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- Asma Al-Tamimi, Frank L. Lewis, Murad Abu-Khalaf
- IEEE Trans. Systems, Man, and Cybernetics, Part B
- 2008

Convergence of the value-iteration-based heuristic dynamic programming (HDP) algorithm is proven in the case of general nonlinear systems. That is, it is shown that HDP converges to the optimal control and the optimal value function that solves the Hamilton-Jacobi-Bellman equation appearing in infinite-horizon discrete-time (DT) nonlinear optimal control.… (More)

- Murad Abu-Khalaf, Frank L. Lewis
- Automatica
- 2005

We consider the use of nonlinear approximating networks to obtain nearly optimal solutions to constrained control problems. The method is based on least-squares successive approximation solution of the Generalized HamiltonJacobi-Bellman (GHJB) equation which appears in optimization problems. Successive approximation using the GHJB has not yet been… (More)

- Kyriakos G. Vamvoudakis, Frank L. Lewis
- 2009 International Joint Conference on Neural…
- 2009

In this paper we discuss an online algorithm based on policy iteration for learning the continuous-time (CT) optimal control solution with infinite horizon cost for nonlinear systems with known dynamics. We present an online adaptive algorithm implemented as an actor/critic structure which involves simultaneous continuous-time adaptation of both actor and… (More)

- Frank L. Lewis, Aydin Yesildirek, Kai Liu
- IEEE Trans. Neural Networks
- 1996

A multilayer neural-net (NN) controller for a general serial-link rigid robot arm is developed. The structure of the NN controller is derived using a filtered error/passivity approach. No off-line learning phase is needed for the proposed NN controller and the weights are easily initialized. The nonlinear nature of the NN, plus NN functional reconstruction… (More)

- Rafael Fierro, Frank L. Lewis
- J. Field Robotics
- 1997

A dynamical extension that makes possible the integration of a kinematic controller and a torque controller for nonholonomic mobile robots is presented. A combined kinematic/torque control law is developed using backstepping, and asymptotic stability is guaranteed by Lyapunov theory. Moreover, this control algorithm can be applied to the three basic… (More)

Living organisms learn by acting on their environment, observing the resulting reward stimulus, and adjusting their actions accordingly to improve the reward. This actionbased or Reinforcement Learning can capture notions of optimal behavior occurring in natural systems. We describe mathematical formulations for Reinforcement Learning and a practical… (More)

- Rafael B. Fierro, Frank L. Lewis
- IEEE Trans. Neural Networks
- 1998

A control structure that makes possible the integration of a kinematic controller and a neural network (NN) computed-torque controller for nonholonomic mobile robots is presented. A combined kinematic/torque control law is developed using backstepping and stability is guaranteed by Lyapunov theory. This control algorithm can be applied to the three basic… (More)

- Hongwei Zhang, Frank L. Lewis, Abhijit Das
- IEEE Trans. Automat. Contr.
- 2011

This technical note studies synchronization of identical general linear systems on a digraph containing a spanning tree. A leader node or command generator is considered, which generates the desired tracking trajectory. A framework for cooperative tracking control is proposed, including full state feedback control, observer design and dynamic output… (More)

- Abhijit Das, Frank L. Lewis
- Automatica
- 2010

- Draguna Vrabie, Frank L. Lewis
- Neural Networks
- 2009

In this paper we present in a continuous-time framework an online approach to direct adaptive optimal control with infinite horizon cost for nonlinear systems. The algorithm converges online to the optimal control solution without knowledge of the internal system dynamics. Closed-loop dynamic stability is guaranteed throughout. The algorithm is based on a… (More)