Nearly optimal control laws for nonlinear systems with saturating actuators using a neural network HJB approach

By Murad Abu-Khalaf, Frank L. Lewis. at - Automatisierungstechnik, 2005

1,307 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/f5699fa47aa10c95d42015bfe9f788d152fe7e57

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In Computational Theory and Mathematics

In Control and Systems Engineering

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Citations in the corpus

Reinforcement learning and adaptive dynamic programming for feedback control (2009, background): “If the utility has the special form and the dynamics are (1), then the policy improvement step looks like”
Integral reinforcement learning and experience replay for adaptive optimal control of partially-unknown constrained-input continuous-time systems (2014, methodology): “The performance of the final near-optimal controllers which are found at the end of the learning process for case 1 (control law 1) and case 2 (control law 2) are now compared with the performance of the near-optimal control law found in Abu-Khalaf and Lewis (2005) (control law 3).”
Optimal control of unknown nonaffine nonlinear discrete-time systems based on adaptive dynamic programming (2012, background): “…of linear systems and nonlinear systems lies in that the latter often requires solving the nonlinear Hamilton–Jacobi–Bellman (HJB) equation instead of the Riccati equation (Abu-Khalaf & Lewis, 2005; Al-Tamimi, Lewis, & Abu-Khalaf, 2008; Primbs, Nevistic, & Doyle, 2000; Wang, Zhang, & Liu, 2009).”
Online adaptive optimal control for continuous-time Markov jump linear systems using a novel policy iteration algorithm (2015, neutral): “To this end, the definition of admissible control policy for the regular linear/nonlinear [33][18] is generalized to MJLSs as follows.”
Decentralized Stabilization for a Class of Continuous-Time Nonlinear Interconnected Systems Using Online Learning Optimal Control Approach (2014, background): “Specifically, policy iteration represents a class of algorithms containing two basic iterations, i.e., policy evaluation and policy improvement [41]–[46].”
Adaptive Dynamic Programming: An Introduction (2009, background): “To do this, a function is needed to describe the gradient of the instantaneous cost function with respect to the state of the system.”
Discrete-Time Nonlinear HJB Solution Using Approximate Dynamic Programming: Convergence Proof (2008, background): “Hence, the class of controllers need to be stable and guarantee that (2) is finite, i.e. admissible controls [20] The optimal control u * satisfies the first order necessity condition for the gradient of right hand side of (4) with respect to u 1 1 1 ( ) ( ) ( ) 0 T T k k k k k k k k k k k V x x Qx…”
Optimal tracking control of nonlinear partially-unknown constrained-input systems using integral reinforcement learning (2014, methodology): “…is obtained by minimizing the performance function (7), it is not possible to encode the input constraints into the optimization problem by using a nonquadratic performance function, as has been performed in the optimal regulation problem (Abou-Khalaf & Lewis, 2005; Modares et al., 2013, 2014).”
Policy Iteration Adaptive Dynamic Programming Algorithm for Discrete-Time Nonlinear Systems (2014, methodology): “Actually, for all the policy iteration algorithms of ADP, including [17] and [43]–[47], the initial admissible control law is necessary to implement their algorithms.”
Reinforcement-Learning-Based Robust Controller Design for Continuous-Time Uncertain Nonlinear Systems Subject to Input Constraints (2015, methodology): “In order to overcome bounded controls in system (2), inspired by the work of [38]–[40], we define W(u) as”
Adaptive Critic Nonlinear Robust Control: A Survey (2017, methodology): “In general, ADP is a promising technique to approximate optimal control solutions for complex systems [16]–[19], [25]–[28].”
Multi-player non-zero-sum games: Online adaptive learning solution of coupled Hamilton-Jacobi equations (2011, methodology): “…policies the non-linear Lyapunov equations (13) have locally smooth solutions According to the Weierstrass higher-order approximation theorem (Abu-Khalaf & Lewis, 2005; Finlayson, 1990; Hornik, Stinchcombe, & White, 1990), there exist complete independent basis sets such that the solution V…”