Person:

Wardi, Yorai Y.

Permanent Link

https://hdl.handle.net/1853/71821

Associated Organization(s)

Organizational Unit

School of Electrical and Computer Engineering

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Publication Search Results

Now showing 1 - 10 of 12

Optimal Control of Autonomous Switched-Mode Systems: Gradient-Descent Algorithms with Armijo Step Sizes

(Georgia Institute of Technology, 2015-12) Wardi, Yorai Y. ; Egerstedt, Magnus B. ; Hale, M.

This paper concerns optimal mode-scheduling in autonomous switched-mode hybrid dynamical systems, where the objective is to minimize a cost-performance functional defined on the state trajectory as a function of the schedule of modes. The controlled variable, namely the modes’ schedule, consists of the sequence of modes and the switchover times between them. We propose a gradient-descent algorithm that adjusts a given mode-schedule by changing multiple modes over time-sets of positive Lebesgue measures, thereby avoiding the inefficiencies inherent in existing techniques that change the modes one at a time. The algorithm is based on steepest descent with Armijo step sizes along Gˆateaux differentials of the performance functional with respect to schedule-variations, which yields effective descent at each iteration. Since the space of mode-schedules is infinite dimensional and incomplete, the algorithm’s convergence is proved in the sense of Polak’s framework of optimality functions and minimizing sequences. Simulation results are presented, and possible extensions to problems with dwelltime lower-bound constraints are discussed.
Minimizing Mobility and Communication Energy in Robotic Networks: an Optimal Control Approach

(Georgia Institute of Technology, 2014-06) Jaleel, Hassan ; Wardi, Yorai Y. ; Egerstedt, Magnus B.

This paper concerns the problem of minimizing the sum of motion energy and communication energy in a network of mobile robots. The robotic network is charged with the task of transmitting sensor information from a given object to a remote station, and it has to arrange itself in a serial (tandem) configuration for point-to-point transmission, where each robot acts as a relay node. The problem is formulated in a dynamic setting where the robots move and communicate at the same time, and it is cast in the framework of optimal control. The paper proposes an effective algorithm for solving this problem and demonstrates its efficacy on a simulation example. In order to highlight the salient features of the algorithm the network is assumed to be one-dimensional, and the case of planar movement with obstacles is deferred to future research.
A Controlled-Precision Algorithm for Mode-Switching Optimization

(Georgia Institute of Technology, 2012-12) Wardi, Yorai Y. ; Egerstedt, Magnus B. ; Twu, Philip Y.

This paper describes an adaptive-precision algorithm for solving a general optimal mode-scheduling problem in switched-mode dynamical systems. The problem is complicated by the fact that the controlled variable has discrete and continuous components, namely the sequence of modes and the switching times between them. Recently we developed a gradient-descent algorithm whose salient feature is that its descent at a given iteration is independent of the length (number of modes) of the schedule, hence it is suitable to situations where the schedule-lengths at successive iterations grow unboundedly. The computation of the descent direction requires grid-based approximations to solve differential equations as well as minimize certain functions on uncountable sets. However, the algorithm’s convergence analysis assumes exact computations, and it breaks down when approximations are used, because the descent directions are discontinuous in the problem parameters. The purpose of the present paper is to overcome this theoretical gap and its computational implications by developing an implementable, adaptive-precision algorithm that controls the approximation levels by balancing precision with computational workloads. Its asymptotic convergence is proved, and simulation results are provided to support the theoretical developments.
Algorithm for Optimal Mode Scheduling in Switched Systems

(Georgia Institute of Technology, 2012-06) Wardi, Yorai Y. ; Egerstedt, Magnus B.

This paper considers the problem of computing the schedule of modes in an autonomous switched dynamical system, that minimizes a cost functional defined on the trajectory of the system’s continuous state variable. It proposes an algorithm that modifies a finite but unbounded number of modes at each iteration, whose computational workload at the various iterations appears to be independent on the number of modes being changed. The algorithm is based on descent directions defined by Gˆateaux differentials of the performance function with respect to variations in mode-sequences, and its convergence to (local) minima is established in the framework of optimality functions and minimizing sequences, devised by Polak for infinite-dimensional optimization problems.
A Power Capping Controller for Multicore Processors

(Georgia Institute of Technology, 2011) Almoosa, Nawaf ; Song, William ; Wardi, Yorai Y. ; Yalamanchili, Sudhakar

