Linear quadratic control with risk constraints
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Date
2025-04
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Journal Article
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Abstract
We propose a new risk-constrained formulation of the Linear Quadratic (LQ) stochastic control problem for general partially-observed systems. Classical risk-neutral LQ controllers, although optimal in expectation, might be ineffective under infrequent, yet statistically significant extreme events. To effectively trade between average and extreme event performance, we introduce a new risk constraint, which restricts the cumulative expected predictive variance of the state penalty by a user-prescribed level. We show that, under certain conditions on the process noise, the optimal risk-aware controller can be evaluated explicitly and in closed form. In fact, it is affine relative to the minimum mean square error (mmse) state estimate. The affine term pushes the state away from directions where the noise exhibits heavy tails, by exploiting the third-order moment (skewness) of the noise. The linear term regulates the state more strictly in risky directions, where both the prediction error (conditional) covariance and the state penalty are simultaneously large; this is achieved by inflating the state penalty within a new filtered Riccati difference equation. We also prove that the new risk-aware controller is internally stable, regardless of parameter tuning, in the special cases of (i) fully-observed systems, and (ii) partially-observed systems with Gaussian noise. The properties of the proposed risk-aware LQ framework are lastly illustrated via indicative numerical examples.
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published
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Volume
174
Pages / Article No.
112095
Publisher
Elsevier
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Subject
Risk-aware control; Stochastic control; Optimal control
Organisational unit
03751 - Lygeros, John / Lygeros, John