Data-Driven Model-Free Model-Reference Nonlinear Virtual State Feedback Control from Input-Output Data

Rădac, Mircea-Bogdan; Precup, Radu‐Emil; Hedrea, Elena‐Lorena; Mituletu, Ion-Cornel

doi:10.1109/med.2018.8442894

Cited by 5 publications

(8 citation statements)

References 28 publications

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“…Proof: See [51]. A virtual state vector is next introduced as [51] showed that, based on (1) and (2), a new virtual state-space system with output equation is defined as…”

Section: A the Unknown Observable Systemmentioning

confidence: 99%

“…The summarized ideas from [51] are: a) System (3) is IO controllable since it has the same input and output as (1); b) With unknown state dimension n in (1), r from Lemma 1 corresponds to an observability index and it is also unknown. Increasing r (and, subsequently the dimension of the virtual state k z ) is the general advice.…”

Section: A the Unknown Observable Systemmentioning

confidence: 99%

“…Increasing r (and, subsequently the dimension of the virtual state k z ) is the general advice. As [51] shows, beyond some value of r, no information gain about the state k x is obtained from k z ; c) Controlling (1) and (3) is the same issue, except that (3) uses a "measurable" state information. It means that learning control for (3) will render the control for (1); d) Model (1) accommodates a wide range of processes, including time-delay ones.…”

Section: A the Unknown Observable Systemmentioning

confidence: 99%

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Robust Control of Unknown Observable Nonlinear Systems Solved as a Zero-Sum Game

Rădac

Lala

2020

IEEE Access

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An optimal robust control solution for general nonlinear systems with unknown but observable dynamics is advanced here. The underlying Hamilton-Jacobi-Isaacs (HJI) equation of the corresponding zero-sum two-player game (ZS-TP-G) is learned using a Q-learning-based approach employing only input-output system measurements, assuming system observability. An equivalent virtual state-space model is built from the system's input-output samples and it is shown that controlling the former implies controlling the latter. Since the existence of a saddle-point solution to the ZS-TP-G is assumed unverifiable, the solution is derived in terms of upper-optimal and lower-optimal controllers. The learning convergence is theoretically ensured while practical implementation is performed using neural networks that provide scalability to the control problem dimension and automatic feature selection. The learning strategy is checked on an active suspension system, a good candidate for the robust control problem with respect to road profile disturbance rejection. INDEX TERMS active suspension system, approximate dynamic programming, neural networks, optimal control, reinforcement learning, state feedback, zero-sum two-player games

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“…Proof: See [51]. A virtual state vector is next introduced as [51] showed that, based on (1) and (2), a new virtual state-space system with output equation is defined as…”

Section: A the Unknown Observable Systemmentioning

confidence: 99%

Section: A the Unknown Observable Systemmentioning

confidence: 99%

Section: A the Unknown Observable Systemmentioning

confidence: 99%

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Robust Control of Unknown Observable Nonlinear Systems Solved as a Zero-Sum Game

Rădac

Lala

2020

IEEE Access

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“…The authors would like to mention that their paper is an extended version of the IEEE conference paper [1] from the same authors. It builds on the output reference model tracking problem for unknown systems that was also discussed in work [2] but in a different, observability-based, framework.…”

mentioning

confidence: 99%

“…Additionally, the references [1] and [2] (below) are better acknowledged throughout the revised manuscript as references [12] and [46], respectively.…”

mentioning

confidence: 99%