Realistic feedback control of two interconnected turbogenerators

In this paper, the optimal control of a system with two identical interconnected turbogenerators, which are connected to an infinite bus, is considered. The alternators are controlled through a linear feedback of the state variables. The feedback parameters are obtained by solving a nonlinear, two-point boundary-value problem. The values obtained for these parameters depend on the strength and duration of the disturbance, since the model is nonlinear, contrary to the usual feedback control of a linear model. In contrast to the model used in Ref. 1, the model used here includes the transfer function of the governors, the turbines, and the voltage regulators.This work was supported in part by the National Science and Engineering Research Council of Canada, Grant No. A4146. The authors wish to express their appreciation to Mr. T. L. Gan for his help in computations.     

Lyapunov type functions for classes of autonomous parabolic feedback control problems and applications

In this note we provide sufficient conditions for the existence of a Lyapunov function for a class of parabolic feedback control problems. The results are applied to the long-time behavior of state functions for the following problems: (i) a model of combustion in porous media; (ii) a model of conduction of electrical impulses in nerve axons; and (iii) a climate energy balance model.     

A feedback fluid queue with two congestion control thresholds

Feedback fluid queues play an important role in modeling congestion control mechanisms for packet networks. In this paper we present and analyze a fluid queue with a feedback-based traffic rate adaptation scheme which uses two thresholds. The higher threshold B ₁ is used to signal the beginning of congestion while the lower threshold B ₂ signals the end of congestion. These two parameters together allow to make the trade-off between maximizing throughput performance and minimizing delay. The difference between the two thresholds helps to control the amount of feedback signals sent to the traffic source. In our model the input source can behave like either of two Markov fluid processes. The first applies as long as the upper threshold B ₁ has not been hit from below. As soon as that happens, the traffic source adapts and switches to the second process, until B ₂ (smaller than B ₁) is hit from above. We analyze the model by setting up the Kolmogorov forward equations, then solving the corresponding balance equations using a spectral expansion, and finally identifying sufficient constraints to solve for the unknowns in the solution. In particular, our analysis yields expressions for the stationary distribution of the buffer occupancy, the buffer delay distribution, and the throughput.     

Vaccination strategies based on feedback control techniques for a general SEIR-epidemic model

This paper presents several simple linear vaccination-based control strategies for a SEIR (susceptible plus infected plus infectious plus removed populations) propagation disease model. The model takes into account the total population amounts as a refrain for the illness transmission since its increase makes more difficult contacts among susceptible and infected. The vaccination control objective is the asymptotically tracking of the removed-by-immunity population to the total population while achieving simultaneously that the remaining populations (i.e. susceptible plus infected plus infectious) tend asymptotically to zero.     

On open-loop and feedback attainability of a closed set for nonlinear control systems

In this note, we investigate the existence of controls which allow to reach a given closed set K through trajectories of a nonlinear control system. In the case where the set is sufficiently regular we give a condition allowing to find a feedback control law which ensures the existence of trajectories to reach the set. We also consider the case where all the trajectories reach K. When K is not necessarily attainable but only viable, we build a set-valued feedback for which the set is invariant. Our approach concerns continuous dynamics, possibly not C¹, so our methods do not come from geometric control theory. Furthermore, we do not require any regularity of the set K in order to obtain our results, except when we want to establish the existence of a feedback control law to achieve our goals.     

Interface feedback control stabilization of a nonlinear fluid-structure interaction

We consider a model of fluid-structure interaction in a bounded domain Ω∈Rⁿ, n=2, where Ω is comprised of two open adjacent sub-domains occupied, respectively, by the solid and the fluid. This leads to a study of the Navier-Stokes equation coupled on the boundary with the dynamic system of elasticity. We shall consider models where the elastic body exhibits small but rapid oscillations. These are established models arising in engineering applications when the structure is immersed in a viscous flow of liquid. Questions related to the stability of finite energy solutions are of paramount interest.It was shown in Lasiecka and Lu (2011) [14] that all data of finite energy produce solutions whose energy converges strongly to zero. The cited result holds under “partial flatness” geometric condition whose role is to control the effects of the pressure in the NS equation. Related conditions has been used in Avalos and Triggiani (2008) [23] for the analysis of the linear model. The goal of the present work is to study uniform stability of all finite energy solutions corresponding to nonlinear interaction. This particular question, of interest in its own rights, is also a necessary preliminary step for the analysis of optimal control strategies arising in infinite-horizon control problems associated with the structure. It is shown in this paper that a stress type feedback control applied on the interface of the structure produces solutions whose energy is exponentially stable.     

Optimal feedback control policies for stochastic,distributed-parameter systems

This paper considers optimal feedback control policies for a class of discrete stochastic distributed-parameter systems. The class under consideration has the property that the random variable in the dynamic systems depends only on the time and possesses the Markovian property with stationary transition probabilities. A necessary condition for optimality of a feedback control policy, which has form similar to the Hamiltonian form in the deterministic case, is derived via a dynamic programming approach.     

Multiple positive periodic solutions of nonlinear functional differential system with feedback control

In this paper, we employ Avery-Henderson fixed point theorem to study the existence of positive periodic solutions to the following nonlinear nonautonomous functional differential system with feedback control:

     

Permanence and existence of periodic solutions for a generalized system with feedback control

Sufficient conditions are obtained for the permanence and the existence of positive periodic solutions of the delay differential system with feedback control

(0.1)     

THE FEEDBACK DELAY IN DIGITAL CONTROL

It is a fact that the feedback delay actually ariese in digital control systems.It is necessary to modify the structure of digital control systems and develop new control algorithms,which is done in this paper.A great number of digital computer simulation experiments have shown the obvious advantage of the new algorithms.     

