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This paper considers the problem of error in variables identification for switched affine models. Since it is well known that this problem is generically NP hard, several relaxations have been proposed in the literature. However, while these approaches work well for low dimensional systems with few subsystems, they scale poorly with both the number of subsystems and their memory. To address this difficulty, we propose a computationally efficient alternative, based on embedding the data in the manifold of positive semidefinite matrices, and using a manifold metric there to perform the identification. Our main result shows that, under dwell-time assumptions, the proposed algorithm is convergent, in the sense that it is guaranteed to identify the system for suitably low noise. In scenarios with larger noise levels, we provide experimental results showing that the proposed method outperforms existing ones. The paper concludes by illustrating these results with academic examples and a non-trivial application: action video segmentation. 

This paper presents a method to lower-bound the distance of closest approach between points on an unsafe set and points along system trajectories. Such a minimal distance is a quantifiable and interpretable certificate of safety of trajectories, as compared to prior art in barrier and density methods which offers a binary indication of safety/unsafety. The distance estimation problem is converted into a infinitedimensional linear program in occupation measures based on existing work in peak estimation and optimal transport. The moment-SOS hierarchy is used to obtain a sequence of lower bounds obtained through solving semidefinite programs in increasing size, and these lower bounds will converge to the true minimal distance as the degree approaches infinity under mild conditions (e.g. Lipschitz dynamics, compact sets). 

This paper considers the problem of learning models to be used for controller design. Using a simple example, it argues that in this scenario the objective should reflect the closed-loop, rather than open-loop distance between the learned model and the actual plant, a task that can be accomplished by using a gap metric motivated approach. This is particularly important when identifying open-loop unstable plants, since typically in this case the open-loop distance is unbounded. In this context, the paper proposes a convex optimization approach to learn its coprime factors. This approach has a dual advantage: (1) it can easily handle open-loop unstable plants, since the coprime factors are stable, and (2) it is "self certified", since a simple norm computation on the learned factors indicates whether or not a controller designed based on these factors will stabilize the actual (unknown) plant. If this test fails, it indicates that further learning is needed. 

This work bounds extreme values of state functions for a class of input-affine continuous-time systems that are affected by polyhedral-bounded uncertainty. Instances of these systems may arise in data-driven peak estimation, in which the state function must be bounded for all systems that are consistent with a set of state-derivative data records corrupted under L-infinity bounded noise. Existing occupation measure-based methods form a convergent sequence of outer approximations to the true peak value, given an initial set, by solving a hierarchy of semidefinite programs in increasing size. These techniques scale combinatorially in the number of state variables and uncertain parameters. We present tractable algorithms for peak estimation that scale linearly in the number of faces of the uncertainty-bounding polytope rather than combinatorially in the number of uncertain parameters by leveraging convex duality and a theorem of alternatives (facial decomposition). The sequence of decomposed semidefinite programs will converge to the true peak value under mild assumptions (convergence and smoothness of dynamics). 

Peak estimation bounds extreme values of a function of state along trajectories of a dynamical system. This paper focuses on extending peak estimation to continuous and discrete settings with time-independent and time-dependent uncertainty. Techniques from optimal control are used to incorporate uncertainty into an existing occupation measure-based peak estimation framework, which includes special consideration for handling switching-type (polytopic) uncertainties. The resulting infinite-dimensional linear programs can be solved approximately with Linear Matrix Inequalities arising from the moment-SOS hierarchy.