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This paper proposes a class of basis functions for realizing the input-to-state stability verification of identified models obtained from the true system (assumed to be input-to-state stable) using the Koopman operator. The formulated input-to-state stability conditions are in the form of linear matrix inequalities. Two extensions are presented to relax the imposed restrictions on the basis functions. Several numerical examples are provided to demonstrate the efficacy of the proposed results.

Modern mobile applications have grown rapidly in binary size, which restricts user growth and hinders updates for existing users. Thus, reducing the binary size is important for application developers. Recent studies have shown the possibility of using link-time code size optimizations by re-invoking certain compiler optimizations on the linked intermediate representation of the program. However, such methods often incur significant build time overhead and require intrusive changes to the existing build pipeline. In this paper, we propose several novel optimization techniques that do not require significant customization to the build pipeline and reduce binary size with low build time overhead. As opposed to re-invoking the compiler during link time, we perform true linker optimization directly as optimization passes within the linker. This enables more optimization opportunities such as pre-compiled libraries that prior work often could not optimize. We evaluate our techniques on several commercial iOS applications including NewsFeedApp, ShortVideoApp, and CollaborationSuiteApp, each with hundreds of millions of daily active users. Our techniques on average achieve 18.4% binary size reduction across the three commercial applications without any user-perceivable performance degradations.

This letter deals with the optimization problems of stochastic switching buffer networks, where the switching law is governed by Markov process. The dynamical buffer network is introduced, and its application in modeling the car-sharing network is also presented. To address the nonconvexity for getting a solution as close-to-the-global-optimal as possible of the optimization problem, we adopt a succinct but effective nonconvex optimization method called \emph{ DC (difference of convex functions) programming}. By resorting to the log-log convexity of a class of nonlinear functions called posynomials, the optimization problems can be reduced to DC programming problems. Finally, we verify the effectiveness of our results by simulation experiments.

In this paper, we study a class of finite-time control problems for discrete-time positive linear systems with time-varying state parameters. Although several interesting control problems appearing in population biology, economics, and network epidemiology can be described as the class of finite-time control problems, an efficient solution to the control problem has not been yet found in the literature. In this paper, we propose an optimization framework for solving the class of finite-time control problems via convex optimization. We illustrate the effectiveness of the proposed method by numerical simulation in the context of dynamical product development processes.

Resource allocation is an essential aspect of successful Product Development (PD). In this paper, we formulate the dynamic resource allocation of the PD process as a convex optimization problem. Specially, we build and solve two variants of this issue: the budget-constrained problem and the performance-constrained problem. By using convex optimization, we propose a framework to optimally solve large problem instances at a relatively small computational cost. The solutions to both problems exhibit similar trends regarding resource allocation decisions and performance evolution. Furthermore, we show that the product architecture affects resource allocation, which in turn affects the performance of the PD process. By introducing centrality metrics for measuring the location of the modules and design rules within the product architecture network, we find that resource allocation decisions correlate to their metrics. These results provide simple, but powerful, managerial guidelines for efficiently designing and managing the PD process. Finally, for validating the model and its results, we introduce and solve two design case studies for a mechanical manipulator and for an automotive appearance design process.

This paper investigates state feedback control laws for Markov jump linear systems with state and mode-observation delays. An assumption in this study is that the delay of mode observation obeys an exponential distribution. Also, we raise an unknown time-varying state delay applied in the composition of the state feedback controller. A method of remodeling the closed-loop system as a standard Markov jump linear system with state delay is shown. Furthermore, on the basis of this remodeling, several Linear Matrix Inequalities (LMI) for designing feedback gains for stabilization and mixed $H_2/H_{\infty}$ control are proposed. Finally, we apply a numerical simulation for examining the effectiveness of the proposed mixed $H_2/H_{\infty}$ controller designing method., Comment: Accepted for publication in IET Control Theory & Applications

In this paper, we study the problem of optimizing the stability of positive semi-Markov jump linear systems. We specifically consider the problem of tuning the coefficients of the system matrices for maximizing the exponential decay rate of the system under a budget-constraint. By using a result from the matrix theory on the log-log convexity of the spectral radius of nonnegative matrices, we show that the stability optimization problem reduces to a convex optimization problem under certain regularity conditions on the system matrices and the cost function. We illustrate the validity and effectiveness of the proposed results by using an example from the population biology.