Switching Time Sequence Research Articles

Simultaneous Improvement of array factor directivity and side lobe level of time‐modulated linear antenna arrays using opposition‐based harmony search algorithm

SummaryIn this paper, simultaneous improvement of array factor directivity and side lobe level of time‐modulated linear antenna arrays using opposition‐based harmony search algorithm has been dealt with. Because of the periodic function of switching time, the same antenna array will radiate at fundamental (center) frequency as well as its harmonic frequencies. The first two harmonic frequencies are (f0 + Fp) and (f0 + 2Fp), where f0 and Fp are operating frequency and pulse repetition frequency, respectively. Four case studies have been adapted; Case‐1: optimal switching time sequence of each element; Case‐2: optimal switching time sequence of each element and optimal non‐uniform inter‐element spacing; Case‐3: optimal switching time sequence of each element, optimal excitation phase of each element, and optimal uniform inter‐element spacing; Case‐4 refers to optimal switching time sequence of each element and optimal uniform inter‐element spacing. Simulation results reflect that Case‐4 outperforms Case‐1, Case‐2, and Case‐3. The objective function was judiciously chosen in such a way that it can simultaneously improve the array factor directivity as well as side lobe level. Considered for the analysis was 16‐element linear antenna array. Various simulation results are presented showing better side lobe performance, better side band performance, and improved array factor directivity with respect to the uniform array having the same number of elements. The numerical results show the power radiated by any harmonic frequency is less as compared with the power radiated at the center frequency called the fundamental frequency. It has also been observed that as the harmonic frequency increases, sideband level and power radiated by the antenna at its harmonic frequency decrease. Copyright © 2015 John Wiley & Sons, Ltd.

Synchronization for complex networks with Markov switching via matrix measure approach

This paper devotes to almost sure synchronization and almost sure quasi-synchronization of complex networks with Markov switching. Some sufficient conditions are derived in terms of the ergodic theory of continuous time Markov chain and the matrix measure approach, which can guarantee that the dynamical networks almost surely synchronize or quasi-synchronize to a given manifold. According to the property of Markov chain and the exponential distribution of switching time sequence, we also estimate the probability distribution of the quasi-synchronization error for a two-state Markov chain and then generalize them to a finite state space Markov chain. Meanwhile, some examples with numerical simulations are given to show that the Markov chain plays an important role in synchronization of networks.

Finite-time control of switching linear systems: The uncertain resetting times case

Summary In recent years, a number of papers have treated the problem of the finite-time stability and stabilization of impulsive (or, more in general, switching) dynamical linear systems. Generally, these works assume that the sequence of switching (in the following resetting) times is a priori known. In this paper, we remove such (strong) assumption, so making the technique more appealing from the practical control engineering point of view. A first result provided in this work is a sufficient condition for finite-time stability when the resetting times are known with a certain degree of uncertainty. Such condition requires the solution of a suitable feasibility problem based on coupled difference/differential LMIs. We show that as the uncertainty intervals reduce in size, our condition becomes less conservative, becoming necessary and sufficient in the certain case (i.e., the resetting instants are perfectly known). Eventually, we consider the conceptually different situation in which the resetting times are totally unknown, namely, the arbitrary switching case. The analysis results are then used to derive sufficient conditions for the existence of state-feedback controllers that finite time stabilizes the closed-loop system in the three cases mentioned earlier. A nontrivial example, considering the finite-time control of the liquid levels into three interconnected reservoirs, shows the effectiveness of the proposed approach. Copyright © 2014 John Wiley & Sons, Ltd.

Controllability for a class of time-varying controlled switching impulsive systems with time delays

This paper investigates two types of controllability for time-varying switching impulsive control systems with time delays and the relation between the two concepts. By characterizing the solution of the system, we establish necessary and sufficient conditions of the controllability of delayed switching impulsive systems with respect to a given switching time sequence. For some special cases, linear time-varying switching impulsive systems with or without time delay, the corresponding criteria are obtained. Compared with some existing results, the results presented here are more general and less conservative. Numerical examples are provided to show the effectiveness of the proposed methods.

Vector-based reference location estimating for space vector modulation technique

Space vector modulation (SVM) has become a popular pulse width modulation technique (PWM) for multilevel inverters. In SVM technique, the determination of the angular position of the reference voltage vector is very important to generate the required output voltage by the inverter. The switching time and switching sequence of SVM are calculated by vector location. The calculation of vector location and switching time become difficult and more complex when the numbers of output voltage levels increase for a given number of inverter levels. In this paper, a new SVM method is developed to determine the actual vector location. The proposed method can increase RMS value of the inverter output voltage; can reduce the algorithm complexity and computation time when compared to conventional SVM methods. In addition, the calculation of switching times for two-level inverter is generalized for N-level inverters. PSCAD/EMTDC simulation program is used to create the test system and to perform the case studies. Extensive simulation results are given to validate the performance of the proposed algorithm.

