Yorai Wardi

Yorai Wardi, Magnus Egerstedt

This paper considers the problem of computing the schedule of modes in a switched dynamical system, that minimizes a cost functional defined on the trajectory of the system's continuous state variable. A recent approach to such optimal control problems consists of algorithms that alternate between computing the optimal switching times between modes in a given sequence, and updating the mode-sequence by inserting to it a finite number of new modes. These algorithms have an inherent inefficiency due to their sparse update of the mode-sequences, while spending most of the computing times on optimizing with respect to the switching times for a given mode-sequence. This paper proposes an algorithm that operates directly in the schedule space without resorting to the timing optimization problem. It is based on the Armijo step size along certain Gateaux derivatives of the performance functional, thereby avoiding some of the computational difficulties associated with discrete scheduling parameters. Its convergence to local minima as well as its rate of convergence are proved, and a simulation example on a nonlinear system exhibits quite a fast convergence.

Shashwat Shivam, Ian Buckley, Yorai Wardi et al.

This paper concerns applications of a recently-developed output-tracking technique to trajectory control of autonomous vehicles. The technique is based on three principles: Newton-Raphson flow for solving algebraic equations,output prediction, and controller speedup. Early applications of the technique, made to simple systems of an academic nature,were implemented by simple algorithms requiring modest computational efforts. In contrast, this paper tests it on commonly-used dynamic models to see if it can handle more complex control scenarios. Results are derived from simulations as well as a laboratory setting, and they indicate effective tracking convergence despite the simplicity of the control algorithm.

Keith Paarporn, Ceyhun Eksin, Joshua S. Weitz et al.

We study a dynamical model of a population of cooperators and defectors whose actions have long-term consequences on environmental "commons" - what we term the "resource". Cooperators contribute to restoring the resource whereas defectors degrade it. The population dynamics evolve according to a replicator equation coupled with an environmental state. Our goal is to identify methods of influencing the population with the objective to maximize accumulation of the resource. In particular, we consider strategies that modify individual-level incentives. We then extend the model to incorporate a public opinion state that imperfectly tracks the true environmental state, and study strategies that influence opinion. We formulate optimal control problems and solve them using numerical techniques to characterize locally optimal control policies for three problem formulations: 1) control of incentives, and control of opinions through 2) propaganda-like strategies and 3) awareness campaigns. We show numerically that the resulting controllers in all formulations achieve the objective, albeit with an unintended consequence. The resulting dynamics include cycles between low and high resource states - a dynamical regime termed an "oscillating tragedy of the commons". This outcome may have desirable average properties, but includes risks to resource depletion. Our findings suggest the need for new approaches to controlling coupled population-environment dynamics.

Evanns Morales-Cuadrado, Luke Baird, Yorai Wardi et al.

We investigate the performance of a lightweight tracking controller, based on a flow version of the Newton-Raphson method, applied to a miniature blimp and a mid-size quadrotor. This tracking technique admits theoretical performance guarantees for certain classes of systems and has been successfully applied in simulation studies and on mobile robots with simplified motion models. We evaluate the technique through real-world flight experiments on aerial hardware platforms subject to realistic deployment and onboard computational constraints. The technique's performance is assessed in comparison with established baseline control frameworks of feedback linearization for the blimp, and nonlinear model predictive control for both the quadrotor and the blimp. The performance metrics under consideration are (i) root mean square error of flight trajectories with respect to target trajectories, (ii) algorithms' computation times, and (iii) CPU energy consumption associated with the control algorithms. The experimental findings show that the Newton-Raphson-based tracking controller achieves competitive or superior tracking performance to the baseline methods with substantially reduced computation time and energy expenditure.

Shashwat Shivam, Yorai Wardi, Magnus Egerstedt et al.

This paper concerns an application of a recently-developed nonlinear tracking technique to trajectory control of autonomous vehicles at traffic intersections. The technique uses a flow version of the Newton-Raphson method for controlling a predicted system-output to a future reference target. Its implementations are based on numerical solutions of ordinary differential equations, and it does not specify any particular method for computing its future reference trajectories. Consequently it can use relatively simple algorithms on crude models for computing the target trajectories, and more-accurate models and algorithms for trajectory control in the tight loop. We demonstrate this point at an extant predictive traffic planning-and-control method with our tracking technique. Furthermore, we guarantee safety specifications by applying to the tracking technique the framework of control barrier functions.

Karthik Rao, William Song, Yorai Wardi et al.

The consistent demand for better performance has lead to innovations at hardware and microarchitectural levels. 3D stacking of memory and logic dies delivers an order of magnitude improvement in available memory bandwidth. The price paid however is, tight thermal constraints. In this paper, we study the complex multiphysics interactions between performance, energy and temperature. Using a cache coherent multicore processor cycle level simulator coupled with power and thermal estimation tools, we investigate the interactions between (a) thermal behaviors (b) compute and memory microarchitecture and (c) application workloads. The key insights from this exploration reveal the need to manage performance, energy and temperature in a coordinated fashion. Furthermore, we identify the concept of "effective heat capacity" i.e. the heat generated beyond which no further gains in performance is observed with increases in voltage-frequency of the compute logic. Subsequently, a real-time, numerical optimization based, application agnostic controller (TRINITY) is developed which intelligently manages the three parameters of interest. We observe up to $30\%$ improvement in Energy Delay$^2$ Product and up to $8$ Kelvin lower core temperatures as compared to fixed frequencies. Compared to the \texttt{ondemand} Linux CPU DVFS governor, for similar energy efficiency, TRINITY keeps the cores cooler by $6$ Kelvin which increases the lifetime reliability by up to 59\%.