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Wardi,
Yorai Y.
Wardi,
Yorai Y.
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ItemOptimal Control of Autonomous SwitchedMode Systems: GradientDescent Algorithms with Armijo Step Sizes(Georgia Institute of Technology, 201512) Wardi, Yorai Y. ; Egerstedt, Magnus B. ; Hale, M.This paper concerns optimal modescheduling in autonomous switchedmode hybrid dynamical systems, where the objective is to minimize a costperformance 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 gradientdescent algorithm that adjusts a given modeschedule by changing multiple modes over timesets 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 schedulevariations, which yields effective descent at each iteration. Since the space of modeschedules 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 lowerbound constraints are discussed.

ItemMinimizing Mobility and Communication Energy in Robotic Networks: an Optimal Control Approach(Georgia Institute of Technology, 201406) 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 pointtopoint 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 onedimensional, and the case of planar movement with obstacles is deferred to future research.

ItemA ControlledPrecision Algorithm for ModeSwitching Optimization(Georgia Institute of Technology, 201212) Wardi, Yorai Y. ; Egerstedt, Magnus B. ; Twu, Philip Y.This paper describes an adaptiveprecision algorithm for solving a general optimal modescheduling problem in switchedmode 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 gradientdescent 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 schedulelengths at successive iterations grow unboundedly. The computation of the descent direction requires gridbased 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, adaptiveprecision 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.

ItemAlgorithm for Optimal Mode Scheduling in Switched Systems(Georgia Institute of Technology, 201206) 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 modesequences, and its convergence to (local) minima is established in the framework of optimality functions and minimizing sequences, devised by Polak for infinitedimensional optimization problems.

ItemA Power Capping Controller for Multicore Processors(Georgia Institute of Technology, 2011) Almoosa, Nawaf ; Song, William ; Wardi, Yorai Y. ; Yalamanchili, SudhakarThis paper presents an online controller for tracking powerbudgets in multicore processors using dynamic voltagefrequency scaling. The proposed control law comprises an integral controller whose gain is adjusted online based on the derivative of the powerfrequency 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 offline 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 cyclelevel 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.

ItemOnline Optimal Timing Control of Switched Systems(Georgia Institute of Technology, 201012) Wardi, Yorai Y. ; Egerstedt, Magnus B. ; Twu, Philip Y.This paper considers a realtime algorithm for performance optimization of switchedmode 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 firstorder 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.

ItemOptimal Switching Surfaces in BehaviorBased Robotics(Georgia Institute of Technology, 200612) 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 precomputed (optimal) solution. Therefore the solution lends itself nicely to realtime implementations. Experiments moreover verify that the proposed methods transitions well onto a real robotic platform.

ItemAn Optimal Control Approach to Mode Generation in Hybrid Systems(Georgia Institute of Technology, 200609) Egerstedt, Magnus B. ; Azuma, Shunichi ; Wardi, Yorai Y.Optimal switchtime 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 switchtime control problem for singleswitch, 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 switchtime remains optimal as the state estimates evolve, and that ensures this in a computationally feasible manner, thus rendering the method applicable to realtime applications. An extension is moreover considered where constraints on the switchtime provides the observer with sufficient time to settle. The viability of the proposed method is illustrated through a number of examples.

ItemObstacle Avoidance for Mobile Robots Using Switching Surface Optimization(Georgia Institute of Technology, 200507) 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 multimodal 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.

ItemReactive Robot Navigation Using Optimal Timing Control(Georgia Institute of Technology, 200506) 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 realtime implementations. The feasibility of the approach is verified in real robotics experiments.