State Observability and Observers of Linear-Time-Invariant Systems Under Irregular Sampling and Sensor Limitations

State observability and observer designs are investigated for linear-time-invariant systems in continuous time when the outputs are measured only at a set of irregular sampling time sequences. The problem is primarily motivated by systems with limited sensor information in which sensor switching generates irregular sampling sequences. State observability may be lost and the traditional observers may fail in general, even if the system has a full-rank observability matrix. It demonstrates that if the original system is observable, the irregularly sampled system will be observable if the sampling density is higher than some critical frequency, independent of the actual time sequences. This result extends Shannon's sampling theorem for signal reconstruction under periodic sampling to system observability under arbitrary sampling sequences. State observers and recursive algorithms are developed whose convergence properties are derived under potentially dependent measurement noises. Persistent excitation conditions are validated by designing sampling time sequences. By generating suitable switching time sequences, the designed state observers are shown to be convergent in mean square, with probability one, and with exponential convergence rates. Schemes for generating desired sampling sequences are summarized.

The explicit solution to a sequential switching problem with non-smooth data

We consider the problem faced by a decision maker who can switch between two random payoff flows. Each of these payoff flows is an additive functional of a general 1D Itô diffusion. There are no bounds on the number or on the frequency of the times at which the decision maker can switch, but each switching incurs a cost, which may depend on the underlying diffusion. The objective of the decision maker is to select a sequence of switching times that maximizes the associated expected discounted payoff flow. In this context, we develop and study a model in the presence of assumptions that involve minimal smoothness requirements from the running payoff and switching cost functions, but which guarantee that the optimal strategies have relatively simple forms. In particular, we derive a complete and explicit characterization of the decision maker's optimal tactics, which can take qualitatively different forms, depending on the problem data.

Fast high-fidelity information transmission through spin-chain quantum wires

Spin chains have been proposed as quantum wires for information transfer in solid-state quantum architectures. We show that huge gains in both transfer speed and fidelity are possible using a minimalist control approach that relies only on a single local on-off switch actuator. Effective switching time sequences can be determined using optimization techniques for both ideal and disordered chains. Simulations suggest that effective optimization is possible even in the absence of knowledge of the Hamiltonian or accurate models.

State Observers and Stabilization of Systems with Binary-Valued Observations

This paper introduces an observer for linear time invariant systems in continuous time whose outputs are measured only by binary-valued sensors. The traditional observers will fail in general, even if the system has a full-rank observability matrix. It is shown that by controlling the sensor threshold, it is always possible to cause the output to cross the sensor threshold within a designated time interval. Information on the time instants of threshold crossing is then used to develop state estimates. Convergence properties of the state observer are established. It is shown that by generating appropriate switching time sequences, state observers are convergent in the mean squares sense, with probability one, and exponentially. Combined with a state feedback using the state estimates, this state estimator leads to a stabilizing output feedback.

Controllability and Observability for a Class of Controlled Switching Impulsive Systems

In this note, we study the controllability and observability problem for a class of controlled switching impulsive systems. By proposing several formula of variation of parameters for this type of time-varying systems and employing the characteristic polynomial theory of matrix, we establish necessary and sufficient conditions for controllability and controlled observability with respect to a given switching time sequence. Specializing the obtained results to the case of time-invariant linear switching impulsive systems, we derive some simple algebraic criteria, which include the results reported in the literature for time-invariant linear switching systems, linear impulsive systems and classical linear systems. One example is worked out for illustration.

Switched Controllability via Bumpless Transfer Input and Constrained Switching

In this note, we investigate the controllability of linear hybrid systems via bumpless transfer input and constrained switching. By bumpless transfer input, we mean that the control input signals are as close as possible at switching times. By constrained switching, we mean that the switching index sequence is cyclic and the switching time sequence is possibly with pre-assigned duration intervals. While the problem is well motivated in several practical situations, it is also theoretically interesting. A complete criterion for controllability is presented, and a computational procedure is developed for finding a switching signal and a control input to achieve the controllability.

Mitigation of loss within a molecular Stark decelerator

The transverse motion inside a Stark decelerator plays a large role in the total efficiency of deceleration. We differentiate between two separate regimes of molecule loss during the slowing process. The first mechanism involves distributed loss due to coupling of transverse and longitudinal motion, while the second is a result of the rapid decrease of the molecular velocity within the final few stages. In this work, we describe these effects and present means for overcoming them. Solutions based on modified switching time sequences with the existing decelerator geometry lead to a large gain of stable molecules in the intermediate velocity regime, but fail to address the loss at very low final velocities. We propose a new decelerator design, the quadrupole-guiding decelerator, which eliminates distributed loss due to transverse/longitudinal couplings throughout the slowing process and also exhibits gain over normal deceleration to the lowest velocities.

