In this paper, we generalize all previously known results on the controllability of discrete-time linear systems with conic input and/or state constraints. In addition, we single out two cases of the problem which did not appear in the literature before. We provide a characterization for the first one of these new cases. For the second newly introduced case, we show that it is rare and pathological. Moreover, we show that the classical results cannot be extended to this last pathological case. These results altogether lead to an almost complete spectral characterization of controllability for discrete-time linear systems with conic input and/or state constraints. Introduction.Ever since introduced by Kalman, controllability has become one of the most fundamental system-theoretical notions. Well-known algebraic characterizations of Kalman [13] and Hautus [10] for the controllability of (unconstrained) linear systems are among the classical results of systems and control theory.In the presence of input constraints, controllability has been studied in [4, 28] for continuous-time and in [7] for discrete-time systems when the input constraint set is the positive orthant. In the more general context of convex input constraints, controllability and related notions have been studied in [6,17,19] for discrete-time and [18] for continuous-time systems. A unified treatment of both the continuousand discrete-time cases can be found in [31] for the case when the input constraint set is a compact set containing the origin in its interior. Based on the foundations laid by these papers, variants of controllability such as instantaneous controllability and small-time controllability as well as the structure of reachable sets for continuous-time linear systems with input constraints have been investigated in [2,3,5,8,9,14,32]. All these papers provide elegant characterizations for controllability as well as the related notions of reachability and null controllability for input constraints case.Although controllability has been extensively studied and well understood with input constraints, it is overlooked to a great extent in the presence of state constraints. To the best of the authors' knowledge, controllability was investigated in [11,12,15,16] under state constraints either for very particular constraint sets or with restrictive assumptions. As such, the controllability problem for linear systems subject to state constraints remains still unsolved in general. In a way, this is somewhat surprising as constrained control problems have been of great interest to the control community due to the importance of state constraints in practical control problems.In this paper, we focus on discrete-time systems that are subject to conic input/state constraints. Apart from being interesting on their own, conic constraints

We present a Reinforcement Learning (RL) solution to the view planning problem (VPP), which generates a sequence of view points that are capable of sensing all accessible area of a given object represented as a 3D model. In doing so, the goal is to minimize the number of view points, making the VPP a class of set covering optimization problem (SCOP). The SCOP is N P -hard, and the inapproximability results tell us that the greedy algorithm provides the best approximation that runs in polynomial time. In order to find a solution that is better than the greedy algorithm, (i) we introduce a novel score function by exploiting the geometry of the 3D model, (ii) we model an intuitive human approach to VPP using this score function, and (iii) we cast VPP as a Markovian Decision Process (MDP), and solve the MDP in RL framework using well-known RL algorithms. In particular, we use SARSA, Watkins-Q and TD with function approximation to solve the MDP. We compare the results of our method with the baseline greedy algorithm in an extensive set of test objects, and show that we can outperform the baseline in almost all cases.

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Classical results in sparse recovery guarantee the exact reconstruction of s-sparse signals under assumptions on the dictionary that are either too strong or NP-hard to check. Moreover, such results may be pessimistic in practice since they are based on a worst-case analysis. In this paper, we consider the sparse recovery of signals defined over a graph, for which the dictionary takes the form of an incidence matrix. We derive necessary and sufficient conditions for sparse recovery, which depend on properties of the cycles of the graph that can be checked in polynomial time. We also derive support-dependent conditions for sparse recovery that depend only on the intersection of the cycles of the graph with the support of the signal. Finally, we exploit sparsity properties on the measurements and the structure of incidence matrices to propose a specialized sub-graph-based recovery algorithm that outperforms the standard 1-minimization approach.

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