When Is a Linear Control System Optimal

By R. Kálmán. 1964

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Citations in the corpus

Reinforcement learning in robotics: A survey (2013, background): “Inverse optimal control was initially studied in the control community (Kalman, 1964) and in the field of economics (Keeney and Raiffa, 1976).”
An Algorithmic Perspective on Imitation Learning (2018, methodology): “We organize our work by dividing imitation learning into directly replicating desired behavior (sometimes called behavioral cloning [Bain and Sammut, 1996]) and learning the hidden objectives of the desired behavior from demonstrations (called inverse optimal control [Kalman, 1964] or inverse reinfo”
Inverse Optimal Control with Linearly-Solvable MDPs (2010, background): “between optimality and stability within the linearquadratic-Gaussian framework [6].”
Min-max approximate dynamic programming (2011, background): “In this case optimal control policy is affine in the state variable, with coefficients that are readily computable [1], [2], [3], [4].”
A Tour of Reinforcement Learning: The View from Continuous Control (2018, background): “This becomes a problem of inverse optimal control [40] or inverse reinforcement learning [55], where we have to estimate the reward functions of the human and understand the loss accrued for crudely modeling these rewards.”
Distributed Cooperative Optimal Control for Multiagent Systems on Directed Graphs: An Inverse Optimal Approach (2015, background): “Proposition 4: For the IOCP (5), K is optimal and the corresponding ARE has a symmetric positive definite solution P for some Q = QT and R = RT > 0, if and only if the following holds.”
Performance bounds for linear stochastic control (2009, background): “, there are no constraints on the input) and "x and "u are convex quadratic functions [14].”
Learning to search: Functional gradient techniques for imitation learning (2009, background): “The concept is to leverage the older notion of inverse optimal control (Kalman, 1964; Boyd et al., 1994; Anderson & Moore, 1990): imitation learning is achieved by first recovering a cost function by observing an expert perform a task, and then executing new tasks using an optimal controller/planner”
Control Lyapunov-Razumikhin functions and robust stabilization of time delay systems (2001, methodology): “For , we obtain the classical stability result that applies when is a nondelay system and is an optimal control law [11], [16], [19].”
An Invitation to Imitation (2015, background): “Amusingly, while Kalman’s work was critical in advancing the use of state-space techniques for control, his solution to the IOC problem was rooted fundamentally in frequency domain techniques.”
Constructive nonlinear control: a historical perspective (2001, methodology): “A connection between optimality and passivity for a linear system with a quadratic cost (the LQR problem) was established by Kalman (1964) who analyzed the inverse LQR problem.”
Integrating robustness, optimality and constraints in control of nonlinear processes (2001, methodology): “An alternative approach to robust optimal controller design which avoids the unwieldy task of solving the HJI equation is the inverse optimal approach proposed by Kalman (1964) and introduced recently in the context of robust stabilization in Freeman and Kokotovic (1996).”
Differentiable Convex Optimization Layers (2019, background): “Note that if u were unconstrained, (7) could be solved exactly, via linear quadratic regulator (LQR) theory [50].”
Cooperative Filters and Control for Cooperative Exploration (2010, background): “Derivation of these sufficient conditions is based on fundamental results connecting controllability and observability of a (time-varying) filtering system to its convergence in [20]–[22].”
Modeling Interaction via the Principle of Maximum Causal Entropy (2010, background): “On the other hand, the function learned by MaxCausalEnt IOC not only induces the same feature counts– and hence equal cost on the unknown cost function– under the learned probabilistic policy, but because of the quadratic cost function its learned controller’s optimal policy is always at least as go”
Approximate dynamic programming via iterated Bellman inequalities (2015, background): “) Another famous special case is when X D R, U D R, and ` is a convex quadratic function [1].”