Controller Synthesis for Linear Switched Systems

A method of designing switching controllers for a class of switched systems is presented. It is shown how the design of the switching controller can be broken down into separate design problems for the continuous and the discrete controller parts. The main advantage of this approach is that it leads to smaller design problems of manageable complexity and it gives the designer more flexibility. In contrast to other switching controller design methods which seek to find a switching sequence and/or a sequence of switching times, the approach presented in this paper considers the interaction between the continuous and the discrete dynamics and yields a switching controller which works in closed-loop. The approach is illustrated by its application to a manufacturing cell

Optimal State-Feedback Quadratic Regulation of Linear Hybrid Automata

For linear hybrid automata, namely switched linear autonomous systems whose mode of operation is determined by a controlled automaton, in this paper we face the problem of optimal control, where the objective is to minimize a quadratic performance index over an infinite time horizon. The quantities to be optimized are the sequence of switching times and the sequence of modes (or “locations”), under the following constraints: the sequence of modes has a finite length; the discrete dynamics of the automaton restricts the possible switches from a given location to the next location, with a cost associated to each switch; the time interval between two consecutive switching times is greater than a fixed quantity. We show how a state-feedback solution can be computed off-line through a numerical procedure.

Suitable switching policies for FMS scheduling

Switching server, otherwise known as hybrid dynamical approaches can be used highly effectively to solve flexible manufacturing systems scheduling problems. Papers published in this field have accepted that the demand rates determining the production tasks have some given values. In the present paper it is shown that the demand rates should be selected from some given domains. The “control variables” to realize suitable processes are the switching policies, and the demand rates. These uniquely determine the processes through the switching time sequences. In the present paper, two variants: the single machine processing, and the multiple machine processing cases are analyzed. It is very problematic to use continuously coupled parts flows for stable and effective production. To eliminate this difficulty, in the present paper, the method called controlled buffer technique is proposed, which uses the opportunity that the computer controlled “virtual buffers” can be filled up before the regular working time, and used for part flow compensation.

Optimizing acyclic traffic signal switching sequences through an Extended Linear Complementarity Problem formulation

In this paper we first show how the Extended Linear Complementarity Problem, which is a mathematical programming problem, can be used to design optimal switching schemes for a class of switched systems with linear dynamics subject to saturation. More specifically, we consider the determination of the optimal switching time instants (the switching sequences are acyclic, but the phase sequence is pre-fixed). Although this method yields globally optimal switching time sequences, it is not feasible in practice due to its computational complexity. Therefore, we also discuss some approximations that lead to suboptimal switching time sequences that can be computed very efficiently and for which the value of the objective function is close to the global optimum. Finally we use these results to design optimal switching time sequences for a traffic signal controlled intersection so as to minimize criteria such as average queue length, worst case queue length, average waiting time, and so on.

Dynamical Systems that Compute Time-Optimal Switchings

It is well known that minimum-time bounded control of linear systems is generically bang-bang and that the number of switchings does not exceed the dimension of the system if the eigenvalues of the system matrix are real. We propose a synthesis method for such problems based on dynamical systems that 'compute' the optimal sequence of switching times.

Optimal Control of a Class of Linear Hybrid Systems with Saturation

We consider a class of first order linear hybrid systems with saturation. A system that belongs to this class can operate in several modes or phases; in each phase each state variable of the system exhibits a linear growth until a specified upper or lower saturation level is reached, and after that the state variable stays at that saturation level until the end of the phase. A typical example of such a system is a traffic signal controlled intersection. We develop methods to determine optimal switching time sequences for first order linear hybrid systems with saturation that minimize criteria such as average queue length, worst case queue length, average waiting time, and so on. First we show how the extended linear complementarity problem (ELCP), which is a mathematical programming problem, can be used to describe the set of system trajectories of a first order linear hybrid system with saturation. Optimization over the solution set of the ELCP then yields an optimal switching time sequence. Although this method yields globally optimal switching time sequences, it is not feasible in practice due to its computational complexity. Therefore, we also present some methods to compute suboptimal switching time sequences. Furthermore, we show that if there is no upper saturation, then for some objective functions the globally optimal switching time sequence can be computed very efficiently. We also discuss some approximations that lead to suboptimal switching time sequences that can be computed very efficiently. Finally, we use these results to design optimal switching time sequences for traffic signal controlled intersections.

The Transient Stabilization of a Synchronous Machine by Discontinuous Supplemantary Excitation Control

This paper presents the results of a laboratory implementation of discontinuous supplementary excitation (DSE). control to stabilize a synchronous machine through the use of local information such as okachine slip and acceleration. It is an extension to a previous theoretical investigation and evaluates the effects of the various control signals and the switching time sequences. The transient response of the DSE controlled machine is compared to state feedback optimal control. The results show that DSE control is effective and reliable and simple to implement.

Controlled one dimensional diffusions with switching costs—average cost criterion

This paper deals with a one-dimensional controlled diffusion process on a compact interval with reflecting boundaries. The set of available actions is finite and the action can be changed only at countably many stopping times. The cost structure includes both a continuous movement cost rate depending on the state and the action, and a switching cost when the action is changed. The policies are evaluated with respect to the average cost criterion. The problem is solved by looking at, for each stationary policy, an embedded stochastic process corresponding to the state intervals visited in the sequence of switching times. The communicating classes of this process are classified into closed and transient groups and a method of calculating the average cost for the closed and transient classes is given. Also given are conditions to guarantee the optimality of a stationary policy. A Brownian motion control problem with quadratic cost is worked out in detail and the form of an optimal policy is established.