A Periodic Systems Toolbox for MATLAB

The recently developed Periodic Systems Toolbox for MATLAB is described. The basic approach to develop this toolbox was to exploit the powerful object manipulation features of MATLAB via flexible andfunctionally rich high level m-functions, while simultaneously enforcing highly efficient and numerically sound computations via the mex-function technology of MATLAB to solve critical numerical problems.The m-functions based user interfaces ensure user-friendliness in operating with the functions of this toolbox via an object oriented approach to handle periodic system descriptions. The mex-functions are based on Fortran implementations of recently developed structure exploiting and structure preserving numerical algorithms for periodic systems which completely avoid forming of lifted representations

Real-Time Motion Planning of Legged Robots: A Model Predictive Control Approach

We introduce a real-time, constrained, nonlinear Model Predictive Control for the motion planning of legged robots. The proposed approach uses a constrained optimal control algorithm known as SLQ. We improve the efficiency of this algorithm by introducing a multi-processing scheme for estimating value function in its backward pass. This pass has been often calculated as a single process. This parallel SLQ algorithm can optimize longer time horizons without proportional increase in its computation time. Thus, our MPC algorithm can generate optimized trajectories for the next few phases of the motion within only a few milliseconds. This outperforms the state of the art by at least one order of magnitude. The performance of the approach is validated on a quadruped robot for generating dynamic gaits such as trotting.Comment: 8 page

Deep Reinforcement Learning for Event-Triggered Control

Event-triggered control (ETC) methods can achieve high-performance control with a significantly lower number of samples compared to usual, time-triggered methods. These frameworks are often based on a mathematical model of the system and specific designs of controller and event trigger. In this paper, we show how deep reinforcement learning (DRL) algorithms can be leveraged to simultaneously learn control and communication behavior from scratch, and present a DRL approach that is particularly suitable for ETC. To our knowledge, this is the first work to apply DRL to ETC. We validate the approach on multiple control tasks and compare it to model-based event-triggering frameworks. In particular, we demonstrate that it can, other than many model-based ETC designs, be straightforwardly applied to nonlinear systems

Stochastic Sensor Scheduling via Distributed Convex Optimization

In this paper, we propose a stochastic scheduling strategy for estimating the states of N discrete-time linear time invariant (DTLTI) dynamic systems, where only one system can be observed by the sensor at each time instant due to practical resource constraints. The idea of our stochastic strategy is that a system is randomly selected for observation at each time instant according to a pre-assigned probability distribution. We aim to find the optimal pre-assigned probability in order to minimize the maximal estimate error covariance among dynamic systems. We first show that under mild conditions, the stochastic scheduling problem gives an upper bound on the performance of the optimal sensor selection problem, notoriously difficult to solve. We next relax the stochastic scheduling problem into a tractable suboptimal quasi-convex form. We then show that the new problem can be decomposed into coupled small convex optimization problems, and it can be solved in a distributed fashion. Finally, for scheduling implementation, we propose centralized and distributed deterministic scheduling strategies based on the optimal stochastic solution and provide simulation examples.Comment: Proof errors and typos are fixed. One section is removed from last versio

Quantum computers in phase space

We represent both the states and the evolution of a quantum computer in phase space using the discrete Wigner function. We study properties of the phase space representation of quantum algorithms: apart from analyzing important examples, such as the Fourier Transform and Grover's search, we examine the conditions for the existence of a direct correspondence between quantum and classical evolutions in phase space. Finally, we describe how to directly measure the Wigner function in a given phase space point by means of a tomographic method that, itself, can be interpreted as a simple quantum algorithm.Comment: 16 pages, 7 figures, to appear in Phys Rev

Optimization approaches for controller and schedule codesign in networked control

We consider the offline optimization of a sequence for communication scheduling in networked control systems. Given a continuous-time Linear Quadratic Regulator (LQR) problem we design a sampled-data periodic controller based on the continuous time LQR controller that takes into account the limited communication medium and inter-sampling behavior. To allow for a Riccati equation approach, singularities in the weighting matrices and time-variance are accounted for using a lifting approach. Optimal scheduling can be obtained by solving a complex combinatorial optimization problem. Two stochastic algorithms will be proposed to find a (sub)optimal sequence and the associated optimal controller which is the result of a discrete algebraic Riccati equation for the given optimal sequence

The Thermal-Constrained Real-Time Systems Design on Multi-Core Platforms -- An Analytical Approach

Over the past decades, the shrinking transistor size enabled more transistors to be integrated into an IC chip, to achieve higher and higher computing performances. However, the semiconductor industry is now reaching a saturation point of Moore’s Law largely due to soaring power consumption and heat dissipation, among other factors. High chip temperature not only significantly increases packing/cooling cost, degrades system performance and reliability, but also increases the energy consumption and even damages the chip permanently. Although designing 2D and even 3D multi-core processors helps to lower the power/thermal barrier for single-core architectures by exploring the thread/process level parallelism, the higher power density and longer heat removal path has made the thermal problem substantially more challenging, surpassing the heat dissipation capability of traditional cooling mechanisms such as cooling fan, heat sink, heat spread, etc., in the design of new generations of computing systems. As a result, dynamic thermal management (DTM), i.e. to control the thermal behavior by dynamically varying computing performance and workload allocation on an IC chip, has been well-recognized as an effective strategy to deal with the thermal challenges. Over the past decades, the shrinking transistor size, benefited from the advancement of IC technology, enabled more transistors to be integrated into an IC chip, to achieve higher and higher computing performances. However, the semiconductor industry is now reaching a saturation point of Moore’s Law largely due to soaring power consumption and heat dissipation, among other factors. High chip temperature not only significantly increases packing/cooling cost, degrades system performance and reliability, but also increases the energy consumption and even damages the chip permanently. Although designing 2D and even 3D multi-core processors helps to lower the power/thermal barrier for single-core architectures by exploring the thread/process level parallelism, the higher power density and longer heat removal path has made the thermal problem substantially more challenging, surpassing the heat dissipation capability of traditional cooling mechanisms such as cooling fan, heat sink, heat spread, etc., in the design of new generations of computing systems. As a result, dynamic thermal management (DTM), i.e. to control the thermal behavior by dynamically varying computing performance and workload allocation on an IC chip, has been well-recognized as an effective strategy to deal with the thermal challenges. Different from many existing DTM heuristics that are based on simple intuitions, we seek to address the thermal problems through a rigorous analytical approach, to achieve the high predictability requirement in real-time system design. In this regard, we have made a number of important contributions. First, we develop a series of lemmas and theorems that are general enough to uncover the fundamental principles and characteristics with regard to the thermal model, peak temperature identification and peak temperature reduction, which are key to thermal-constrained real-time computer system design. Second, we develop a design-time frequency and voltage oscillating approach on multi-core platforms, which can greatly enhance the system throughput and its service capacity. Third, different from the traditional workload balancing approach, we develop a thermal-balancing approach that can substantially improve the energy efficiency and task partitioning feasibility, especially when the system utilization is high or with a tight temperature constraint. The significance of our research is that, not only can our proposed algorithms on throughput maximization and energy conservation outperform existing work significantly as demonstrated in our extensive experimental results, the theoretical results in our research are very general and can greatly benefit other thermal-related research