Worst-case Throughput Analysis for Parametric Rate and Parametric Actor Execution Time Scenario-Aware Dataflow Graphs

Scenario-aware dataflow (SADF) is a prominent tool for modeling and analysis of dynamic embedded dataflow applications. In SADF the application is represented as a finite collection of synchronous dataflow (SDF) graphs, each of which represents one possible application behaviour or scenario. A finite state machine (FSM) specifies the possible orders of scenario occurrences. The SADF model renders the tightest possible performance guarantees, but is limited by its finiteness. This means that from a practical point of view, it can only handle dynamic dataflow applications that are characterized by a reasonably sized set of possible behaviours or scenarios. In this paper we remove this limitation for a class of SADF graphs by means of SADF model parametrization in terms of graph port rates and actor execution times. First, we formally define the semantics of the model relevant for throughput analysis based on (max,+) linear system theory and (max,+) automata. Second, by generalizing some of the existing results, we give the algorithms for worst-case throughput analysis of parametric rate and parametric actor execution time acyclic SADF graphs with a fully connected, possibly infinite state transition system. Third, we demonstrate our approach on a few realistic applications from digital signal processing (DSP) domain mapped onto an embedded multi-processor architecture

Parametrized dataflow scenarios

The FSM-based scenario-aware dataflow (FSM-SADF) model of computation has been introduced to facilitate the analysis of dynamic streaming applications. FSM-SADF interprets application's execution as an execution of a sequence of static modes of operation called scenarios. Each scenario is modeled using a synchronous dataflow (SDF) graph (SDFG), while a finite-state machine (FSM) is used to encode scenario occurrence patterns. However, FSM-SADF can precisely capture only those dynamic applications whose behaviors can be abstracted into a reasonably sized set of scenarios (coarse-grained dynamism). Nevertheless, in many cases, the application may exhibit thousands or even millions of behaviours (fine-grained dynamism). In this work, we generalize the concept of FSM-SADF to one that is able to model dynamic applications exhibiting fine-grained dynamism. We achieve this by applying parametrization to the FSM-SADF's base model, i.e. SDF, and defining scenarios over parametrized SDFGs. We refer to the extension as parametrized FSM-SADF (PFSM-SADF). Thereafter, we present a novel and a fully parametric analysis technique that allows us to derive tight worst-case performance (throughput and latency) guarantees for PFSM-SADF specifications. We evaluate our approach on a realistic case-study from the multimedia domain

Model-Free All-Source-All-Destination Learning as a Model for Biological Reactive Control

We present here a model-free method for learning actions that lead to an all-source-all-destination shortest path solution. We motivate our approach in the context of biological learning for reactive control. Our method involves an agent exploring an unknown world with the objective of learning how to get from any starting state to any goal state in shortest time without having to run a path planning algorithm for each new goal selection. Using concepts of Lyapunov functions and Bellman's principle of optimality, our agent learns universal state-goal distances and best actions that solve this problem

Parametrized dataflow scenarios

Although well-suited for capturing concurrency in streaming applications, purely dataflow-based models of computation are lacking in expressing intricate control requirements that many modern streaming applications have. Consequently, a number of modeling approaches combining dataflow and finite-state machines has been proposed. However, these FSM/dataflow hybrids struggle with capturing the ne-grained data-dependent dynamics of modern streaming applications. In this article, we enrich the set of such FSM/dataflow hybrids with a novel formalism that uses parameterized dataflow as the concurrency model. We call the model FSM-based parameterized scenario-aware dataflow (PFSM-SADF). Through the use of parameterized dataflow, the formalism can capture the application ne-grained data-dependent dynamics while the enveloping FSM enables the capturing of the application control flow. We demonstrate the application of our modeling framework to synchronous dataflow (SDF), for which we propose a worst-case performance analysis framework based on the Max-plus algebraic semantics of SDF and the theory of Max-plus automata. We show that using the novel hybrid one can give tighter bounds on worst-case performance metrics such as throughput and latency for streaming applications exposing fine-grained dynamic behavior embedded inside a control-flow structure then by using the existing hybrids. We evaluate our approach on a realistic case-study from the multimedia domain

Global asymptotic stabilization of a pendulum using a single Lyapunov proportional bang-bang control strategy

The existence of a Lyapunov function is known to ensure either local or global stability of a system’s equilibrium state. Inspired by the control-Lyapunov method, we here construct a Lyapunov candidate function by analyzing a pendulum system’s total energy and then applying appropriate control actions such that the conditions of a Lyapunov function are met. More specifically, our controller evaluates the Lyapunov function’s time derivative at each time step, and applies control torque such as to ensure that the Lyapunov function decreases for each step toward the goal upright state. Unlike the control-Lyapunov method, which aims to select control input as to minimize the Lyapunov function’s time derivative, our method provides up front the satisfactory conditions that yield a globally stable controller by using a rigorously designed proportional bang-bang control strategy. We show how to derive the controllers evaluation function, and how the controller is implemented in code. We further demonstrate the effectiveness of our method through numerical simulations. The result of our approach is a globally stable upright pendulum using a single-controller strategy