This general setting gathers different existing fault detection schemes within a unifying framework, and allows for the definition of new ones. A comparative simulation example illustrates the behavior of the proposed schemes.

Control of a Teleoperation System by State Convergence with Variable Time Delay

In this paper, we propose a novel control scheme for bilateral teleoperation of n degree-of-freedom (DOF) nonlinear robotic systems with time-varying communication delay. We consider that the human operator contains a constant force on the local manipulator. The local and remote manipulators are coupled using state convergence control scheme. By choosing a Lyapunov-Krasovskii functional, we show that the local-remote teleoperation system is asymptotically stable. It is also shown that, in the case of reliable communication protocols, the proposed scheme guarantees that the remote manipulator tracks the delayed trajectory of the local manipulator. The time delay of communication channel is assumed to be unknown and randomly time varying, but the upper bounds of the delay interval and the derivative of the delay are assumed to be known.

Stability Analysis of Teleoperation System by State Convergence with Variable Time Delay

We propose a novel control scheme for bilateral teleoperation of n degree-of-freedom (DOF) nonlinear robotic systems with time-varying communication delay. A major contribution from this work lies in the demonstration that the structure of a state convergence algorithm can be also applied to nth-order nonlinear teleoperation systems. By choosing a Lyapunov Krasovskii functional, we show that the local-remote teleoperation system is asymptotically stable. The time delay of communication channel is assumed to be unknown and randomly time varying, but the upper bounds of the delay interval and the derivative of the delay are assumed to be known.

Comments on multiple oscillatory solutions in systems with time-delay feedback

A complex Ginzburg-Landau equation subjected to local and global time-delay feedback terms is considered. In particular, multiple oscillatory solutions and their properties are studied. We present novel results regarding the disappearance of limit cycle solutions, derive analytical criteria for frequency degeneration, amplitude degeneration, frequency extrema. Furthermore, we discuss the influence of the phase shift parameter and show analytically that the stabilization of the steady state and the decay of all oscillations (amplitude death) cannot happen for global feedback only. Finally, we explain the onset of traveling wave patterns close to the regime of amplitude death.

An improved stability criterion for time-delay power systems with electric vehicles and high voltage direct current power links

This paper presents an improved stability criterion for load frequency control (LFC) of time-delay power systems including AC/HVDC transmission links and EVs. By employing a novel refined Jensen-based inequality, an improved stability condition is derived in terms of feasible linear matrix inequalities (LMIs) which allow us to compute the maximal upper bounds of time-delay ensuring stability of the LFC scheme equipped with an embedded controller. Cases studies here are implemented for LFC scheme of a two-area power system, which is interconnected by parallel (AC/HVDC) links, with embedded proportional integral (PI) controller for discharged EVs. The relationships between the parameters of PI controller, supplementary control of HVDC links and delay margins of the LFC scheme are also discussed. As a consequence of facts, the results of delay margins can be used as a guideline to tune PI controller and set-up parameters for HVDC control.

Observer design for one-sided Lipschitz discrete-time systems subject to delays and unknown inputs

In this paper, we address the problem of observer design for a class of nonlinear discrete-time systems in the presence of delays and unknown inputs. The nonlinearities studied in this work satisfy the one-sided Lipschitz and quadratically inner-bounded conditions which are more general than the traditional Lipschitz conditions. Both H∞ observer design and asymptotic observer design with reduced-order are considered. The designs are novel compared to other relevant nonlinear observer designs subject to time delays and disturbances in the literature. In order to deal with the time-delay issue as well as the bilinear terms which usually appear in the problem of designing observers for discrete-time systems, several mathematical techniques are utilized to deduce observer synthesis conditions in the linear matrix inequalities form. A numerical example is given to demonstrate the effectiveness and high performance of our results.

Chaotic synchronization of time-delay coupled Hindmarsh–Rose neurons via nonlinear control

Chaotic synchronization of two time-delay coupled Hindmarsh–Rose neurons via nonlinear control is investigated in this paper. Both the intrinsic slow current delay in a single Hindmarsh–Rose neuron and the coupling delay between the two neurons are considered. When there is no control, chaotic synchronization occurs for a limited range of the coupling strength and the time-delay values. To obtain complete chaotic synchronization irrespective of the time-delay or the coupling strength, we propose two nonlinear control schemes. The first uses adaptive control for chaotic synchronization of two electrically coupled delayed Hindmarsh–Rose neuron models. The second derives the sufficient conditions to ensure a complete synchronization between master and slave models through appropriate Lyapunov–Krasovskii functionals and the linear matrix inequality technique. Numerical simulations are carried out to show the effectiveness of the proposed methods.