This paper presents an online controller for tracking power-budgets in multicore processors using dynamic voltage-frequency scaling. The proposed control law comprises an integral controller whose gain is adjusted online based on the derivative of the power-frequency relationship. The control law is designed to achieve rapid settling time, and its tracking property is formally proven. Importantly, the controller design does not require off-line analysis of application workloads making it feasible for emerging heterogeneous and asymmetric multicore processors. Simulation results are presented for controlling power dissipation in multiple cores of an asymmetric multicore processor. Each core is i) equipped with the controller, ii) assigned a power budget, and iii) operates independently in tracking to its power budget. We use a cycle-level multicore simulator driven by traces from SPEC2006 benchmarks demonstrating that the proposed algorithm achieves a faster settling time than examples of a static setting of the controller gain.
On-line Optimal Timing Control of Switched Systems

(Georgia Institute of Technology, 2010-12) Wardi, Yorai Y. ; Egerstedt, Magnus B. ; Twu, Philip Y.

This paper considers a real-time algorithm for performance optimization of switched-mode hybrid dynamical systems. The controlled parameter consists of the switching times between the modes, and the cost criterion has the form of the integral of a performance function defined on the system's state trajectory. The dynamic response functions (state equations) associated with the modes are not known in advance; rather, at each time t, they are estimated for all future times s ≥ t. A first-order algorithm is proposed and its behavior is analyzed in terms of its convergence rate. Finally, an example of a mobile robot tracking a moving target while avoiding obstacles is presented.
Optimal Switching Surfaces in Behavior-Based Robotics

(Georgia Institute of Technology, 2006-12) Axelsson, Henrik ; Egerstedt, Magnus B. ; Wardi, Yorai Y.

In this paper an optimal solution is presented for the problem of avoiding obstacles while progressing towards a goal for a single robot. In particular, the solution is obtained by allowing the robot to switch between a fixed number of behaviors and optimizing over what behaviors to use and when to switch between them. It is moreover shown that the structure of the switching law only depends on the distance between the obstacle and the goal. Hence, once initial simulations are done, a guard can be generated with a fixed structure, and, given that the robot knows the distance between the obstacle and the goal, it knows when to switch in order to execute the pre-computed (optimal) solution. Therefore the solution lends itself nicely to real-time implementations. Experiments moreover verify that the proposed methods transitions well onto a real robotic platform.
An Optimal Control Approach to Mode Generation in Hybrid Systems

(Georgia Institute of Technology, 2006-09) Egerstedt, Magnus B. ; Azuma, Shun-ichi ; Wardi, Yorai Y.

Optimal switch-time control is an area that investigates how best to switch between different control modes. In this paper we present an algorithm for solving the optimal switch-time control problem for single-switch, linear systems where the state of the system is only partially known through the outputs. A method is presented that both guarantees that the current switch-time remains optimal as the state estimates evolve, and that ensures this in a computationally feasible manner, thus rendering the method applicable to real-time applications. An extension is moreover considered where constraints on the switch-time provides the observer with sufficient time to settle. The viability of the proposed method is illustrated through a number of examples.
Obstacle Avoidance for Mobile Robots Using Switching Surface Optimization

(Georgia Institute of Technology, 2005-07) Boccadoro, Mauro ; Egerstedt, Magnus B. ; Wardi, Yorai Y.

This paper studies the problem of letting an autonomous mobile robot negotiate obstacles in an optimal manner. In particular, a multi-modal control problem is addressed, where different modes of operation control the robot at different locations in the state space. The specification of the optimal discrete event dynamics is pursued through the design of optimal, parametrized switching surfaces, using results on switching surface optimization.
Reactive Robot Navigation Using Optimal Timing Control

(Georgia Institute of Technology, 2005-06) Axelsson, Henrik ; Egerstedt, Magnus B. ; Wardi, Yorai Y.

In this paper a solution is presented for the problem of avoiding obstacles while progressing towards a goal for a single robot. In particular, an optimal solution is obtained by allowing the robot to switch between a fixed number of behaviors and optimizing over what behaviors to use and when to switch between them. We moreover show that the structure of the switch law only depends on the distance between the obstacle and the goal. Hence, once initial simulations are done, the structure of the guard is known to the robot and, given that the robot knows the distance between the obstacle and the goal, it knows when to switch to obtain the optimal solution. Therefore the solution lends itself to real-time implementations. The feasibility of the approach is verified in real robotics experiments.