How conservative is frozen-time interpolation?

It is shown in this note that for SISO systems under l² disturbances, when data commute approximately with the shift, the optimal interpolation (over all linear time-varying interpolants) can be approximated by the supremum of the frozen-time Hankel norms. This confirms the intuition that the frozen-time constructed optimal or suboptimal interpolants are in fact nearly optimal when data vary slowly.     

Gabor transform of time-varying systems: exact representation andapproximation

Approximate modeling of discrete-time linear time-varying systems is studied based on a representation of linear systems in the Gabor time-frequency space. The time-varying system is assumed to be given in input-output or kernel representation. This representation has previously received attention because of its applicability in frozen-time analysis and design of optimal control for time-varying systems but requires a large number of coefficients. Motivated by its application to signal analysis, the Gabor transform is considered as a tool for the representation and approximation of linear time-variant systems. In order to show the main results, the class of systems considered is restricted to the one usually considered in the frozen-time approach. An example is included to illustrate the potential application of the technique     

Control of slowly-varying linear systems

State feedback control of slowly varying linear continuous-time and discrete-time systems with bounded coefficient matrices is studied in terms of the frozen-time approach. This study centers on pointwise stabilizable systems. These are systems for which there exists a state feedback gain matrix placing the frozen-time closed-loop eigenvalues to the left of a line Re s=-γ<0 in the complex plane (or within a disk of radius ρ<1 in the discrete-time case). It is shown that if the entries of a pointwise stabilizing feedback gain matrix ar continuously differentiable functions of the entries of the system coefficient matrices, then the closed-loop system is uniformly asymptotically stable if the rate of time variation of the system coefficient matrices is sufficiently small. It is also shown that for pointwise stabilizable systems with a sufficiently slow rate of time variation in the system coefficients, a stabilizing feedback gain matrix can be computed from the positive definite solution of a frozen-time algebraic Riccati equation     

New sufficient conditions for the stability of slowly varyinglinear systems

The frozen-time approach is used to state some new sufficient conditions for the stability of linear time-varying systems. An upper bound on the norm of the time derivative of system matrix which, under different assumptions on frozen-time system eigenvalues, guarantees asymptotic stability or exponential stability of the system is established     

Partial‐state stabilization and optimal feedback control

In this paper, we develop a unified framework to address the problem of optimal nonlinear analysis and feedback control for partial stability and partial‐state stabilization. Partial asymptotic stability of the closed‐loop nonlinear system is guaranteed by means of a Lyapunov function that is positive definite and decrescent with respect to part of the system state, which can clearly be seen to be the solution to the steady‐state form of the Hamilton–Jacobi–Bellman equation and hence guaranteeing both partial stability and optimality. The overall framework provides the foundation for extending optimal linear‐quadratic controller synthesis to nonlinear nonquadratic optimal partial‐state stabilization. Connections to optimal linear and nonlinear regulation for linear and nonlinear time‐varying systems with quadratic and nonlinear nonquadratic cost functionals are also provided. Finally, we also develop optimal feedback controllers for affine nonlinear systems using an inverse optimality framework tailored to the partial‐state stabilization problem and use this result to address polynomial and multilinear forms in the performance criterion. Copyright © 2015 John Wiley & Sons, Ltd.     

Optimal regulation performance of discrete time-delay systems based on quantization and input energy constraints

In this paper, we study the optimal regulation problem of networked control systems and propose a new performance index for a given discrete time-delay system. The regulation performance of the controlled plant is investigated by considering the effects of various constraints on the communication channel such as quantization, bandwidth, and packet dropouts using frequency domain methods and two-degree-of-freedom control techniques. The results show that the regulation performance is not only related to the location and direction of the non-minimum phase zeros and unstable poles of a given system but also related to the internal time delay of the controlled plant. Packet dropouts, quantization, and bandwidth limitations can also negatively affect the optimal performance. In addition, the trade-off of the input energy constraint can also make the optimal regulation performance suffer. Finally, the reliability of this innovative result is illustrated by some simulation examples.     

