On Imitation Learning of Linear Control Policies: Enforcing Stability and Robustness Constraints via LMI Conditions

Havens, Aaron; Hu, Bin

doi:10.23919/acc50511.2021.9483019

Cited by 7 publications

(15 citation statements)

References 11 publications

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“…IT (z(pT )) (0)z(pT ). Therefore, for all t ∈ [pT, (p + 1)T ], the controller (26) applies the input equal to that applied by the following controller:…”

Section: 2mentioning

confidence: 99%

“…Since the matrices Ψ j (t) are bounded for t ∈ [0, T ], the system (9) in closed loop with controller ( 26) is uniformly exponentially stable. Uniform asymptotic stability of the origin for the system ( 9)- (26) in the (z, v)-coordinates implies uniform asymptotic stability of the origin for the feedback equivalent system ( 5)-( 8)-( 26) in (x, u)-coordinates [35]. Typically, there are several triangulations one can define given a set of sample points Z(0).…”

Section: 2mentioning

confidence: 99%

“…Assume that {Φ(x i (t))} M i=1 is affinely independent for all t ∈ [0, T ]. For any z 0 ∈ conv Z(0), the controller κ DT based on the Delaunay triangulation DT (Z(0)) defined as in (26) results in closed-loop trajectories in z-coordinates that have the smallest worst-case trajectory approximation error on the interval [0, T ] as defined in Definition 4.2.…”

Section: Lemma 43 ([43]mentioning

confidence: 99%

“…They guarantee that the resulting controller is optimal with respect to some quadratic cost by adding an additional set of constraints (originally proposed in [25]) to the optimization problem. This work has been extended in [26] to enforce other properties, such as stability, optimality, and H ∞ -robustness. Our methodology is different from those in [24] and [26] because we do not assume the expert to be a linear time-invariant controller.…”

mentioning

confidence: 99%

“…This work has been extended in [26] to enforce other properties, such as stability, optimality, and H ∞ -robustness. Our methodology is different from those in [24] and [26] because we do not assume the expert to be a linear time-invariant controller.…”

mentioning

confidence: 99%

See 4 more Smart Citations

Learning to control from expert demonstrations

Sultangazin¹,

Pannocchi²,

Fraile³

et al. 2022

Preprint

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In this paper, we revisit the problem of learning a stabilizing controller from a finite number of demonstrations by an expert. By first focusing on feedback linearizable systems, we show how to combine expert demonstrations into a stabilizing controller, provided that demonstrations are sufficiently long and there are at least n + 1 of them, where n is the number of states of the system being controlled. When we have more than n + 1 demonstrations, we discuss how to optimally choose the best n + 1 demonstrations to construct the stabilizing controller. We then extend these results to a class of systems that can be embedded into a higher-dimensional system containing a chain of integrators. The feasibility of the proposed algorithm is demonstrated by applying it on a CrazyFlie 2.0 quadrotor.

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“…IT (z(pT )) (0)z(pT ). Therefore, for all t ∈ [pT, (p + 1)T ], the controller (26) applies the input equal to that applied by the following controller:…”

Section: 2mentioning

confidence: 99%

Section: 2mentioning

confidence: 99%

Section: Lemma 43 ([43]mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

See 3 more Smart Citations

Learning to control from expert demonstrations

Sultangazin¹,

Pannocchi²,

Fraile³

et al. 2022

Preprint

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show abstract

Risk verification of stochastic systems with neural network controllers

Cleaveland

Lindemann

Ivanov

et al. 2022

Artificial Intelligence

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Dissipative Imitation Learning for Robust Dynamic Output Feedback

Strong

LoCicero

Bridgeman

2022

2022 IEEE 61st Conference on Decision and Control (CDC)

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Imitation learning enables the synthesis of controllers for complex objectives and highly uncertain plant models. However, methods to provide stability guarantees to imitation learned controllers often rely on large amounts of data and/or known plant models. In this paper, we explore an input-output (IO) stability approach to dissipative imitation learning, which achieves stability with sparse data sets and with little known about the plant model. A closed-loop stable dynamic output feedback controller is learned using expert data, a coarse IO plant model, and a new constraint to enforce dissipativity on the learned controller. While the learning objective is nonconvex, iterative convex overbounding (ICO) and projected gradient descent (PGD) are explored as methods to successfully learn the controller. This new imitation learning method is applied to two unknown plants and compared to traditionally learned dynamic output feedback controller and neural network controller. With little knowledge of the plant model and a small data set, the dissipativity constrained learned controller achieves closed loop stability and successfully mimics the behavior of the expert controller, while other methods often fail to maintain stability and achieve good performance.

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On Imitation Learning of Linear Control Policies: Enforcing Stability and Robustness Constraints via LMI Conditions

Cited by 7 publications

References 11 publications

Learning to control from expert demonstrations

Learning to control from expert demonstrations

Risk verification of stochastic systems with neural network controllers

Dissipative Imitation Learning for Robust Dynamic Output Feedback

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