Static output feedback frequency stabilization of time-delay power systems with coordinated electric vehicles state of charge control

In this paper, for the first time, electric vehicles are used for both the primary and secondary frequency controls to support power plants to rapidly suppress fluctuations in the system frequency due to load disturbances. Via networked control and wide-area communication infrastructures, multiple interval time-varying delays exist in the communication channels between the control center, power plant, and an aggregation of electric vehicles. By coordinating batteries’ state of charge control, the behaviors of the vehicle owners and the uncertainties imposed by the changes of the batteries’ state of charge are taken intoconsideration. A power system model incorporating multiple time-varying delays and uncertainties is first proposed. Then, a robust static output feedback frequency controller is designed to guarantee the resulting closed-loop system stable with an H∞ attenuation level. By utilizing a novel integral inequality, namely refined-Jensen inequality, and an improved reciprocally convex combination, the design conditions are formulated in terms of tractable linear matrix inequalities which can be efficiently solved by various computational tools. The effectiveness of the proposed control scheme is verified by extensive simulations.

The non-linear response of a gyrostabilized platform: Effects of correction torque time delay and of random inputs

First, the non-linear response of a gyrostabilized platform to a small constant input torque is analyzed in respect to the effect of the time delay (inherent or deliberately introduced) in the correction torque supplied by the servomotor, which itself may be non-linear to a certain extent. The equation of motion of the platform system is a third order nonlinear non-homogeneous differential equation. An approximate analytical method of solution of this equation is utilized. The value of the delay at which the platform response becomes unstable has been calculated by using this approximate analytical method. The procedure is illustrated by means of a numerical example. Second, the non-linear response of the platform to a random input has been obtained. The effects of several types of non-linearity on reducing the level of the mean square response have been investigated, by applying the technique of equivalent linearization and solving the resulting integral equations by using laguerre or Gaussian integration techniques. The mean square responses to white noise and band limited white noise, for various values of the non-linear parameter and for different types of non-linearity function, have been obtained. For positive values of the non-linear parameter the levels of the non-linear mean square responses to both white noise and band-limited white noise are low as compared to the linear mean square response. For negative values of the non-linear parameter the level of the non-linear mean square response at first increases slowly with increasing values of the non-linear parameter and then suddenly jumps to a high level, at a certain value of the non-linearity parameter.

The non-linear response of a gyrostabilized platform: Effects of correction torque time delay and of random inputs

First, the non-linear response of a gyrostabilized platform to a small constant input torque is analyzed in respect to the effect of the time delay (inherent or deliberately introduced) in the correction torque supplied by the servomotor, which itself may be non-linear to a certain extent. The equation of motion of the platform system is a third order nonlinear non-homogeneous differential equation. An approximate analytical method of solution of this equation is utilized. The value of the delay at which the platform response becomes unstable has been calculated by using this approximate analytical method. The procedure is illustrated by means of a numerical example. Second, the non-linear response of the platform to a random input has been obtained. The effects of several types of non-linearity on reducing the level of the mean square response have been investigated, by applying the technique of equivalent linearization and solving the resulting integral equations by using laguerre or Gaussian integration techniques. The mean square responses to white noise and band limited white noise, for various values of the non-linear parameter and for different types of non-linearity function, have been obtained. For positive values of the non-linear parameter the levels of the non-linear mean square responses to both white noise and band-limited white noise are low as compared to the linear mean square response. For negative values of the non-linear parameter the level of the non-linear mean square response at first increases slowly with increasing values of the non-linear parameter and then suddenly jumps to a high level, at a certain value of the non-linearity parameter.

Reduced Order Suboptimal Control Design for a Class of Nonlinear Distributed Parameter Systems Using POD and /spl thetas/-D Techniques

A new computational tool is presented in this paper for suboptimal control design of a class of nonlinear distributed parameter systems. First proper orthogonal decomposition based problem-oriented basis functions are designed, which are then used in a Galerkin projection to come up with a low-order lumped parameter approximation. Next, a suboptimal controller is designed using the emerging /spl thetas/-D technique for lumped parameter systems. This time domain sub-optimal control solution is then mapped back to the distributed domain using the same basis functions, which essentially leads to a closed form solution for the controller in a state feedback form. Numerical results for a real-life nonlinear temperature control problem indicate that the proposed method holds promise as a good suboptimal control design technique for distributed parameter systems.

Techniques for Analysis of Certain Nonlinear Systems

This paper suggests the use of simple transformations like ÿ=kx, kx2 for second-order nonlinear differential equations to effect rapid plotting of the phase-plane trajectories. The method is particularly helpful in determining quickly the trajectory slopes along simple curves in any desired region of the phase plane. New planes such as the tÿ-x, tÿ2-x are considered for the study of some groups of nonlinear time-varying systems. Suggestions for solving certain higher-order nonlinear systems are also made.