Optimizing checkpoint-based fault-tolerance in distributed stream processing systems: Theory to practice

Fault-tolerance is an essential part of a stream processing system that guarantees data analysis could continue even after failures. State-of-the-art distributed stream processing systems use checkpointing to support fault-tolerance for stateful computations where the state of the computations is periodically persisted. However, the frequency of performing checkpoints impacts the performance (utilization, latency, and throughput) of the system as the checkpointing process consumes resources and time that can be used for actual computations. In practice, systems are often configured to perform checkpoints based on crude values ignoring factors such as checkpoint and restart costs, leading to suboptimal performance. In our previous work, we proposed a theoretical optimal checkpoint interval that maximizes the system utilization for stream processing systems to minimize the impact of checkpointing on system performance. In this article, we investigate the practical benefits of our proposed theoretical optimal by conducting experiments in a real-world cloud setting using different streaming applications; we use Apache Flink, a well-known stream processing system for our experiments. The experiment results demonstrate that an optimal interval can achieve better utilization, confirming the practicality of the theoretical model when applied to real-world applications. We observed utilization improvements from 10% to 200% for a range of failure rates from 0.3 failures per hour to 0.075 failures per minute. Moreover, we explore how performance measures: latency and throughput are affected by the optimal interval. Our observations demonstrate that significant improvements can be achieved using the optimal interval for both latency and throughput.     

Resource-bounded sensing and planning in autonomous systems

This paper is concerned with the implications of limited computational resources and uncertainty on the design of autonomous systems. To address this problem, we redefine the principal role of sensor interpretation and planning processes. Following Agre and Chapman's plan-as-communication approach, sensing and planning are treated as computational processes that provide information to an execution architecture and thus improve the overall performance of the system. We argue that autonomous systems must be able to trade off the quality of this information with the computational resources required to produce it. Anytime algorithms, whose quality of results improves gradually as computation time increases, provide useful performance components for time-critical sensing and planning in robotic systems. In our earlier work, we introduced a compilation scheme for optimal composition of anytime algorithms. This paper demonstrates the applicability of the compilation technique to the construction of autonomous systems. The result is a flexible approach to construct systems that can operate robustly in real-time by exploiting the tradeoff between time and quality in planning, sensing and plan execution.     

Linear time invariant minimax filtering

The problem of filtering a signal from a linear time invariant system with white Gaussian observation and unknown driving noise bounded at each instant of time is considered. We review the minimax filter of Johansen and Berkovitz–Pollard for the double integrator. While their solution is very elegant, the optimal filter is infinite dimensional. In a previous paper we showed that nearly the same performance can be achieved by a two dimensional filter and we generalized their approach to other linear time invariant systems. In this paper we show how to design nearly optimal filters for any linear time invariant system.     

Efficient optimal design of uncertain discrete time dynamical systems

In this paper we consider the problem of optimal design of an uncertain discrete time nonlinear dynamical system. The problem is formulated using an a-posterori design criterion, which can account for uncertainties generated by the dynamics of the system itself as well as parametric uncertainties. In general, for most uncertain complex dynamical systems, this type of method is difficult to solve analytically. A numerical scheme is developed for the optimal design that involves two steps. First, in order to obtain a numerical algorithm for the optimal solution, we apply randomized algorithms for average performance synthesis to approximate the optimal solution. Second, using the properties of the Perron–Frobenius operator we develop an efficient computation approach to calculate the stationary distribution for the uncertain dynamical systems and the average performance criteria.     

