Fuzzy impulsive control of high order interpolative lowpass sigma delta modulators

In this paper, a fuzzy impulsive control strategy is proposed. The state vectors that the impulsive controller resets to are determined so that the state vectors of interpolative low-pass sigma-delta modulators (SDMs) are bounded within any arbitrary nonempty region no matter what the input step size, the initial condition and the filter parameters are, the occurrence of limit cycle behaviors and the effect of audio clicks are minimized, as well as the state vectors are close to the invariant set if it exists. To work on this problem, first, the local stability criterion and the condition for the occurrence of limit cycle behaviors are derived. Second, based on the derived conditions, as well as a practical consideration based on the boundedness of the state variables and a heuristic measure on the strength of audio clicks, fuzzy membership functions and a fuzzy impulsive control law are formulated. The controlled state vectors are then determined by solving the fuzzy impulsive control law. One of the advantages of the fuzzy impulsive control strategy over the existing linear control strategies is the robustness to the input signal, the initial condition and the filter parameters, and that over the existing nonlinear control strategy are the efficiency and the effectiveness in terms of lower frequency of applying the control force and higher signal-to-noise ratio (SNR) performanc

Impulsive control systems

Impulsive control systems arose from classical control systems described by differential equations where the control functions could be unbounded. Passing to the limit of trajectories whose velocities are changing very rapidly leads to the state vector to jump , or exhibit impulsive behavior. The mathematical model in this thesis uses a differential inclusion and a measure-driven control, and it becomes possible to deal with the discontinuity of movements happening over a small interval. We adopt the formulism of impulsive systems in which the velocities are decomposed by the slow and fast ones. The fast time velocity is expressed as the multiplication of point-mass measure with a state-depended term. Our methodology is deeply grounded in the concept of a graph completion, which is a technique to interpret and make rigorous the multiplication of a discontinuous function with a vector-valued measure. After reviewing how this concept is used to define the trajectory of impulsive system, the thesis works out a sampling method to estimate a solution and simultaneously construct a control measure, which is the first part of my research. The second part studies the stability of systems through invariance properties. Invariance of the system involves evolution properties on a given closed set with respect to the initial state belonging to that set. The third and last part of the thesis considers the Hamilton-Jacobi (HJ) theory of impulsive systems, which is related to the minimal time problem, an optimization topic of considerable interest. The minimal time function is uncovered to be the unique solution of HJ equation. Many discussions have earlier been offered in non-impulsive systems, especially in autonomous case, and we attempt to extend these results to impulsive control system. Final thoughts and considerations are put in the last chapter of conclusions and future work

Impulsive control realization applied to non-dissipative first order plants: an academic electronic implementation

Impulsive control design is a control strategy mainly based on the impulsive differential model of the plant to be stabilized. Hence, this system should have at least one state variable able to be driven by impulsive commands. On the other hand, analog electronic realization of an impulsive control algorithm may be an important competition for engineering students. Therefore, the main objective of this paper is to pose an impulsive control method to non-dissipative first order systems along with an electronic circuit design to validate a contribution on impulsive control aim. According to our experimental results, our electronic architecture to reproduce an impulsive control law results effective to accomplished asymptotic stability of the closed-loop system in the Lyapunov’s sense.Peer ReviewedPostprint (published version

Practical stability for fractional impulsive control systems with noninstantaneous impulses on networks

This paper investigates practical stability for a class of fractional-order impulsive control coupled systems with noninstantaneous impulses on networks. Using graph theory and Lyapunov method, new criteria for practical stability, uniform practical stability as well as practical asymptotic stability are established. In this paper, we extend graph theory to fractional-order system via piecewise Lyapunov-like functions in each vertex system to construct global Lyapunov-like functions. Our results are generalization of some known results of practical stability in the literature and provide a new method of impulsive control law for impulsive control systems with noninstantaneous impulses. Examples are given to illustrate the effectiveness of our result

Estimation problem for impulsive control systems under ellipsoidal state bounds and with cone constraint on the control

The paper deals with the state estimation problem for the linear control system containing impulsive control terms (or measures). The problem is studied here under uncertainty conditions when the initial system state is unknown but bounded, with given bound. It is assumed also that the system states should belong to the given ellipsoid in the state space. So the main problem of estimating the reachable set of the control system is studied here under more complicated assumption related to the case of state constraints. It is assumed additionally that impulsive controls in the dynamical system must belong to the intersection of a special cone with a generalized ellipsoid both taken in the space of functions of bounded variation. The last constraint is motivated by problems of impulsive control theory and by models from applied areas when not every direction of control impulses is acceptable in the system. We present here the state estimation algorithms that use the special structure of the control system and take into account additional restrictions on states and controls. The algorithms are based on ellipsoidal techniques for estimating the trajectory tubes of uncertain dynamical systems. Numerical simulation results related to proposed procedures are also given. © 2012 American Institute of Physics

Optimal Partial Harvesting Schedule for Aquaculture Operations

Abstract When growth is density dependent, partial harvest of the standing stock of cultured species (fish or shrimp) over the course of the growing season (i.e., partial harvesting) would decrease competition and thereby increase individual growth rates and total yield. Existing studies in optimal harvest management of aquaculture operations, however, have not provided a rigorous framework for determining "discrete" partial harvesting (i.e., partially harvest the cultured species at several discrete points until the final harvest). In this paper, we develop a partial harvesting model that is capable of addressing discrete partial harvesting and other partial harvesting using impulsive control theory. We derive necessary conditions of the efficient partial harvesting scheme for a single production cycle. We also present a numerical example to illustrate how partial harvesting can improve the profitability of an aquaculture enterprise compared to single-batch harvesting and gradual thinning. The study results indicate that well-designed partial harvesting schemes can enhance the profitability of aquaculture operations.Partial harvesting, impulsive control theory, aquaculture., Livestock Production/Industries, C61, Q22,

An impulsive framework for the control of hybrid systems

An impulsive control formulation suitable for analyzing hybrid systems is presented. Besides a continuous evolution, the trajectory of an impulsive control system may also exhibit jumps. The jump trajectory is well characterized in this impulsive framework. These jumps can be interpreted as the discrete evolution of an hybrid system. Several examples of hybrid systems modeled in the impulsive framework are given. An impulsive formulation of a formation control problem, regarded as an hybrid system is detailed. Finally, an overview of important classes of control results available for impulsive control systems, notably, stability and optimality, attest the importance of this paradigm for the control of hybrid systems. These results are essential to investigate the properties of model predictive control schemes for hybrid systems