Dynamic feedback control and exponential stabilization of a compound system

We studied the exponential stabilization problem of a compounded system composed of a flow equation and an Euler–Bernoulli beam, which is equivalent to a cantilever Euler–Bernoulli beam with a delay controller. We designed a dynamic feedback controller that stabilizes exponentially the system provided that the eigenvalues of the free system are not the zeros of controller. In this paper we described the design detail of the dynamic feedback controller and proved its stabilization property.     

Existence and global attractivity of positive periodic solutions of functional differential equations with feedback control

Sufficient conditions are obtained for the existence and global attractivity of positive periodic solutions of the delay differential system with feedback control

The method involves the application of Krasnoselskii's fixed point theorem and estimates of uniform upper and lower bounds of solutions. When these results are applied to some special delay population models with multiple delays, some new results are obtained and some known results are generalized.     

Positive periodic solution for a neutral Logarithmic population model with feedback control

In this paper, a neutral delay Logarithmic population model with feedback control is studied. By using the abstract continuous theorem of k-set contractive operator, some new results on the existence of the positive periodic solution are obtained; after that, by constructing a suitable Lyapunov functional, a set of easily applicable criteria is established for the global asymptotically stability of the positive periodic solution.     

Graph completions for impulsive feedback controls

The paper considers impulsive control systems, where the evolution equation depends linearly on the time derivatives of the control function. The basic theory of “graph completions” is here extended to control functions in feedback form. In the case where the control u=u(t,x)$u=u(t,x)$ is piecewise smooth, with a jump along a hypersurface Σ in the t–x space, results are proved on the existence and uniqueness of solutions, and on their approximation by means of smooth feedbacks. The paper is concluded with a couple of examples, concerning the feedback control of mechanical systems by means of active constraints.     

Asymmetric games for convolution systems with applications to feedback control of constrained parabolic equations

The paper is devoted to the study of some classes of feedback control problems for linear parabolic equations subject to hard/pointwise constraints on both Dirichlet boundary controls and state dynamic/output functions in the presence of uncertain perturbations within given regions. The underlying problem under consideration, originally motivated by automatic control of the groundwater regime in irrigation networks, is formalized as a minimax problem of optimal control, where the control strategy is sought as a feedback law. Problems of this type are among the most important in control theory and applications — while most challenging and difficult. Based on the Maximum Principle for parabolic equations and on the time convolution structure, we reformulate the problems under consideration as certain asymmetric games, which become the main object of our study in this paper. We establish some simple conditions for the existence of winning and losing strategies for the game players, which then allow us to clarify controllability issues in the feedback control problem for such constrained parabolic systems.     

Stabilization of a reaction-diffusion system modelling a class of spatially structured epidemic systems via feedback control

A two-component reaction-diffusion system modelling a class of spatially structured epidemic systems is considered. The system describes the spatial spread of infectious diseases mediated by environmental pollution. A relevant problem, related to the possible eradication of the epidemic, is the so called zero stabilization. In a series of papers, necessary conditions, and sufficient conditions of stabilizability have been obtained. It has been proved that it is possible to diminish exponentially the epidemic process in the whole habitat, just by reducing the concentration of the pollutant in a nonempty and sufficiently large subset of the spatial domain. The stabilizability with a feedback control of the harvesting type is related to the magnitude of the principal eigenvalue of a certain operator which is not selfadjoint. In this paper, we have proposed an approximating method for this principal eigenvalue. Further, we have faced the problem of finding the optimal position (by translation) of the support of the feedback stabilizing control in order to minimize both the infected population and the pollutant at a certain finite time.     

Controlling hyperchaos in hyperchaotic Lorenz system using feedback controllers

In this paper, the control strategies for hyperchaotic Lorenz system is investigated. The ordinary, dislocated, enhancing and speed feedback controls are used to suppress hyperchaos to unstable equilibrium. The Routh-Hurwitz criterion is used to derive the conditions of stability of the controlled hyperchaotic systems. It is found that the coefficients of enhancing feedback control and dislocated feedback control may be smaller than those of ordinary feedback control, so, the complexity and cost of the system control are reduced. Numerical simulations are given to illustrate the effectiveness of the proposed controllers.     

Optimal feedback control of bilinear systems

Feedback synthesis of optimal constrained controls for single-input bilinear systems is considered. Quadratic cost functionals (with and without quadratic control penalization) are modified by the inclusion of additional nonnegative state penalizing functions in the respective cost integrands. The latter functions are chosen so as to regularize the problems, in the sense that feedback solutions of particularly simple form are obtained. Finite and infinite time horizon problem formulations are treated, and associated aspects of feedback stabilization of bilinear systems are discussed.     

Global asymptotic stability in n-species non-autonomous Lotka–Volterra competitive systems with infinite delays and feedback control

A non-autonomous Lotka–Volterra competition system with infinite delays and feedback control and without dominating instantaneous negative feedback is investigated. By means of a suitable Lyapunov functional, sufficient conditions are derived for the global asymptotic stability of the system. Some new results are obtained.