Optimal resource allocation in synchronized multi-tier Internet services

Modern Internet systems have evolved from simple monolithic systems to complex multi-tiered architectures. For these systems, providing good response time performance is crucial for commercial success. In practice, the response-time performance of multi-tiered systems is often degraded by severe synchronization problems, causing jobs to wait for responses from different tiers. Synchronization between different tiers is a complicating factor in the optimal control and analysis of performance. In this paper, we study a generic multi-tier model with synchronization in a queuing-theoretical setting. The system is able to share processing capacity between arriving jobs that need to be sent to other tiers and the responses that have arrived after processing from these tiers. We provide structural results on the optimal resource allocation policy and provide a full characterization of the policy in the framework of Markov decision theory. We also highlight important effects of synchronization in the model. We validate our expressions through extensive experimentations for a wide range of resource configurations.     

Optimal dynamic quantizers for discrete-valued input control

This paper discusses an optimal design problem of dynamic quantizers for a class of discrete-valued input systems, i.e., linear time-invariant systems actuated by discrete-valued input signals. The quantizers considered here are in the form of a linear difference equation, for which we find a quantizer such that the system composed of a given linear plant and the quantizer is an optimal approximation of the given linear plant in the sense of the input-output relation. First, we derive a closed form expression for the performance of a class of dynamic quantizers. Next, based on the performance analysis, an optimal dynamic quantizer and its performance are provided. This result further shows that even for such discrete-valued input systems, a controller can be easily designed by the existing tools for the linear system design such as robust control theory. Finally, the relation among the optimal dynamic quantizer and two other quantizers, i.e., the receding horizon quantizer and the ΔΣ modulator, is discussed.     

Optimal control of preemptive systems with loss

We consider the problem of optimal preemption control in preemptive systems with loss. Based on a designed cost function composed by the following criteria: blocking cost function, preemption cost function, degradation cost function, and processing and signaling load cost function; we use the semi-Markov decision process framework as well as the value iteration algorithm to get the optimal policies. To evaluate the optimal policies, we outline their structures and the system performance for different configurations. An interesting result happens when the lower priority service becomes profitable. In this case, the performance of higher priority calls, which have the right to preempt, may be degraded. This is against the well known traffic engineering, which is solely concentrated on the resource guarantee characteristic of the preemptive priority that always improves the higher priority call performance by lowering its blocking probability.     

Optimal quadratic solution for the non-Gaussian finite-horizon regulator problem

In this paper, the problem of the optimal quadratic regulator for non-Gaussian discrete-time stochastic systems with a quadratic cost function is considered. The main result here obtained is that such optimal control can be derived from the classical LQG solution by substituting the linear filtering part with a quadratic optimal filter. Numerical results show high performance of this method.     

Finite horizon optimal control of discrete-time nonlinear systems with unfixed initial state using adaptive dynamic programming

In this paper, we aim to solve the finite horizon optimal control problem for a class of discrete-time nonlinear systems with unfixed initial state using adaptive dynamic programming (ADP) approach. A new ε-optimal control algorithm based on the iterative ADP approach is proposed which makes the performance index function converge iteratively to the greatest lower bound of all performance indices within an error according to ε within finite time. The optimal number of control steps can also be obtained by the proposed ε-optimal control algorithm for the situation where the initial state of the system is unfixed. Neural networks are used to approximate the performance index function and compute the optimal control policy, respectively, for facilitating the implementation of the ε-optimal control algorithm. Finally, a simulation example is given to show the results of the proposed method.     

Relative Time Quantum-based Enhancements in Round Robin Scheduling

Modern human life is heavily dependent on computing systems and one of the core components affecting the performance of these systems is underlying operating system. Operating systems need to be upgraded to match the needs of modern-day systems relying on Internet of Things, Fog computing and Mobile based applications. The scheduling algorithm of the operating system dictates that how the resources will be allocated to the processes and the Round Robin algorithm (RR) has been widely used for it. The intent of this study is to ameliorate RR scheduling algorithm to optimize task scheduling. We have carried out an experimental study where we have developed four variations of RR, each algorithm considers three-time quanta and the performance of these variations was compared with the RR algorithm, and results highlighted that these variations performed better than conventional RR algorithm. In the future, we intend to develop an automated scheduler that can determine optimal algorithm based on the current set of processes and will allocate time quantum to the processes intelligently at the run time. This way the task performance of modern-day systems can be improved to make them more efficient.     

