Applied Optimal Control: Optimization, Estimation, and Control

By G. Siouris. 1979

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Citations in the corpus

Deep learning in neural networks: An overview (2014, background): “Steepest descent in such systems can be performed (Bryson, 1961; Kelley, 1960; Bryson and Ho, 1969) by iterating the ancient chain rule (Leibniz, 1676; L’Hôpital, 1696) in Dynamic Programming (DP) style (Bellman, 1957).”
Deep Imitation Learning for Complex Manipulation Tasks from Virtual Reality Teleoperation (2017, background): “Demonstrations could instead be collected from running trajectory optimization [12], [13], [14], [15] or reinforcement learning [16], [17], [18], [19], [20], [21], [22], but these meth-ods require well-shaped, carefully designed reward functions, access to dynamics model, and substantial robot…”
Automatic differentiation in machine learning: a survey (2015, methodology): “This method was understood in the control theory community (Bryson, 1962; Bryson and Ho, 1969) and cast in more formal terms with discrete-time variables topologically sorted in terms of dependency by Werbos (1974).”
Reinforcement-Learning-Based Robust Controller Design for Continuous-Time Uncertain Nonlinear Systems Subject to Input Constraints (2015, background): “The important and valuable insights into the optimal control theory were presented in [5] and [6].”
Analytical Solution to the Minimum Energy Consumption Based Velocity Profile Optimization Problem With Variable Road Grade (2014, background): “The Hamiltonian Function is defined as: Hi(z(t),u(t),λ (t)) = L(z(t),u(t))+λ T fi(z(t),u(t)) for i = 1,2, · · · ,M (11) From calculus of variation theory (Bryson and Ho (1975) and Kirk (2012) ) the optimal trajectories minimizing J, render δJ = 0 δJ = [( ρT ∂ψ ∂ t +L+λ T ż ) dt ] t=t f + [( ρT ∂ψ…”
Machine learning of motor skills for robotics (2007, methodology): “General optimal control techniques on the other hand are often not applicable as a closed-form solution usually does not exist and numerical solutions for high-dimensional systems are often prohibitively expensive in terms of computations due to the ‘Curse of Dimensionality’ (Bellman & Kalaba, 1965)”
Storage Size Determination for Grid-Connected Photovoltaic Systems (2011, background): “Even though it might be possible to find the optimal control using the minimum principle [21], it is still hard to get an explicit expression for the cost function .”