R. K. P. Bhatt

Brief paper: Experience inclusion in iterative learning controllers: Fuzzy model based approaches

Iterative learning control (ILC) is a new domain in control system that motivates, whether mechanical robots can learn a prescribed ideal motion by themselves using information represented by the measured data gathered in the previous practice. For each new desired trajectory task, the conventional ILC methods have to start its learning with zero initial input assumption. Instead of such zero initial input assumption, in this paper, the idea of using the past trajectory tracking experiences on the initial input selection for tracking new trajectory-tracking tasks have been highlighted. Certain methods of experience inclusion in iterative learning controllers (ILC) are proposed. Approximate fuzzy data model (AFDM) and type-1 fuzzy logic system (FLS) techniques have been adopted for the process of initial input selection. Performance of the proposed fuzzy rule based model-based ILC approaches on initial error reduction and in error convergence issues are proved. Numerical experimentation on a two-link manipulator model with the inclusion of actuator dynamics verifies the performance of the proposed fuzzy model-based ILC approaches. Comparison with existing local learning technique on the selection of initial input for ILC algorithm proves the efficacy of the proposed AFDM and type-1 FLS-based methods.

A Novel Discrete Distribution and Process to Model Self-Similar Traffic

Network traffic is modeled as Poisson process for analytic simplicity, even though a number of traffic studies have shown that packet interarrivals are not exponentially distributed. Packet arrivals deviate considerably from Poissonity and follow statistical self-similar and long-range dependent behavior (LRD). We propose a novel discrete distribution for the counting process and show that for such a process the interarrivals are Pareto distributed. This new process is self-similar and exhibits long-range dependent behavior.

Delay-distribution-dependent Robust Stability Analysis of Uncertain Lurie Systems with Time-varying Delay

Abstract In this paper, the problem of robust absolute stability of Lurie system with probabilistic time-varying delay and norm-bounded parametric uncertainty is considered. The time delay variation range is divided into two subintervals. By considering the probability distribution of the time-varying delay between the two subintervals and the knowledge of the delay variation range, a novel linear matrix inequalities (LMIs) based stability condition is derived by defining a Lyapunov Krasovskii functional. It is illustrated with the help of numerical examples that the derived stability criteria can lead to less conservative results as compared to the results obtained by the traditional method of using the delay variation range information only.

Wavelet series based iterative learning controller design for industrial robot manipulators

In this paper, a wavelet series based learning controller has been proposed for the tracking control of robot manipulator. Wavelet series approximation is used to approximate the desired and actual trajectories of the system into finite number of wavelet coefficients. A learning controller is designed in wavelet domain which forces the wavelet coefficients of the actual output approach to the corresponding wavelet coefficients of the desired trajectory, which are known constants, such that the tracking of robot manipulator is achieved. Numerical experimentation studies show the ability of the learning controller designed in wavelet domain in the presence of uncertainties in robot manipulator system.

NHPP process associated with heavy tail interarrivals in network traffic

Packet arrival processes for data network are not consistent with Poisson processes. It has been established that arrival process is self-similar and the number of TCP connections initiated by a user session is heavy-tailed. The heavy tail or long tail distributions yield better model for data packet arrival models than exponential models. In particular it is observed that the Weibull, Pareto and Lognormal distribution give a good fit for the interarrival times for Web applications, LAN, MAN, WAN etc. We show that for Weibull interarrivals, the counting process formed is a Duane process, a less known counting process. In this paper we show that if packet interarrivals are modeled according to Lognormal distribution which is a example of a class of heavy-tail distributions, than the corresponding renewal process is not a Poisson process. We give a new result of approximate mean arrival rate of counting process for Lognormal interarrivals. We show that packet arrival process of heavy-tailed distributed interarrivals form Non Homogeneous Poisson Process and thus mean packet arrival rate is not constant but it is time varying.

Offered-load model for Pareto inter-arrival network traffic

In the network data, interarrival times are heavy-tail distributed. Weibull, Pareto and Lognormal are the best examples of heavy-tail distributions. These distributions give time-varying arrival rates. Also, renewal processes for these interarrivals are Non-homogeneous Poisson processes. The network traffic is, thus, non-stationary. Many of the theoretical tools, such as equilibrium probabilities for Markov chains, matrix geometric solutions and Laplace transforms are not available for queue with time varying rates. Since no closed form expressions of Laplace transform of Weibull, Pareto and Lognormal distributions are available, the queueing analysis becomes complicated. In this paper we present queueing analysis of heavy-tail network traffic, and thus, time dependent queuing model Mt/G/∞ is analyzed for heavy-tail Pareto arrivals. In particular, we find analytical expressions for the time-dependent mean function (offered load), denoted here as m(t), which depends on the time-dependent arrival rate function λ(t) and service time distribution.

Absolute stability analysis of neutral type Lurie system with unbounded distributed delay and interval time-varying probabilistic delay

In this paper, a novel stability criterion for the absolute stability of neutral type Lurie system with unbounded distributed and interval time-varying delay is proposed. The delay range is divided into two segments for stability analysis. The probability distribution of interval time-varying delay in the two segments is assumed to be known a priori. A tighter bounding technique is developed for the integral terms arising in the derivative of Lyapunov-Krasovskii functional (LKF). This bounding technique along with the Wirtinger inequality is used to develop the absolute stability criteria in terms of linear matrix inequalities. The proposed stability analysis has been further extended to the robust absolute stability of uncertain Lurie system of neutral type with mixed delays. The effectiveness of the proposed approach has been illustrated through numerical examples.

Region Reaching and Obstacle Avoidance for Autonomous Underwater Vehicle without Velocity Measurement

Abstract In this paper, we have designed a region reaching controller for an Autonomous Underwater Vehicle(AUV) using potential energy concept. The proposed controller also ensures static obstacle avoidance with obstacles considered as repulsive region. A filtering technique is utilized to produce an auxiliary velocity signal and thus, eliminate the requirement of velocity measurement. The control strategy provides asymptotic regulation of AUV pose. A simulation study of the proposed controller on ODIN AUV is also presented.

New synchronization criteria for fuzzy complex dynamical network with time-varying delay

This paper addresses the problem of synchronization analysis of Takagi-Sugeno (T-S) fuzzy complex dynamical network in the presence of interval time-varying delay. A novel synchronization criteria is obtained in terms of linear matrix inequalities (LMIs) by defining a Lyapunov-Krasovskii functional (LKF). The delay-range is divided into two segments for stability analysis. A tighter bounding technique for integral terms arising in the derivative of LKF is developed. The Wirtinger inequality and a bounding technique developed by authors are employed to develop the stability criteria. Further, the proposed approach has also been adopted to develop stability criteria for a single T-S fuzzy system with interval time-varying delay. It is shown with the help of numerical examples that the proposed results are less conservative as compared to the other recently reported results.

Delay-distribution based stability analysis of time-delayed port-Hamiltonian systems

In this paper, the problem of stability analysis of time-delayed port-Hamiltonian systems with probabilistic time-varying delay has been considered. The time-delay variation range is divided into two sub-intervals. By considering the probability distribution of the time-varying delay between the two sub-intervals and the knowledge of the delay variation range, a novel linear matrix inequality (LMI) based stability condition is derived by defining a Lyapunov-Krasovskii functional. It is illustrated with the help of a numerical example that as the probability of delay taking a small value increases, the upper delay bound increases.