An analysis of content-based classification of audio signals using a fuzzy c-means algorithm

Content-based audio signal classification into broad categories such as speech, music, or speech with noise is the first step before any further processing such as speech recognition, content-based indexing, or surveillance systems. In this paper, we propose an efficient content-based audio classification approach to classify audio signals into broad genres using a fuzzy c-means (FCM) algorithm. We analyze different characteristic features of audio signals in time, frequency, and coefficient domains and select the optimal feature vector by employing a noble analytical scoring method to each feature. We utilize an FCM-based classification scheme and apply it on the extracted normalized optimal feature vector to achieve an efficient classification result. Experimental results demonstrate that the proposed approach outperforms the existing state-of-the-art audio classification systems by more than 11% in classification performance.     

Optimal ensemble control of stochastic time-varying linear systems

We consider the optimal guidance of an ensemble of independent, structurally identical, finite-dimensional stochastic linear systems with variation in system parameters between initial and target states of interest by applying a common control function without the use of feedback. Our exploration of such ensemble control systems is motivated by practical control design problems in which variation in system parameters and stochastic effects must be compensated for when state feedback is unavailable, such as in pulse design for nuclear magnetic resonance spectroscopy and imaging. In this paper, we extend the notion of ensemble control to stochastic linear systems with additive noise and jumps, which we model using white Gaussian noise and Poisson counters, respectively, and investigate the optimal steering problem. In our main result, we prove that the minimum norm solution to a Fredholm integral equation of the first kind provides the optimal control that simultaneously minimizes the mean square error (MSE) and the error in the mean of the terminal state. The optimal controls are generated numerically for several example ensemble control problems, and Monte Carlo simulations are used to illustrate their performance. This work has immediate applications to the control of dynamical systems with parameter dispersion or uncertainty that are subject to additive noise, which are of interest in quantum control, neuroscience, and sensorless robotic manipulation.     

Worst Case Power Generating Capabilities of Nonlinear Systems

In this paper we analyze the worst case power generating capabilities of a class of nonlinear systems which exhibit a power gain property. This class of systems includes systems which exhibit persistent excitation in the absence of inputs. Examples include limit cycle systems and chaotic systems. In order to capture the power generating capability of a nonlinear system, we define a worst case average cost per unit time performance index. This performance index, called the available power, is in effect the most power that can be generated by a system via the application of any input. The main result of the paper is that the input which achieves this worst case performance is typically a persistent input whose power is given explicitly by a function of the derivative of the available power with respect to the power gain of the system. A natural corollary of this result is that the available power may be recast as an optimization over power inputs. Date received: 24 February 2000. Date revised: 11 May 2001.     

Decoupling and tracking control using eigenstructure assignment for linear time-varying systems

This work is concerned with the assignment of a desired PD-eigenstructure for linear time-varying systems. Despite its well-known limitations, gain scheduling control appeared to be a focus of the research efforts. Scheduling of frozen-time, frozen-state controllers for fast time-varying dynamics is known to be mathematically fallacious, and practically hazardous. Therefore, recent research efforts are being directed towards applying time-varying controllers. In this paper, (a) we introduce a differential algebraic eigenvalue theory for linear time-varying systems, and then (b) a novel decoupling and tracking control scheme is proposed by using the PD-eigenstructure assignment scheme via a differential Sylvester equation and a Command Generator Tracker for linear time-varying systems. The PD-eigenstructure assignment is utilized as a regulator. A feedforward gain for tracking control is computed by using the command generator tracker. The whole design procedure of the proposed PD-eigenstructure assignment scheme is systematic in nature. The scheme could be used to determine stability of linear time-varying systems easily as well as to provide a new horizon of designing controllers for the linear time-varying systems. The presented method is illustrated by numerical examples.